Concept explainers
To calculate: The first and third quartile for the stem-lead plot.
Answer to Problem 2ST
The first quartile is 21 and third quartile is 33 for the stem-lead plot.
Explanation of Solution
Given information:
Thedistribution in stem-leaf plot is provided below,
Formula used:
For a distribution median is the middle value of the number.
For a distribution first quartile is the median of the lower half of the data.
For a distribution third quartile is the median of the upper half of the data.
Calculation:
Consider the distribution in stem-leaf plot is provided below,
In a stem leaf plot ten’s digit of the number is on left side of vertical line and one’s digit is on the right side.
For a distribution median is the middle value of the number.
There are 18 number, so median is average of
That is average of 26 and 28.
Therefore, median of distribution is 27.
For a distribution first quartile is the median of the lower half of the data.
Lower half of data has 9 values so the middle number is 21.
Therefore, first quartile is 21.
For a distribution third quartile is the median of the upper half of the data.
Upper half of data has 9 values so the middle number is 33.
Therefore, third quartile is 33.
Thus, the first quartile is 21 and third quartile is 33 for the stem-lead plot.
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