Descriptive Statistics, Part 1

Summary

En este tutorial, Amanda Rockson Appq introduce conceptos clave de las estadísticas descriptivas, como la distribución, las medidas de tendencia central (media, mediana y moda) y la dispersión (rango, varianza y desviación estándar). Utiliza ejemplos para ilustrar cómo calcular estas medidas y cuándo es apropiado reportar cada una, destacando la importancia de la variación en los datos. También explica cómo usar SPSS para generar estadísticas descriptivas y cómo reportarlas en formato APA, proporcionando tanto descripciones narrativas como ejemplos de tablas formateadas.

Takeaways

• 📊 Una distribución es una lista de puntajes tomados en una variable particular y es fundamental en estadísticas.
• 🔢 Los tres medidores de tendencia central son la media, la mediana y la moda.
• 💡 La media es el promedio aritmético de un grupo de puntajes, o la suma de puntajes dividida por el número de puntajes.
• 📈 La mediana es el punto central de todos los puntajes en una distribución ordenada de menor a mayor.
• 📦 La moda es el valor con la mayor frecuencia en la distribución.
• 📑 El tipo de datos y la distribución de los datos determinan qué medida de tendencia central se informará.
• 🔄 La variación ocurre en cada distribución y es causada por diferentes variables.
• 📋 La importancia de la variación se entiende mejor cuando se conoce cómo se dispersan los datos y cómo varían.
• 📏 La dispersión se mide por el rango, la varianza y la desviación estándar.
• 📘 La varianza es la media de las diferencias al cuadrado de la media y es fundamental para la desviación estándar.
• 📊 La desviación estándar es una medida común de dispersión y es simplemente la raíz cuadrada de la varianza.
• 📐 La desviación estándar muestra cómo se dispersan los puntajes alrededor de la media, y un valor más grande indica una mayor dispersión.

Q & A

¿Qué es una distribución en estadística?

Una distribución es una lista de puntuaciones obtenidas en una variable específica. Es fundamental para el análisis estadístico, ya que permite identificar patrones y realizar cálculos, como la tendencia central y la dispersión.

¿Cuáles son las tres medidas de tendencia central?

Las tres medidas de tendencia central son la media, la mediana y la moda. La media es el promedio, la mediana es el valor central en una lista ordenada, y la moda es el valor que aparece con mayor frecuencia.

¿Cómo se calcula la media?

La media se calcula sumando todas las puntuaciones y dividiendo esa suma por el número total de puntuaciones. Por ejemplo, si las puntuaciones son 69, 77, 84, 85, 87, 92 y 98, la media sería 83.1.

¿Qué indica la mediana en un conjunto de datos?

La mediana es el punto medio de un conjunto de datos ordenados de mayor a menor. Si el número de datos es impar, es el valor central; si es par, es el promedio de los dos valores centrales.

¿Qué es la moda y cómo se identifica?

La moda es el valor que aparece con mayor frecuencia en una distribución. En el ejemplo del guion, 77 es la moda porque aparece tres veces en el conjunto de datos.

¿Cuándo se utiliza la media, la mediana o la moda?

La media se usa con datos de nivel de intervalo o de razón, la mediana con datos ordinales, y la moda con datos categóricos. Sin embargo, en casos de valores atípicos o distribuciones sesgadas, la mediana puede ser más representativa que la media.

¿Qué es la variación en una distribución?

La variación es el grado de diferencia entre las puntuaciones de una distribución. Puede deberse a diferentes factores, como la experiencia previa de los estudiantes o sus hábitos de estudio.

¿Qué es la varianza y cómo se calcula?

La varianza es el promedio de las diferencias al cuadrado respecto a la media. Se calcula restando la media de cada puntuación, elevando al cuadrado esa diferencia, y luego promediando los resultados.

¿Qué es la desviación estándar?

La desviación estándar es la raíz cuadrada de la varianza. Mide qué tan dispersas están las puntuaciones alrededor de la media. Un valor alto indica mayor dispersión y un valor bajo indica menor dispersión.

