Question

Find the five number summary for the data given in the following stem and leaf plot.

4	0	2	7	8
5	8
6	0	7	9	9
7	0	2	3	7	8	9
8	1	1	4	8

Min =
Q₁ =
Median =
Q₃ =
Max =

Answer 1

The maximum and the minimum values are as follows
Minimum value = 40.0
Maximum value = 88.0

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 odd number of data points, this implies that
Median = 70.0

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.
Lower half of our list is [40.0, 42.0, 47.0, 48.0, 58.0, 60.0, 67.0, 69.0, 69.0]
Since our lower half list have even number of data points, this implies that
Q1 = 58.0
Upper half of our list is [72.0, 73.0, 77.0, 78.0, 79.0, 81.0, 81.0, 84.0, 88.0]
Since our upper half list have even number of data points, this implies that
Q3 = 79.0

Five point summary = 40.0, 58.0, 70.0, 79.0, 88.0
Min = 40.0
Q1 = 58.0
Median = 70.0
Q3 = 79.0
Max = 88.0

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