Question

A sample of five data entry clerks employed in the Horry County Tax Office revised the

following number of tax records last hour: 73, 98, 60, 92, and 84.

(a) Find the mean, median, and the standard deviation.

(b) Compute the coefficient of skewness using Pearson’s method.

(c) Calculate the coefficient of skewness using the software method.

Answer each of the three questions that relate to the data given above. Discuss how you derived your answers and your conclusion regarding the skewness of the data.

Answer 1

Solution:

a)We have

X	X​​​​​​2
73	5329
98	9604
60	3600
92	8464
84	7056
Sum=407	Sum=34053

Mean===81.4

Hence,

Mean=81.4

Now for calculating median the data in ascending order is

60,73,84,92,98

Since the sample size n =5 is odd, we have that (n+1)/2 = (5+1)/2 = 3(n+1)/2=(5+1)/2=3 is an integer value, the median is computed directly by finding the value located at position 3^rd which is 84

Hence ,

Median=84

The standard deviation is given by,

S=

=

=

S =15.192

b)The coefficient of skewness is given by

S_{​​​​​​k}=  

=

S_{​​​​​​k} = -0.51342812

c) We calculate skewness in excel,

The function is

S_k=SKEW(73,98,60,92,84)

=0.6368

The excel output is givne