
Example 1: If a die is rolled, then find the variance and standard
deviation of the possibilities.
Solution: When a die is rolled, the possible number of outcomes is 6. So the
sample space, n = 6 and the data set = { 1;2;3;4;5;6}.
To find the variance, first, we need to calculate the mean of the data set.
Mean, x̅ = (1+2+3+4+5+6)/6 = 3.5
We can put the value of data and mean in the formula to get;
σ2 = Σ (xi – x̅ )2/n
σ2 = ⅙ (6.25+2.25+0.25+0.25+2.25+6.25)
σ2 = 2.917
Answer: Therefore the variance is σ2 = 2.917, and standard deviation,σ
= √2.917 = 1.708

Example 2: Find the standard deviation of the average temperatures
recorded over a five-day period last winter:
18, 22, 19, 25, 12 (The mean = 19.2)
Solution:
This time we will use a table for our calculations.
Mean = 19.2
To find the variance, we divide 5-1 = 4
94.8/4 = 23.7
Finally, we find the square root of this variance. √23.7 = 4.9
So the standard deviation for the temperatures recorded is 4.9; the variance is
23.7
Finally, we find the square root of this variance. √23.7 ≈ 4.9
Answer: So the standard deviation for the temperatures recorded is 4.9;
the variance is 23.7.
Q.1. Find the mean and standard deviation of the following data set.
5,8,9,10,19
Responses b

Mean = 10.2 Sample standard deviation = 4.26
Mean = 10.2 Sample standard deviation = 4.26

Mean = 10.2 Sample standard deviation = 5.26
Mean = 10.2 Sample standard deviation = 5.26

Mean = 9.2 Sample standard deviation = 5.26
Mean = 9.2 Sample standard deviation = 5.26

Mean = 11 Sample standard deviation = 6
Q.2. What is the sample standard deviation of all the months in a year that has 31 days?
Responses

0.5
0.5

1
1

0
0

1.5
1.5