¿Cómo se interpretan los resultados de una distribución normal en términos de desviación estándar?

En una distribución normal, aproximadamente el 68% de las puntuaciones caen dentro de una desviación estándar de la media, el 95% dentro de dos desviaciones estándar y el 99.7% dentro de tres desviaciones estándar.

Outlines

00:00

🎓 Introducción a las estadísticas descriptivas

En este párrafo, Amanda Rockson presenta el tutorial sobre estadísticas descriptivas, explicando que es la primera parte de dos. Se discutirán las distribuciones, medidas de tendencia central, dispersión y cómo calcular estas estadísticas en SPSS y reportarlas en formato APA. También se introduce el concepto de distribución como una lista de puntuaciones de una variable específica.

05:00

📊 Medidas de tendencia central: Media, Mediana y Moda

Aquí se explican las tres medidas principales de tendencia central: la media, la mediana y la moda. Se utiliza una distribución de diez puntuaciones de un examen de estadística para ilustrar cómo calcular cada medida. La media se obtiene sumando todas las puntuaciones y dividiendo entre el número de puntuaciones, la mediana es el punto medio de una distribución ordenada, y la moda es el valor más frecuente.

10:01

🔍 Variación en las puntuaciones: Ejemplos y causas

El párrafo aborda la variación en las puntuaciones de los estudiantes en un curso de estadística y el concepto de dispersión. Se da un ejemplo de cómo las puntuaciones en las pruebas varían debido a diferentes factores, como la experiencia previa y el tiempo de estudio. Se introducen los conceptos de rango y dispersión en las puntuaciones, que son clave para interpretar las estadísticas correctamente.

15:03

📉 Importancia de la variación y dispersión en los datos

Este párrafo resalta la importancia de entender la dispersión en los datos, especialmente en casos con datos socioeconómicos. Se ilustra cómo las medidas de dispersión, como el rango, la varianza y la desviación estándar, brindan una visión más completa de los datos. Se muestra un ejemplo donde el promedio puede ser engañoso debido a la presencia de valores atípicos.

20:04

📏 Medidas de dispersión: Rango, varianza y desviación estándar

Aquí se explican en detalle las medidas de dispersión: rango, varianza y desviación estándar. Se muestran cálculos paso a paso usando una distribución de puntuaciones. El rango es la diferencia entre el valor más alto y el más bajo, la varianza mide la dispersión de las puntuaciones respecto a la media, y la desviación estándar es la raíz cuadrada de la varianza.

25:05

🔬 Desviación estándar y la distribución normal

Este párrafo explora cómo la desviación estándar describe la dispersión de puntuaciones alrededor de la media. También se introduce la curva de campana o distribución normal, explicando que el 68% de las puntuaciones caen dentro de una desviación estándar de la media, el 95% dentro de dos, y el 99.7% dentro de tres desviaciones estándar.

📊 Ejemplo de cálculo de varianza y desviación estándar

Se presenta un ejemplo de cálculo de la varianza y la desviación estándar utilizando puntuaciones de cinco estudiantes en un curso. Se explica cómo se calcula primero la varianza y luego la desviación estándar. Además, se compara cómo cambia el cálculo al utilizar una población completa frente a una muestra, destacando la diferencia entre las fórmulas.

🔍 Comparación de distribuciones y dispersión de los datos

Este párrafo compara tres distribuciones con diferentes medias y desviaciones estándar. Se muestra cómo la dispersión de las puntuaciones afecta la interpretación de los datos, destacando que una mayor desviación estándar indica mayor dispersión y una menor desviación estándar indica menor dispersión.

💻 Uso de SPSS para calcular estadísticas descriptivas

Se explican las tres funciones principales en SPSS para calcular estadísticas descriptivas: 'frequencies', 'descriptives' y 'explore'. Se anima a explorar estas funciones y se dan instrucciones para calcular medidas de tendencia central y dispersión tanto manualmente como en SPSS.

