CONTOH SOAL UKURAN PEMUSATAN DATA - 01

Summary

In this video, Ahmad Lamuna explains a statistical problem involving the ages and frequencies of people living in City A. He details a scenario where the data changes due to the migration of individuals, leading to a shift in the average age. Ahmad guides viewers through how to adjust the age data, remove individuals who have moved, and calculate the new average age for the remaining 16 residents. He uses a clear, step-by-step approach to demonstrate the mathematical process, ultimately determining that the new average age is 9 years. The video is part of an educational series on statistics.

Takeaways

• 😀 The script discusses a statistical problem involving the average age of people living in City A.
• 😀 The dataset provided shows the ages and frequencies of 20 people living in City A two years ago.
• 😀 The problem introduces a scenario where three 7-year-olds and one 8-year-old move away from City A.
• 😀 The objective is to calculate the average age of the remaining 16 people after these individuals move.
• 😀 The script demonstrates how to adjust the frequency for each age group based on the change in population.
• 😀 The process of calculating the average age involves using the formula: sum of (age × frequency) ÷ total frequency.
• 😀 The frequency adjustments are made by subtracting the individuals who moved, which reduces the count for the 7 and 8-year-olds.
• 😀 The revised frequency table is used to compute the sum of the weighted ages for the remaining individuals.
• 😀 The final calculation shows the average age of the remaining 16 people as 9 years.
• 😀 The explanation provides clarity on how to adjust age data in statistical calculations when people move or leave a group.
• 😀 The script encourages viewers to understand the method and invites them to explore other related educational videos.

Q & A

What is the context of the discussion in the video?

The video discusses a statistical problem related to the average age of residents in City A, based on a frequency table of their ages. The problem involves updating the data with people who have moved away, and calculating the new average age of the remaining residents.

How many people were originally in City A 22 years ago?

The original table shows data for 20 people living in City A 22 years ago.

What changes occurred in the population of City A in the current year?

Three people aged 7 and one person aged 8 moved away from City A, reducing the total number of residents to 16.

How is the age data from 22 years ago adjusted for the current year?

The age data is adjusted by adding 5 years to each person's age from the original table, as 22 years ago corresponds to their age 5 years before the current year.

What is the new frequency distribution after the people have moved away?

The frequency distribution after the move shows the remaining residents with adjusted ages, including a frequency of 7 for people aged 6, 8 for people aged 7, 4 for people aged 8, and so on.

How is the average age of the remaining 16 people calculated?

The average age is calculated by multiplying the age of each group by its frequency, summing the results, and then dividing by the total frequency (16). For example, (8 * 4) + (9 * 8) + (10 * 4) = 144, and dividing by 16 gives an average age of 9.

What formula was used to calculate the weighted average age?

The formula used is the sum of the products of each age and its frequency, divided by the total frequency: (8 * 4 + 9 * 8 + 10 * 4) / 16 = 144 / 16 = 9.

What is the significance of the numbers 8, 9, and 10 in the calculation?

The numbers 8, 9, and 10 represent the adjusted ages of the remaining people, and the frequencies of these ages are used to calculate the weighted average age.

Why did the speaker explain the age adjustments step by step?

The speaker explained the age adjustments to ensure that viewers understand how to update the data from 22 years ago and account for the people who moved away before calculating the new average.

What is the final result of the average age calculation?

The final average age of the 16 remaining residents is 9 years.