Question

5, 7, 7, 8, 10, 11, 12, 15, 17. Q1 = 7, Q2 = 11, Q3 = 15 Q1 = 7, Q2 = 10, Q3 = 13.5 Q1 = 6, Q2 = 9, Q3 = 12 Q1 = 7.5, Q2 = 10.5, Q3 = 13.5

Answer 1

`Q_1 = 7`

`Q_2 = 10`

`Q_3 = 13.5`

Explanation:

Given

5, 7, 7, 8, 10, 11, 12, 15, 17.

Required

Determine Q1, Q2 and Q3

The number of data is 9

Calculating Q1:

Q1 is calculated as:

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

Substitute 9 for N

`Q_1 = (1)/(4)(9 + 1)`

`Q_1 = (1)/(4)*10`

`Q_1 = 2.5th\ item`

This means that the Q1 is the mean of the 2nd and 3rd data.

So:

`Q_1 = (1)/(2)(7+7)`

`Q_1 = (1)/(2)*14`

`Q_1 = 7`

Calculating Q2:

Q2 is calculated as:

`Q_2 = (1)/(2)(N + 1)`

Substitute 9 for N

`Q_2 = (1)/(2)(9 + 1)`

`Q_2 = (1)/(2)*10`

`Q_2 = 5th\ item`

`Q_2 = 10`

Calculating Q3:

Q3 is calculated as:

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

Substitute 9 for N

`Q_3 = (3)/(4)(9 + 1)`

`Q_3 = (3)/(4)*10`

`Q_3 = 7.5th\ item`

This means that the Q3 is the mean of the 7th and 8th data.

So:

`Q_3 = (1)/(2)(12+15)`

`Q_3 = (1)/(2)*27`

`Q_3 = 13.5`