Question

Use the following stem & leaf plot to complete each part.

Key: 1|2 = 12

1|2 5

2|3 5 5

3|3 5

4|0 2 4 8

5|0 3 5 5 9

6|1 3

a) Write the data values represented by the stem and leaf plot.

b) Find the five number summary for the data.

c) Draw a boxplot to represent the five number summary from part a.

Answer 1

a)12 15 23 25 25 33 35 40 42 44 48 50 53 55 55 59 61 63

b) The maximum and the minimum values are as follows
Maximum value = 63.0
Minimum value = 12.0

Since we know that
Median for a list of even number of data point is the mean of 2 middle most values if we sort the list in increasing order while for a list of odd number it is the middle most value if the list is sorted in increasing order.
Since our list have even number of data points, this implies that
Median = 43.0

b) Since we know that
The lower quartile(Q1) is the median of the lower half of the data set while upper quartile(Q3) is the median of the upper half of the data set.
Also, median for a list of even number of data point is the mean of 2 middle most values if we sort the list in increasing order while for a list of odd number it is the middle most value if the list is sorted in increasing order.
Since our list have even number of data points, this implies that
Median = 43.0
Lower half of our list is [12.0, 15.0, 23.0, 25.0, 25.0, 33.0, 35.0, 40.0, 42.0]
Since our lower half list have even number of data points, this implies that
Q1 = 25.0
Upper half of our list is [44.0, 48.0, 50.0, 53.0, 55.0, 55.0, 59.0, 61.0, 63.0]
Since our upper half list have even number of data points, this implies that
Q3 = 55.0
Min = 12
Q1 = 25
Median = 43
Q3 = 55
Max = 63
c) For a box plot, the ends of the box are located at the first third quartiles. The median is the vertical line with the box, The whiskers of the box plot connents the ends of the box to the smallest and largest data values within 1.5 interquartile ranges from the ends of the box. Points outside these plots are outliers.

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