Multiple choice

Find the mean and median of the following data: (Mean by step deviation method) Age of children 5 - 15 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 Number of children 5 10 20 30 15 20

  1. 40 and 42

  2. 41 and 40

  3. 40 and 40

  4. 38 and 40
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total frequency = 100. Mean = sum(f*x)/sum(f). Midpoints: 10, 20, 30, 40, 50, 60. f*x: 50, 200, 600, 1200, 750, 1200. Sum = 4000. Mean = 4000/100 = 40. Median class is where cumulative frequency reaches 50, which is 35-45. Median = L + ((N/2 - cf)/f) * h = 35 + ((50 - 35)/30) * 10 = 35 + (15/30)*10 = 35 + 5 = 40.

AI explanation

Using the step deviation method with an assumed mean of 40, the sum of the frequency multiplied by the deviation step is 5(-3) + 10(-2) + 20(-1) + 30(0) + 15(1) + 20(2), which equals 0. Dividing this by the total frequency of 100 yields a mean of 40. Because the cumulative frequency reaches 50 within the 35 to 45 class interval, the median is also 40.

Keep practicing — related questions