Question

question 6
the following table summarizes the ages of a sample of 49 adults that are members club. use the frequency distribution table to estimate their mean age.

age	frequency
10 - 14	1
15 - 19	3
20 - 24	6
25 - 29	11
30 - 34	16
35 - 39	12

Explanation:

Step1: Find mid - points of age intervals

For 10 - 14, mid - point $x_1=\frac{10 + 14}{2}=12$; for 15 - 19, $x_2=\frac{15+19}{2}=17$; for 20 - 24, $x_3=\frac{20 + 24}{2}=22$; for 25 - 29, $x_4=\frac{25+29}{2}=27$; for 30 - 34, $x_5=\frac{30 + 34}{2}=32$; for 35 - 39, $x_6=\frac{35+39}{2}=37$.

Step2: Calculate the product of mid - points and frequencies

$x_1f_1=12\times1 = 12$; $x_2f_2=17\times3 = 51$; $x_3f_3=22\times6 = 132$; $x_4f_4=27\times11 = 297$; $x_5f_5=32\times16 = 512$; $x_6f_6=37\times12 = 444$.

Step3: Sum up the products

$\sum_{i = 1}^{6}x_if_i=12 + 51+132+297+512+444=1448$.

Step4: Sum up the frequencies

$\sum_{i=1}^{6}f_i=1 + 3+6+11+16+12=49$.

Step5: Calculate the mean

$\bar{x}=\frac{\sum_{i = 1}^{6}x_if_i}{\sum_{i=1}^{6}f_i}=\frac{1448}{49}\approx29.55$.

Answer:

$29.55$