Question

a random sample of 30 malls shows the number of stores each one contains in the following grouped frequency distribution. find the mean and the modal class.
class boundaries frequency
11 - 15 2
16 - 20 7
21 - 25 3
26 - 30 10
31 - 35 8
make sure to select two answers.
the modal class is 21 - 25.
the modal class is 26 - 30.
the mean is 10.
the mean is 23.
the modal class is 31 - 35.
the mean is 25.5.
question 16 (3 points)

Explanation:

Step1: Find the modal class

The modal class is the class - interval with the highest frequency. Here, the frequency of the class 11 - 15 is 2, 16 - 20 is 7, 21 - 25 is 3, 26 - 30 is 10, and 31 - 35 is 8. Since 10 is the highest frequency, the modal class is 26 - 30.

Step2: Calculate the mid - points of each class

For 11 - 15, mid - point $x_1=\frac{11 + 15}{2}=13$; for 16 - 20, $x_2=\frac{16+20}{2}=18$; for 21 - 25, $x_3=\frac{21 + 25}{2}=23$; for 26 - 30, $x_4=\frac{26+30}{2}=28$; for 31 - 35, $x_5=\frac{31 + 35}{2}=33$.

Step3: Calculate the mean

The formula for the mean of a grouped frequency distribution is $\bar{x}=\frac{\sum_{i = 1}^{n}f_ix_i}{\sum_{i = 1}^{n}f_i}$. Here, $\sum_{i=1}^{n}f_i=2 + 7+3 + 10+8=30$. And $\sum_{i = 1}^{n}f_ix_i=2\times13+7\times18+3\times23+10\times28+8\times33=26 + 126+69+280+264 = 765$. Then $\bar{x}=\frac{765}{30}=25.5$.

Answer:

The modal class is 26 - 30.
The mean is 25.5.