Correct Answer - Option 1 : 50.7
Concept:
Sample Variance:
- Sample variance (s2) is a measure of the degree to which the numbers in a list are spread out.
- If the numbers in a list are all close to the expected values, the variance will be small.
- If they are far away, the variance will be large.
Sample variance of n observations is given by
\(s^2\ =\ \frac{1}{n-1}∑ (x_i\ -\ ̅{x})^2\)
Where x̅ is the sample mean and given by
\(̅{x}\ =\ \frac{∑ x_i}{n}\ =\ \frac{x_1+x_2=\dots x_n}{n}\)
Calculation:
Here, ∑x = 224 and n = 7
Using the formula of sample mean, we will get
x̅ = 224/7 = 32
Observation |
Value |
(xi - x̅)2 |
1 |
25 |
49 |
2 |
26 |
36 |
3 |
38 |
36 |
4 |
45 |
169 |
5 |
31 |
1 |
6 |
30 |
4 |
7 |
29 |
9 |
n = 7 |
∑x = 224 |
∑(xi - x̅)2 = 304 |
Therefore, sample variance
\(s^2\ =\ \frac{1}{n-1}∑ (x_i\ -\ ̅{x})^2\)
\(\Rightarrow\ s^2\ =\ \frac{1}{7-1}(304)\ =\ 50.7\)
Hence, option 1 is correct.