Question

approximate the mean of the grouped data. round to the nearest whole number.
phone calls (per day) | frequency
8 - 11 | 17
12 - 15 | 6
16 - 19 | 3
20 - 23 | 31
24 - 27 | 18

Explanation:

Step1: Find mid - points

For 8 - 11, mid - point $x_1=\frac{8 + 11}{2}=9.5$. For 12 - 15, $x_2=\frac{12+15}{2}=13.5$. For 16 - 19, $x_3=\frac{16 + 19}{2}=17.5$. For 20 - 23, $x_4=\frac{20+23}{2}=21.5$. For 24 - 27, $x_5=\frac{24 + 27}{2}=25.5$.

Step2: Calculate $f_ix_i$

$f_1 = 17,x_1=9.5,f_1x_1=17\times9.5 = 161.5$. $f_2 = 6,x_2=13.5,f_2x_2=6\times13.5 = 81$. $f_3 = 3,x_3=17.5,f_3x_3=3\times17.5 = 52.5$. $f_4 = 31,x_4=21.5,f_4x_4=31\times21.5 = 666.5$. $f_5 = 18,x_5=25.5,f_5x_5=18\times25.5 = 459$.

Step3: Calculate $\sum f_i$ and $\sum f_ix_i$

$\sum f_i=17 + 6+3+31+18=75$. $\sum f_ix_i=161.5+81+52.5+666.5+459 = 1420.5$.

Step4: Calculate the mean

The mean $\bar{x}=\frac{\sum f_ix_i}{\sum f_i}=\frac{1420.5}{75}=18.94\approx19$.

Answer:

E. 19