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

Answer:

$Q_1 = 7$

$Q_2 = 10$

$Q_3 = 13.5$

Step-by-step 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:

$Q_1 = \frac{1}{4}(N + 1)$

Substitute 9 for N

$Q_1 = \frac{1}{4}(9 + 1)$

$Q_1 = \frac{1}{4}*10$

$Q_1 = 2.5th\ item$

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

So:

$Q_1 = \frac{1}{2}(7+7)$

$Q_1 = \frac{1}{2}*14$

$Q_1 = 7$

Calculating Q2:

Q2 is calculated as:

$Q_2 = \frac{1}{2}(N + 1)$

Substitute 9 for N

$Q_2 = \frac{1}{2}(9 + 1)$

$Q_2 = \frac{1}{2}*10$

$Q_2 = 5th\ item$

$Q_2 = 10$

Calculating Q3:

Q3 is calculated as:

$Q_3 = \frac{3}{4}(N + 1)$

Substitute 9 for N

$Q_3 = \frac{3}{4}(9 + 1)$

$Q_3 = \frac{3}{4}*10$

$Q_3 = 7.5th\ item$

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

So:

$Q_3 = \frac{1}{2}(12+15)$

$Q_3 = \frac{1}{2}*27$

$Q_3 = 13.5$