📝 Cómo reportar estadísticas descriptivas en formato APA

El párrafo concluye explicando cómo reportar estadísticas descriptivas en formato APA, ya sea en narrativa o en tablas. Se enfatiza el uso de notaciones como 'M' para la media y 'SD' para la desviación estándar, y se muestra un ejemplo de cómo reportar los resultados de una distribución de datos en un formato APA adecuado.

Keywords

💡distribución

Una distribución es una lista de puntajes obtenidos en una variable específica. Es fundamental para la estadística y permite a los investigadores analizar y entender los datos de una forma más estructurada. En el vídeo, se utiliza la distribución de puntajes de estudiantes en un examen de estadísticas para explicar conceptos como la tendencia central y la dispersión.

💡tendencia central

La tendencia central es un concepto estadístico que se refiere a la representación de un conjunto de datos a través de valores que indican su 'centro'. En el vídeo, se mencionan tres medidas de tendencia central: la media, la mediana y la moda. Estos valores son cruciales para entender la distribución de los datos y para reportar características clave de los datos.

💡media

La media es el promedio aritmético de un grupo de puntajes y se calcula sumando todos los puntajes y dividiendo por la cantidad de puntajes. En el vídeo, se utiliza un ejemplo de puntajes de estudiantes para calcular la media, que resulta en 83.1. La media es una medida de tendencia central que indica el punto promedio de los datos.

💡mediana

La mediana es el punto medio de una distribución de datos ordenada, que divide la distribución en dos partes iguales. Si la cantidad de datos es impar, la mediana es el valor central; si es par, es el promedio de los dos valores centrales. En el vídeo, la mediana de los puntajes de los estudiantes se calcula como 84.5.

💡modal

La moda es el valor que aparece con mayor frecuencia en una distribución de datos. Es una medida de tendencia central que indica el valor más común en los datos. En el vídeo, el puntaje de 77 es la moda porque es el valor que se repite con mayor frecuencia.

💡variación

La variación es la diferencia o la diversidad que existe dentro de un conjunto de datos. Es fundamental para entender la dispersión de los datos y su distribución. En el vídeo, se discute cómo la variación puede ser causada por diferentes factores, como el tiempo de estudio o la exposición previa al tema en el caso de los puntajes de los estudiantes.

💡dispersión

La dispersión se refiere a la distribución de los datos en torno a la tendencia central. Incluye medidas como el rango, la varianza y la desviación estándar. En el vídeo, la dispersión es importante para entender la variabilidad de los datos y para interpretar correctamente las medidas de tendencia central.

💡rango

El rango es una medida de dispersión que representa la diferencia entre el puntaje más alto y el más bajo en una distribución de datos. En el vídeo, se calcula el rango de los puntajes de los estudiantes, que es de 29 puntos, como una forma de entender la dispersión de los datos.

💡varianza

La varianza es una medida de dispersión que indica la variabilidad de los datos en torno a la media. Se calcula como el promedio de las diferencias al cuadrado entre cada valor y la media. En el vídeo, la varianza de los puntajes de los estudiantes se calcula como 7.54, lo que indica la cantidad de variabilidad en los datos.

💡desviación estándar

La desviación estándar es una medida de dispersión que indica la dispersión de los datos en torno a la media. Se calcula como la raíz cuadrada de la varianza. En el vídeo, la desviación estándar se usa para ilustrar cómo los datos se distribuyen en torno a la media y se calcula como 8.39 para los puntajes de los estudiantes.

💡SPSS

SPSS (Statistical Package for the Social Sciences) es un software estadístico utilizado para la manipulación de datos, el modelado estadístico y la reporte de análisis. En el vídeo, se menciona cómo usar SPSS para calcular medidas de tendencia central y dispersión, lo que facilita la tarea de los investigadores y proporciona una salida estructurada para los análisis estadísticos.

Highlights

Introduction to descriptive statistics, including definitions of distributions, central tendency, and dispersion.

Explanation of a distribution: a list of scores taken on a particular variable, with an example using 10 student test scores.

Introduction to measures of central tendency: mean, median, and mode, with clear examples of how to calculate each.

