Question

The weights in pounds of 23 dogs were used to construct the following stem-and-leaf display using the first digit as the stem and the second digit as the leaf:. Stem Leaves

3 2 4
4 0 3 4 5 7 8 9
5 0 1 2 3 4 5
6 1 2 5 6 7
7 0 1
8
9 8Use the stem-and-leaf display to find the lower quartile, median, and upper quartile and then use these values to construct a box plot. Use the box plot to identify any suspect or

Answer 1

The median is 52 pounds. The lower quartile is 45 pounds. The upper quartile is 65 pounds. We can identify that one value is suspicious because one whisker is out of the range.

Explanation:

The median is the value separating the higher half from the lower half of a data sample. According to the diagram, we can find the median of weight of 23 dogs:

3/ 2 4

4/ 0 3 4 5 7 8 9

5/ 0 1 2 3 4 5

6/ 1 2 5 6 7

7/ 0 1

8 /

9/ 8

There are 11 values before and after the median. Median is 52 pounds.

The lower quartile is the value separating from the lowest value and the median and the upper quartile is the value separating from the highest value and the median. These values are underline in the diagram:

3/ 2 4

4/ 0 3 4 5 7 8 9

5/ 0 1 2 3 4 5

6/ 1 2 5 6 7

7/ 0 1

8 /

9/ 8

So, the lower quartile Q1= 45 pounds and the upper quartile Q3= 65 pounds.

The Interquartile Range (IQR) is given by:

IQR=Q3-Q2=65-45=20

In the following box diagram, we can identify the median, the lower quartile and the upper quartile. We calculate the lower and the upper whisker:

The lower 1.5*IQR whisker is given by: Q1 - 1.5 * IQR= 45-1.5*20=15

The upper 1.5*IQR whisker is given by: Q3 + 1.5 * IQR=65+1.5*20=95

Therefore, in the diagram there is un value out of the range.

The weight 98 pounds is out of the range.