The stem and leaf plot shows the number of items in each of the 12 collections in a museum.

stem leaf

0

3

3

3

5

7

9

1

2

2

3

3

3

2

6.

3

9

Key: 2 6 represents a collection with 26 items in it.

Here is the five-number summary for these data:

Five-number summary

min Qi median Q max

3

6

12

13

39

According to the 1.5. IQR rule for outliers, how many high outliers are there in the data set?

Choose 1 answer:

0

1

2

3

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MrRoyal MrRoyal · Answer 1 · 2021-10-06T15:55:28+02:00

Outliers are data elements that are relatively far from the other data elements.

There are 2 high outliers in the data set.

The five number summary is given as:

[tex]\mathbf{Minimum=3}[/tex]

[tex]\mathbf{Q_1=6}[/tex]

[tex]\mathbf{Median=12}[/tex]

[tex]\mathbf{Q_3=13}[/tex]

[tex]\mathbf{Maximum=39}[/tex]

The lower outlier is:

[tex]\mathbf{L = Q_1 - 1.5 \times (Q_3 - Q_1)}[/tex]

So, we have:

[tex]\mathbf{L = 6- 1.5 \times (13 - 6)}[/tex]

[tex]\mathbf{L = -4.5}[/tex]

The upper outlier is:

[tex]\mathbf{U = Q_3 + 1.5 \times (Q_3 - Q_1)}[/tex]

So, we have:

[tex]\mathbf{U = 13 + 1.5 \times (13 - 6)}[/tex]

[tex]\mathbf{U = 23.5}[/tex]

The above computation means that;

Data less than -4.5 or greater than 23.5 are outliers

The data elements in this range are: 26 and 39

Hence, there are 2 high outliers in the dataset