Question

The data below represents the number of workouts each member of Big Muscles Gym attended last month. 4,5,7,7,7,8,10,11,11,13,13,144,5,7,7,7,8,10,11,11,13,13,144, comma, 5, comma, 7, comma, 7, comma, 7, comma, 8, comma, 10, comma, 11, comma, 11, comma, 13, comma, 13, comma, 14 Which box plot correctly summarizes the data?

Answer 1

Given:

The data values are 4, 5, 7, 7, 7, 8, 10, 11, 11, 13, 13, 14.

To find:

The box plot for the given data set.

Solution:

The data values are

4, 5, 7, 7, 7, 8, 10, 11, 11, 13, 13, 14

Divide these values in two equal parts.

(4, 5, 7, 7, 7, 8), (10, 11, 11, 13, 13, 14)

Divide each group again in two equal parts.

(4, 5, 7), (7, 7, 8), (10, 11, 11), (13, 13, 14)

Here,

Minimum value = 4

$Q_1=\dfrac{7+7}{2}=\dfrac{14}{2}=7$

$Median=\dfrac{8+10}{2}=\dfrac{18}{2}=9$

$Q_3=\dfrac{11+13}{2}=\dfrac{24}{2}=12$

Maximum value = 14

It means, the starting point is 4 and end point is 14 of the box plot.

Box is lies from 7 to 12 and one line inside the box at 9.

Therefore, the box plot of the given data set is shown below.