2. Example-2
2. Calculate Box and Whisker Plots from the following data
85,96,76,108,85,80,100,85,70,95
Solution:
Box and Whisker Plots :
85,96,76,108,85,80,100,85,70,95
Steps of Five-Number Summary
Step-1: Arrange the numbers in ascending order
70,76,80,85,85,85,95,96,100,108
Step-2: Find the minimum value
Minimum =70 (the smallest number)
Step-3: Find the maximum value
Maximum =108 (the largest number)
Step-4: Find the median
The median is the middle number in a sorted data set and N is the total number of elements
If N is odd then the median is a single middle number, and if N is even then the median is the average of the two middle numbers.
70,76,80,85,85,85,95,96,100,108
N=10 is even, so median is the average of the two middle numbers at position 5 and 6
We have (85+85)/2=85
:. Median =85
Step-5: Place parentheses around the numbers above and below the median.
{70,76,80,85,85},{85,95,96,100,108}
Step-6: Find Q_1 by finding the median for lower half of data(left of the median)
70,76,80,85,85
N=5 is odd, so median is the middle number at position 3
We have 80
:.Q_1=80
Step-7: Find Q_3 by finding the median for upper half of data(right of the median)
85,95,96,100,108
N=5 is odd, so median is the middle number at position 3
We have 96
:.Q_3=96
Step-8: Summary found in the above steps.
Minimum =70
Q_1=80
Median =85
Q_3=96
Maximum =108
This material is intended as a summary. Use your textbook for detail explanation.
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