Question

The following set of data is from a sample of n= 7: 12 7 4 9 0 7 20

A) compute the mean, median, and mode.

B) compute the range, variance, standard deviation, and coefficient of variation

C) compute the Z score of 0 and 20. Are there any outliers?

D) compute the first quartile, the third quartile, and the interquartile range

Answer 1

given data

Number of sample (n)=7

Samples in ascending order (X)=0,4,7,7,9,12,20

A) mean

median is the centermost sample when samples are arrenged in ascending order so the

median =7

mode is the sample having largest frequency so in this case thee mode=7 (frequency=2)

B)Range = Sample with highest highest value -sample with lowest value

highest value=20

lowest value=0

Range =20-0=20

Variance=

Standard daviation =

Coefficient of variation =

CV=0.6970*100 %=69.70%

C)

we have mean

Standard daviation

now we have to calculate Z score

For X=0

now from the formula of Z score we have

For X=20

from the formula of Z score we have

outlier is a value of individual sample in the population which is abnormally too large or small in the context of given population

here in this case there is no such sample or value found so we can say that there arent any outlier found in the given set of data

D) First quartile :- it is the median value of the first half of the Sample when arranged in ascending order

so we have the first half =0,4,7

So the first quartile Q1=4

third quartile :- it is the median value of the second half of the Sample when arranged in ascending order

so we have the first half =9,12,20

So the first quartile Q3=12

Interquartile range =it is the difference between the third quartile and first quartile

IR=Q3-Q1=12-4=8