Question

Find each value of the five-number summary for this set of data. [Note: Type your answers as numbers. Do not round.] 46, 19, 38, 27, 12, 38, 51 minimum maximum median upper quartile lower quartile

Answer 1

Maximum : 51

Minimum: 12

Median: 38

Lower quartile: 19

Upper quartile: 46

Explanation:

To answer this question, we first order the data from largest to smallest:

46, 19, 38, 27, 12, 38, 51

12, 19, 27, 38, 38, 46, 51

It can be seen that the maximum value is:

51

The minimum value is

12

Let's call N the amount of data.

To calculate the quartiles we use the following formula:

`Q_1 = X_{(1)/(4)(N + 1)}`

So:

`Q_1 = X_{(1)/(4)(7 + 1)}`

`Q_1 = X_2`

Where
`X_2` is the data number 2.

Q1 = 19

As the number of data is imapar, then, the median is the central data:

12, 19, 27, {38}, 38, 46, 51

Median = 38

Finally:

`Q_3 = X_ {(3)/(4)(n + 1)}\\\\Q_3 = X_ {6}`

Where
`X_6` represents the data number 6

`Q_3 = 46`