Answer:
6
Step-by-step explanation:
The interquartile range is a measure of the difference between the upper quartile and the lower quartile.
The first step is to organise the data in ascending order, that is
10, 12, 13, 15, 17, 18, 21
Next find the median which is the middle value of the data.
10, 12, 13, 15, 17, 18, 21
↑ ← the median = 15
Now find the upper and lower quartiles which are the middle values of the data to the right and left of the median.
10, 12, 13, 15, 17, 18, 21
↑ ↑
upper quartile = 18 and lower quartile = 12
interquartile range = 18 - 12 = 6
Interquartile range of the given data set is 6.
Interquartile is the difference between upper quartile and lower quartile
Lower quartile is the median of the lower half of the data set.
Upper quartile is the median of the upper half of the data set.
Given data set 13, 17, 18, 15, 12, 21, 10
Arranging the data set in ascending order we get 10, 12, 13, 15, 17, 18, 21
Number of values in the data set is n = 7
Lower quartile is given by [tex]Q_{1} =\frac{n+1}{4} =\frac{7+1}{4} =\frac{8}{2} =2^{nd} \ value[/tex]
Therefore, the lower quartile is [tex]Q_{1} =12[/tex]
Upper quartile is given by [tex]Q_{3}=\frac{3}{4} (n+1)=\frac{3}{4} (7+1)=\frac{3}{4}(8)=6^{th} \ value[/tex]
Therefore, the upper quartile is [tex]Q_{1} =18[/tex]
Therefore, the inter quartile is given by [tex]Q_{3}-Q_{1} =18-12=6[/tex]
Interquartile range of the given data set is 6.
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