Question

PLEASE HELP!!!! Don't understand how to do this problem.

Sorted total units 1 1 1 1 1 1 4 10 10 10 11 34 34 40 80 86 126 183 255 319

Used Data to do the following:

A. Box plot

B. Mean, standard deviation (sample), range, Q!, Q2, Q3, Q4, IQR

C. Try to run Chebyshev's test

Answer 1

A) We can draw box plot using excel :

First enter the given data set into column A and select the data set.

Go to Insert menu ---> Recommended charts ---> All charts ---> Box and whisker

Click on OK

B)

We can use excel function =AVERAGE( data set range ) to find mean

Mean = 60.4

We can use excel function =STDEV.S(data set range ) to find sample standard deviation

Sample standard deviation = 92.1494

We can find quartiles using the function =QUARTILE ( data set range , number )

Q1 = 1

Q2 = 10.5

Q3 = 81.5

IQR = Q3 -Q1 = 81.5 - 1

IQR = 80.5

C) Mean - (2*SD ) = 60.4 - (2*92.1494) = -123.90

Mean + (2*SD ) = 60.4 + (2*92.1494) = 244.70

There are 18 observations in the data set fall in the interval ( -123.90,244.70 )

Therefore 18*100/20 = 90% data values fall within two standard deviation of the mean.

According to Chebyshev's rule: at least 75% of the data values must be within 2 standard deviations of the mean.

So Chebyshev's test holds good by the given data set.