Demonstration of when to report different measures of central tendency based on data type: mean for interval/ratio data, median for ordinal data, and mode for categorical data.

Explanation of variation and why it's important in understanding data distribution, with examples from student scores and heart rates.

Introduction to measures of dispersion: range, variance, and standard deviation, with a focus on their importance in providing a complete picture of data.

Step-by-step guide to calculating variance and standard deviation, including an example using 10 test scores.

Discussion of how outliers can impact the mean and why the median might be more appropriate in certain cases.

Clarification of standard deviation's role in measuring the spread of scores around the mean, and its relevance in statistical analysis.

Use of a normal bell curve to explain how data distribution relates to standard deviation, with a breakdown of scores within 1, 2, and 3 standard deviations from the mean.

Detailed example calculating descriptive statistics for a group of five students' course points, demonstrating variance and standard deviation.

Important note on the difference between population and sample formulas for variance and standard deviation.

Explanation of how to calculate and interpret standard deviation and its influence on data spread using different distributions.

Introduction to using SPSS to calculate descriptive statistics, highlighting the key functions: frequencies, descriptives, and explore.

Guidance on reporting descriptive statistics in APA format, both in narrative form and through tables.

Transcripts

[Music]

welcome this is Amanda rockson appq and

in this tutorial we are going to talk

about descriptive

statistics this is part one of a

two-part tutorial in part one we are

going to identify and Define

distributions measures of central

tendency dispersion and also briefly

look at how to calculate descriptive

statistics in SPS

as well as how to report them in apa

format let's get

started of distribution is foundational

to everything we are going to talk about

in this tutorial and it's very

foundational to statistics a

distribution is a list of scores taken

on a particular variable for example the

following is a distribution of 10

students scores on a Statistics test AR

ranged from highest to lowest you'll see

that the distribution includes 69 9 77

77 77 84 85 85 87 92 and

98 a researcher can take a distribution

and calculate measures of central

tendency there are three measures of

central tendency and you see them listed

here the mean median and mode the mean

is the arithm average of a group of

scores or it's the sum of scores divided

by the number of scores for example in

our distribution of 10 scores we add 69

+ 77 + 77 + 77 + 84 + 85 + 85 + 87 + 92

+ 98 and we divide that by the number of

scores which is 10 and we find that the

mean is

83.1 now the median is the middle of all

the scores into the distribution when

they are arranged from highest to lowest

it's the midpoint of the distribution

when the distribution has an odd number

of scores or the number is halfway

between the middle or two middle

scores when the uh distribution is an

even number so here for example we

arrang our distribution of 10 test

scores from lowest to highest and we see

that the median is

84.5 finally we have the mode the mode

is the value with the greatest frequency

in the distribution so here for example

in our dist distribution we see that 77

is the mode because it's listed most

frequently it's listed three times in

this

distribution so in statistics the

measure of central tendency that

reported by the researcher depends upon

the type of data as well as the

distribution of the data let's talk

about this for categorical scores the

researcher would report the mode the

score that occurs most frequently to

indicate what response is most typical

for ordinal data or ordinal scores the

researcher would use the median and for

Interval ratio level scores quantitative

data the researcher would use the mean

however sometimes the researcher would

also report the median to describe

central tendency and here she would do

this in cases where there may be

outliers or the distribution of data is

skewed in some manner because the mean

is really less robust in cases like this

and actually the median May May then be

more useful we're going to look at an

example of this so that we can better

understand it however before we do that

let's talk a little bit about

variation now variation occurs in every

distribution before we Define um more

specifically variant let's talk a little

bit about what it is and why it exists I

want you to think for a moment if we

look at students course points in one

online statistics course it's likely

that if we had 20 students all of their

course points would differ why would

this

be well maybe some students have had

more exposure to statistics than others

maybe some have put in more time

studying these are variables that cause

variation and the reason that we have

what we consider the range and scores

why let's say if the course points um

ranged from anywhere from 0 to a th000

that's why we would have scores ranging

anywhere from let's say 700 to

1,000 let's look at another example

let's say that if we would let's say

that we measure everyone um in the

class's heart rate again the score

values would differ across all of the

