In: Statistics and Probability
1. The data give the number of computers sold by an electronic store for a sample of 11 days.(12points)197252026441817121421a) Calculate the values of the three quartiles and the interquartile range.b) Is there an outlier? Justify your answer.c) Find the 68thpercentile. Briefly explain what it means.
GIVEN THAT :-
according to the question we have the values as the given data a sample of 11
19,7,25,20,26,44,18,17,12,14,21
TO FIND :a) Calculate the values of the three quartiles and the interquartile range.
at first arrange the data in ascending order
7, 12, 14, 17, 18, 19, 20, 21, 25, 26, 44
from the above we have the 19 in the middle so taking the second quaritle first
Second quartile ( Median ) : 19
First quartile : 14
Third quartile : 25
IQR = Third quartile - First quartile
IQR = 25 - 14
=11
as we know that interquartile range is 11.
TO FIND :b)Is there an outlier?
first finding the lower fence we have a formula =firstquartile - ( 1.5 * IQR )
= 14 - ( 1.5 * 11 ) (since we have the both values first quertile and IQR from above)
there fore lower fence = -2.5
now finding the upperfence we have a fromula =Second quartile - ( 1.5 * IQR )
= 25 + ( 1.5 * 11 )
there fore upper fence is = 41.5
So the values in between both values are called outliers.
THERE FORE values less than -2.5 and greater than 41.5 are outliers.
44 is an outlier.
TO FIND :-C)Find the 68thpercentile. Briefly explain what it means.
now finding it we need to find that using the values p=0.68 and n=11 from the question
so we have a formula i=p*n
substituting the values of p ,n in the above" i " we get that
i = (0.68 * 11)
i = 7.48 = 8 (approx)
the 68th percentile is the value at 8th position
So from the above accending order 8th position so it is 21 .
Please give us rating