Question

Which data set has the greatest spread for the middle 50% of its data?

A) {18, 13, 22, 17, 21, 24}

B) {17, 19, 22, 26, 17, 14}

C) {13, 17, 12, 21, 18, 20}

D) {18, 21, 16, 22, 24, 15}

Answer 1

Option C.

Explanation:

The highest Interquartile range represents the greatest spread for the middle 50% of its data.

Find the IQR of each data set.

Option A,

18, 13, 22, 17, 21, 24

Arrange the data in ascending order.

13, 17, 18, 21, 22, 24

Divide the data in 4 equal parts.

(13), 17, (18), (21), 22, (24)

`Q_1=17, Median=(18+21)/(2)=19.5, Q_3=22`

Formula for IQR :

`IQR=Q_3-Q_1`

The IQR of first data set is

`IQR=22-17=5`

The IQR of the first data set is 5.

Similarly,

Option B,

17, 19, 22, 26, 17, 14

Arrange and divide the data in 4 equal parts.

(14), 17, (17), (19), 22, (26)

`IQR=22-17=5`

The IQR of the second data set is 5.

Option C,

13, 17, 12, 21, 18, 20

Arrange and divide the data in 4 equal parts.

(12), 13, (17), (18), 20, (21)

`IQR=20-13=7`

The IQR of the third data set is 7.

Option D,

18, 21, 16, 22, 24, 15

Arrange and divide the data in 4 equal parts.

(15), 16, (18), (21), 22, (24)

`IQR=22-16=6`

The IQR of the third data set is 6.

The IQR of third data set is highest, therefore third data set has the greatest spread for the middle 50% of its data.

Therefore, the correct option is C.

Answer 2

C) {13, 17, 12, 21, 18, 20}

Explanation:

A data with the highest IQR ( interquartile range ) has the greatest spread for the middle 50% of its data,

In option A,

The data set is,

{18, 13, 22, 17, 21, 24}

After arranging in ascending order, the data is,

{13, 17, 18, 21, 22, 24}

Find the median of both lower and upper half,

13, 17, 18

Thus, IQR = Upper median - Lower median = 22 - 17 = 5,

Similarly, We can find the IQR for the other set,

In option B,

The data is,

{17, 19, 22, 26, 17, 14}

So, the IQR = 22 - 17 = 5,

In option C,

The data set is,

{13, 17, 12, 21, 18, 20}

So, the IQR = 20 - 13 = 7,

In option D,

The data set is,

{18, 21, 16, 22, 24, 15}

So, the IQR = 22 - 16 = 6

Hence, by the above explanation it is clear that,

The set {13, 17, 12, 21, 18, 20} has the greatest IQR value,

⇒ The set {13, 17, 12, 21, 18, 20} has the greatest spread for the middle 50% of its data

Option C is correct.