Question

Consider the sample: 9, 6, 7, 9, 10, 8

a) Find : the mean, the median, the mode

b) Find : the range, the quartiles Q1, Q3, the variance, the standard deviation.

c) Draw a box-plot for the given data set.

Answer 1

a ) Mean :  

$\bar{x}=\frac{1}{6}\sum_{i=1}^{6}x_i=\frac{49}{6}=8.1667$

Median :

The observations need to be arranged in ascending order first :

6 , 7 , 8 , 9 , 9 , 10

We have 6 observations . The median is the average of the third and fourth observation .

Median = ( 8+9)/2=8.5

Mode = 9 ( the observation having the highest frequency )

b ) Range = 10 - 6 = 4

First quartile =  7.25

Third quartile = 9

Variance :

$s^2=\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2=2.1667$

Standard deviation :

$s=\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2}=1.4720$

c ) The box plot is given below :