Question

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x Cherie measured the growth of each of her plants since last month. Her results are given in the table.

Plant Number

Growth (cm)

Using the 1.5 IQR rule, find the outlier, and state the effect of excluding it on the IQR.

1

35

2 3 456789

16 24

10 11

1 2 9 4 4 11 4

12

A

35 is an outlier, and excluding it changes the IQR to 8.

B

35 is an outlier, and excluding it does not change the IQR.

C

1 is an outlier, and excluding it changes the IQR to 20.

x

D

1 is an outlier, and excluding it does not change the IQR.

Answer 1

The data (sorted) are: 1, 2, 4, 4, 4, 9, 11, 12, 16, 24, 35.

Median = 9. Q1 = median of lower half = 4. Q3 = median of upper half = 16. IQR = 16 − 4 = 12.
1.5·IQR = 18, so upper fence = 16 + 18 = 34 and lower fence = 4 − 18 = −14. Thus 35 (>34) is an outlier.

Remove 35: new data 1,2,4,4,4,9,11,12,16,24. Now Q1 = 4, Q3 = 12, IQR = 12 − 4 = 8.

So choice A is correct: 35 is an outlier, and excluding it changes the IQR to 8.