class members why do you think that the

heart rates would

differ well there's lots of reasons

heart rates would differ

um variables that might cause different

heart rates or cause variation in heart

rate across class members may include

things such as sex age body weight maybe

somebody is drinking a cup of coffee or

even just thinking about

statistics um maybe somebody recently

exercised so on and so forth again these

are variables that cause

variation it's the reason that we have

the range of

scores why then is understanding this

variation or this dispersion of scores

or the distribution

important without knowing something

about how the data is dispersed or how

it varies measures of central tendency

can actually be misleading let's say

that we know that social economic status

influences course grades so a researcher

wants to know the socioeconomic status

of a group of 10 students the group of

10 students that we've been talking

about abouts these 10 students let's say

come from families in which the mean

income is

$200,000 with very little variation from

the mean meaning that most of the

students come from families that make

around

$200,000 however this would be very

different if we had a group of 20

students who came from families in which

the mean score was $220,000 also

but what we knew about these group of

students is that three of the students

um parents or three of the students come

from families that make a combined

income of a million dollar and the other

students come from families that make a

combined income of

$60,000 measures thus of dispersion

provide a more complete picture of the

data set

here um so dispersion includes three

measures it includes range variance and

standard deviation and we're going to

talk about those next but before we move

on and talk about those I want to point

out that this example also provides a

good example of how the mean can be

deceiving when there are outliers in our

second scenario we have three outliers

the students who come from families that

make a million dollars really what we

see is the majority of the families um

have a combined income of $660,000

our median here is then

$60,000 and really provides a better

picture of um central tendency than the

mean does in this second

scenario we are now going to look at the

measures of dispersion range variance

and standard

deviation let's start with range I've

already talked about range so you may

have an idea of what range is but the

range is the distance between the

minimum score and the maximum score for

example in our distribution of 10 test

scores the range would be 29 because our

highest test score was 98 our lowest was

69 and 98 - 69 is

29 now let's talk about variance the

variance tells us about the variation of

the data and it's actually foundational

to uh the next term we're going to talk

about which is standard

deviation variance is defined as the

average of the squar differences from

the mean let's talk about how to

calculate variance so we can better

understand this definition to calculate

variance the first thing that you need

to do is calculate the mean we've

already done that we know it's

83.1 next for each number in the

distribution subtract the mean for

example we have the score of 98 98 minus

we would take 98 minus

83.1 for the score of 92 we take 92

minus 83.1 and so

on then we square that number or each of

those numbers and that's known as the

squared difference finally we calculate

the average of the squared difference

that is we add up the squared difference

and we divide them by the number of

scores which is 10 when we do this what

we get is

[Music]

7.54 so the variance for the

distribution that we've been looking at

is 70.5 4 that brings me finally to

standard deviation

standard deviation is a commonly used

measure of dispersion and it's simply

the square root of the variance here we

know the square root of the variance of

7.54 is

8.39 let's talk a little bit about more

a little bit more about standard

deviation standard de because this is a

really really important term and it's a

and it's also a measure that's used in a

lot of Statistics that we're to talk

about in other

tutorials standard deviation then is

um the measure is a measure as I said of

the dispersion of scores and it measures

the dispersion of scores specifically

around the mean in other words another

way to think about standard deviation is

how spread out a number of or a set of

numbers are or how far numbers are from

what's normal or what's

average the larger the standard

deviation ation then the larger the

spread of scores around the mean and the

smaller the standard deviation the

smaller the spread of scores is going to

be around the

meat let's talk a little bit further

about standard deviation and look at it

in terms of a normal bell curve here we

have a picture of a normal bell curve

and for a normally distributed um data

values here we can see that

approximately

68% of the distribution Falls with one

in one standard deviation of the mean

95% of the distribution Falls within two

standard deviations of the mean and

99.7% of the distribution Falls within

three standard deviations of the mean

now let's talk about this in terms of

the distribution that we've been looking

at if our 10 scores were evenly

distributed with the mean of

83.1 this would mean that 68% % of our

scores would fall between

91.4 n and

74.

