In order decrease the interquartile range by 1 point, the player should score 23 points in the 12th game.
What is Interquartile range?
An interquartile range is one of the measure of variability that measures the spread of middle 50% of the data.
The formula to calculate interquartile range is:
[tex] IQR= Q3 - Q1 [/tex] , where IQR is the interquartile range, Q3 is third quartile and Q1 is the first quartile.
The interquartile range before the 12th game will be calculated as:
Firstly, we will arrange the points in increasing order:
13,15,17,18,20,20,21,22,21,25,27
The Q1 can be calculated as:
(n+1) /4 term , where n is the total number of terms.
[tex] Q1 = 11+1/4 term
Q1 = 12/4term
Q1= 3rd term
Q1= 17 [/tex]
[tex] Q3 = 3(n+1 /4) term
Q3 = 3(12/4) term
Q3 = 9th term
Q3 = 24 [/tex]
Therefore the interquartile range will be:
[tex] IQR= 24 - 17
IQR = 7 [/tex]
The desired interquartile range therefore is 7 - 1 = 6.
To calculate the score of the 12th game, we will use trial and error with all the options.
When we take 23 points as the score of the 12th game:
Q1 = 17.5
Q3 = 23.5
IQR = 23.5 - 17.5
IQR = 6
Therefore the correct option is C.
Learn more about interquartile range here:
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