To calculate: The inter-quartile range and the semi-interquartile range of
Answer to Problem 5CFU
Quartile points are
Interquartile range is
Semi- interquartile range is
Explanation of Solution
Given information:
Formula used:
If each group has the median, the data is divided into four groups. Each group is called quartile.
The difference between the first quartile point and third quartile point is called the inter- quartile range.
The inter- quartile range is divided by 2, the quotient is called the semi- interquartile range.
Median for even terms =
Median for odd terms =
Calculation:
Re-arranging the data in ascending order ,
Since , the number of terms are
So, the median is
Therefore , the data is divided into two parts.
Lower half -
Median of lower half is −
Median of upper half is −
The quartile points are :-
The inter- quartile range is
The semi-interquartile range -
Hence, the Quartile points are
Now, using above data , sketch a box-and-whisker plot.
The graph represents the quartile points with median at 31.5.
Chapter 14 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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