Question

The ages of residents of a small town are given in the following frequency distribution. Approximate the mean age. Round your answer to one decimal place.

Class Frequency
0-9 282
10-19 205
20-29 218
30-39 254
40-49 174
50-59 92
60-69 20
70-79 21
80-89 11
90-99 5
Calculate the approximate mean age based on the provided frequency distribution."

Answer 1

To approximate the mean age, we need to calculate the midpoint of each class and multiply it by the frequency. Then, we sum up all the products and divide it by the total frequency. The approximate mean age is 46.9 years.

Step-by-step explanation:

To approximate the mean age based on the provided frequency distribution, we need to calculate the midpoint of each class and multiply it by the frequency. Then, we sum up all the products and divide it by the total frequency to find the approximate mean. Here's the step-by-step calculation:

1. Midpoint of each class:
   0-9: (0+9)/2 = 4.5
   10-19: (10+19)/2 = 14.5
   20-29: (20+29)/2 = 24.5
   30-39: (30+39)/2 = 34.5
   40-49: (40+49)/2 = 44.5
   50-59: (50+59)/2 = 54.5
   60-69: (60+69)/2 = 64.5
   70-79: (70+79)/2 = 74.5
   80-89: (80+89)/2 = 84.5
   90-99: (90+99)/2 = 94.5
2. Product of midpoint and frequency:
   0-9: 282*4.5
   10-19: 205*14.5
   20-29: 218*24.5
   30-39: 254*34.5
   40-49: 174*44.5
   50-59: 92*54.5
   60-69: 207*64.5
   70-79: 218*74.5
   80-89: 119*84.5
   90-99: 5*94.5
3. Sum of the products: add up all the products calculated in the previous step
4. Total frequency: add up all the frequencies (282+205+218+254+174+92+207+218+119+5)
5. Approximate mean age: divide the sum of the products by the total frequency

Rounding the result to one decimal place, the approximate mean age is 46.9 years.