71 now how um before we go on how did I

get that number well I I got let's talk

about um

91.4 n what I did was was I knew that

our mean was 83.1 and if I add our

standard deviation of um

8.39 what I find is is that the first

standard or scores that are a one

standard deviation above the mean are 8

or 91 or equals 91.4 n then if I take

our mean again of

83.1 and I want to know um scores that

fall below one standard deviation of the

mean or a score that falls below one

standard deviation of the mean I'm going

to mind that if I take um 83.1 minus

8.39 that I'm going to get

74. 71 okay so that's how I'm get that's

how I'm getting those numbers so let's

go back so if our 10 scores again were

evenly distributed with the mean of

83.1 we would know then that 68% of our

scores would fall within one standard

deviation of the mean that means our

scores would fall between 91 .49 and

74.

71 this then we would also know that 95%

of our scores would range between

99.88% of our scores would fall between

108.2 7 and

57.9 3 now now that we've defined

measures of central tendency and also

measure measures of dispersion we're

going to take a little bit closer look

at measures of dispersion just to make

sure that we have a clear understanding

of

them we're going to walk through this

example and calculate variance and

standard deviation while I'm aware that

software such as SPSS automatically

calculates these values for you you

still need to understand the statistic

and how it works and be able to uh know

how to calculate it

um because this will really help you

understand um what the values represent

so that you can clearly describe and

interpret them when you get them in the

SPs SPSS output so let's um take a look

at this example an educational

statistics Professor has a class of five

students the students um course points

range from 0o to 600 and the following

are the students um points there's a

student that has 600 points points a

student that has 470 points a student

that has 170 points a student that has

430 points and a student that has 100

points now remember that variance is

foundational to standard deviation so we

first need to calculate the variance the

first step to calculating the variance

is to calculate the mean and remember we

calculate the mean by adding all of the

scores and dividing it by the number of

scores as you can see I've done here

here we find that the mean is

394 for each number in the distribution

we then subtract the mean and here you

can see all of the numbers with the mean

subtracted for example

600-

374 =

206 and so on and so

forth once those numbers of are

calculated we then Square those numbers

remember those numbers are known as

Square difference or Square differences

we then add the squared differences and

divide them by the number of scores in

this case remember we have five and we

by doing this we find that the variance

is

2174 now that we know the variance we

can calculate the standard deviation the

standard deviation remember is the

square root of the variance here the

square root of

2174 is

147.300 deviation in this example is

147 now that we know the standard

deviation as well as the variance we as

educational researchers or social

science researchers can use the standard

deviation to determine which scores are

within one standard deviation of the

mean here again I've listed um just as a

reminder the distribution of scores we

know that the mean is 394 and the

standard deviation is 147 so how how do

we use these scores well scores between

220 and

541 fall within one standard deviation

of the mean again in order to find the

220

um one standard deviation below the mean

we we take 394 and we subtract 147 which

is the mean minus the standard deviation

and then in order to calculate one

standard deviation above the mean we

take 394 plus 147 and we find

541 so again we know that the the scores

that range between 220 and

541 fall within one standard deviation

of the mean and what we can see if we

look at our distribution is that we have

three scores that fall within one

standard um deviation of the mean we can

also note if we look at our distribution

that one of the uh students is a really

high achiever with a score of 600

whereas one of the students is somewhat

of a low achiever with a score of

170 before we move on from this example

I want to discuss two more important

points you'll note that the formula that

we used to calculate both variance and

standard deviation assumed that we were

using a population of five

students so what we did when we

calculated variance is we divided by n

or five in this case however if the data

was from a sample for example let's say

that we had 10 students in the class and

we randomly selected five of them we

would have divided by n minus one or 5 -

one which was which would be four when

calculating the variance so if we did

this what we would find is that our

sample variance was

27,100 and our standard deviation was

164 so this is just an important uh

important point to note that the

population formula here is different

from the sample population formula and

you'll find that to be the case or to be

true and a number of the statistics will

discuss in these

tutorials I then also wanted to take

