Question

The following is a set of data from a sample of n=5. 4 3 6 7
10.
a. Compute the​ mean, median, and mode.

b. Compute the​ range, variance, standard​deviation, and coefficient of variation.

c. Compute the Z scores. Are there any​outliers?

d. Describe the shape of the data set.

Answer 1

a)

mean =    ΣX/n =    30.000   /   5.000   =   6

Median=0.5(n+1)th value =    3   th value of sorted data
=   6

mode= highest frequency data = so, there is no mode

b)

range=max-min =    10   -   3   =   7
sample variance =    Σ(X - X̄)²/(n-1)=   30.0000   /   4.0000   =   7.5000
                      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   7.5000   =       2.7386

coefficient of variation,CV=σ/µ=   0.4564

c)

X	Z score=(X-mean)/std dev
4	-0.7303
3	-1.0954
6	0.0000
7	0.3651
10	1.4606

no, there is no outliers

d)

skewed to left