Question

this box plot shows the heights (in feet) from a sample of two different type of elephants compare the outliers and interquartile ranges

Answer 1

African Elephants have a greater IQR because there were some very short elephants (low outliers).

Explanation:

Apex

Answer 2

The correct option is C.

Explanation:

Using the given box plots:

The data set for Asian elephant is

6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10

Divide the data set in 4 equal parts.

(6, 6, 7), 7, (7, 8, 8), 8, (8, 8, 8), 9, (9, 9, 10)

`Q_1=7, Median=8, Q_3=9`

IQR of the Asian elephant is

`IQR=Q_3-Q_1=9-7=2`

IQR of the Asian elephant is 2.

If the data set lies in interval
`[Q_1-1.5(IQR),Q_3+1.5(IQR)]`, then the data set has no outliers.

`[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[7-1.5(2),9+1.5(2)]=[4,12]`

All the data lie in [4,12], therefore Asian elephant has no outliers.

The data set for African elephant is

4, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14

Divide the data set in 4 equal parts.

(4, 6, 7, 7, 8, 8, 8), 9,( 9, 9, 10, 10, 10, 10, 11), (11, 11, 11, 11, 11, 12, 12), 12, (12, 12, 12, 13, 13, 14, 14)

`Q_1=9, Median=11, Q_3=12`

IQR of the African elephant is

`IQR=Q_3-Q_1=12-9=3`

IQR of the African elephant is 3.

`[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[9-1.5(3),12+1.5(3)]=[4.5,16.5]`

All the data lie in [4.5,16.5] except 4, therefore African elephant has lower outliers.

African have a greater IQR because there were some very short elephants.

Therefore the correct option is C.