time to refer back to a point that I

made earlier remember when defining

standard deviation I said that the

larger the standard deviation the larger

the spread of scores around the mean in

each

other here we have a um an example of

three distributions you'll first see at

the top the distribution that we've been

talking about where the mean is 394 and

the standard deviation is 147 with um

our scores ranging from 170 to

600 let's say that we took another

sample of score or another we looked at

another sample of scores and this

distribution ranged from 70 to 600 so

the range is a little bit larger what we

see here then is that the mean is

334 so it's a little bit

lower and that our standard deviation is

236.000 what we not is that the lower

score of 70 influenced the mean and we

also can note a larger standard or

larger standard deviation which implies

which we can see by examining the scores

and which we talked about is that the

scores are more spread

out let's say then we have one more um

we take data from one more sample

population and this set of or this

distribution is not as spread out the

range is only for from 370 to 600 and

what we find is is that the mean is 454

and the standard deviation is

8961 in this case what we see is that

the mean is smaller but this or sorry

larger in this case um because the

scores are higher however we all we then

see that the standard deviation is

smaller implying that these scores are

not very spread out at all so so this is

an example of what I meant when I said

the larger the standard deviation the

larger the spread of scores and then the

Opposites also true the smaller the

standard deviation the smaller the

spread of scores now let's take a look

at how do we C now that we understand

how to calculate U measures of central

tendency as well as dispersion let's

take a look at how we can do that in

SPSS now there are three functions that

can be used when you want to calculate

descriptive statistics and SPSS

you can use frequencies descriptives or

explore so you go to descriptive

statistics um from an sorry from Analyze

you go to descriptive statistics and

then you can choose frequency

descriptives or

explore each of these have different

features and different functions within

so I encourage you to explore them

however for the most part you can

calculate uh measures of central

tendency and dispersion using these

three functions

once you've calculated your descriptive

statistics using either SPSS or

calculating them by hand you are then

ready to report them when you're

reporting descriptive statistics you can

either use the name and say the mean is

or you can use notations here are the

notations for different uh descriptive

statistics so for the mean you can see

that it's a capital M for the standard

deviation you can see you can use um a

capital SD I will note here that

whenever you report notations per APA

they should be italicized so it's really

important to make sure that your

statistics are

italicized so using the example

distribution that we've been talking

about here's how I might report the

descriptive statistics for that example

I would say that I have a convenient

sample of undergraduate students I um

enrolled in a statistics course and as

you can see here that n which means the

entire sample population equal equals

five and then I um tell the reader that

the course points ranged from 300 to 600

now I'm going to the the measure of

central tendency that I'm going to

report is the mean because I'm dealing

with course points which are measured at

the uh ratio level of measurement so I

report the mean and then I also can then

report the standard deviation so this is

an example of how I would report scores

you or specifically descriptive

statistics using um a

narrative then here is an example of how

I would report descriptive statistics

using a table now let's say that instead

of just having five students undergrad

students to look at I actually want to

look at two two sets of undergraduate

students students who take maybe a

statistics course online and students

who take it

residentially and I'm not just going to

look at course points here maybe I want

to look at um their scores on a test

also so here I have a descriptive

statistics table disaggregated by the

type of course at the top at the title

you'll note that the um the the n

capital N equals 10 because that's my

entire sample population that I'm

looking at but then down below for on

line I have n equal 5 and you'll note

that that's a lowercase n because that

indicates that's a group within the

entire sample population and you can see

that I had I looked at five online

students and five residential students

you can then also see in this table that

we have the mean and the standard

deviations listed so this is an example

of an APA formatted table that could be

used to report descriptive

statistics this then concludes part one

of the tutorial on descriptive

statistics at this point you should be

able to Define what a distribution is

and explain what it is you should be

able to uh identify Define and calculate

measures of central tendency as well as

dispersion know how to go about

calculating descriptive statistics in

SPSS and then also reporting them in APA

format