Question

A survey asked a group of people the size of their households. The results are shown in the frequency distribution. What is the mean of the frequency distribution?

Household size: 1 2 3 4 5
Frequency: 4 12 6 2 1
a) 2.36
b) 11.8
c) 4
d) 5

Answer 1

To find the mean of the frequency distribution, multiply each household size by its frequency, sum those products, and divide by the total number of households. The mean is 2.36, which is option (a).

Step-by-step explanation:

To calculate the mean of the frequency distribution, we need to multiply each household size by its frequency and then divide the sum by the total number of responses.

1. Multiply each household size by its corresponding frequency. For household size 1 (4 households), 2 (12 households), 3 (6 households), 4 (2 households), and 5 (1 household), we get: 1× 4 = 4, 2× 12 = 24, 3× 6 = 18, 4× 2 = 8, 5× 1 = 5.
2. Add these products together to find the sum of all household sizes. The sum is 4 + 24 + 18 + 8 + 5 = 59.
3. The total frequency is the sum of all frequencies, which is 4 + 12 + 6 + 2 + 1 = 25.
4. Divide the sum of all household sizes by the total frequency to find the mean. Mean = 59 / 25 = 2.36.

Therefore, the mean of the frequency distribution is 2.36, which corresponds to option (a).