Question

the following table summarizes the ages of a sample of 49 ad club. use the frequency distribution table to estimate their me
age frequency
10 - 14 1
15 - 19 3
20 - 24 6
25 - 29 11
30 - 34 16
35 - 39 12
mean age = 29.55

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

$f_1x_1=1\times12 = 12$; $f_2x_2=3\times17 = 51$; $f_3x_3=6\times22 = 132$; $f_4x_4=11\times27 = 297$; $f_5x_5=16\times32 = 512$; $f_6x_6=12\times37 = 444$.

Step3: Sum up the products and frequencies

$\sum_{i = 1}^{6}f_ix_i=12 + 51+132+297+512+444 = 1448$ and $\sum_{i=1}^{6}f_i=1 + 3+6+11+16+12=49$.

Step4: Calculate the mean

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

Answer:

$29.55$