Question

In a statistics class, 10 scores were randomly selected with the following results: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What are the lower and upper limits of a box-and-whiskers display of this data

Answer 1

`L =52` --- Lower Limit

`U =82` --- Upper Limit

Explanation:

Given

`N = 10`

`Data: 74, 73, 77, 77, 71, 68, 65, 77, 67, 66`

Required

Determine the lower and upper limits of box and whisker display

First, arrange the data in ascending order

The sorted data is:

`Data: 65, 66, 67, 68, 71, 73, 74, 77, 77, 77`

The lower limit (L) is calculated using:

`L = Q_1 - 1.5 * (Q_3-Q_1)`

The upper limit (U) is calculated using:

`U =Q_3 + 1.5 * (Q_3-Q_1)`

Q1 is calculated using:

`Q_1 = (1)/(4)(N+1)`

`Q_1 = (1)/(4)(10+1) = 2.75 = 3rd\ data`

`Q_1 = 67`

Q3 is calculated using:

`Q_3 = (3)/(4)(N+1)`

`Q_3 = (3)/(4)(10+1) = 8.25= 8th\ data`

`Q_3 = 77`

So:

`L = Q_1 - 1.5 * (Q_3-Q_1)`

`L =67 - 1.5*(77-67)`

`L =67 - 1.5*10`

`L =67 - 15`

`L =52`

`U =Q_3 + 1.5 * (Q_3-Q_1)`

`U =67 + 1.5*(77-67)`

`U =67 + 1.5*10`

`U =67 + 15`

`U =82`