Match List - I with List - II.

List – I

(Population Mean (μ) and

List - II

(Population Standard Deviation (σ))

A.

I.
8

B.

II.
7

C.

III.
6

D.

IV.
5

Choose the correct answer from the options given below :

Question

Question

Answer 1

The correct answer is - A - IV, B - III, C - II, D - I

Key Points

Population Standard Deviation Calculation
- The formula for the population standard deviation (σ) is derived from the population mean (μ) and the mean of the squared deviations ( $\frac{1}{N}\Sigma x_i^2$ ).
- We use the formula: $\sigma = \sqrt{\frac{1}{N}\Sigma x_i^2 - \mu^2}$ .
- For each pair, we calculate σ to match the correct option:
  - A: $\sigma = \sqrt{50 - 5^2} = \sqrt{50 - 25} = \sqrt{25} = 5$
  - B: $\sigma = \sqrt{52 - 4^2} = \sqrt{52 - 16} = \sqrt{36} = 6$
  - C: $\sigma = \sqrt{58 - 3^2} = \sqrt{58 - 9} = \sqrt{49} = 7$
  - D: $\sigma = \sqrt{100 - 6^2} = \sqrt{100 - 36} = \sqrt{64} = 8$

Additional Information

Population Mean ( $\mu$ )
- The population mean ( $\mu$ ) is the average of all the values in the population.
- It is calculated as $\mu = \frac{1}{N}\sum_{i=1}^{N} x_i$ .
Mean of Squared Deviations ( $\frac{1}{N}\Sigma x_i^2$ )
- This value represents the average of the squares of the individual data points.
- It is used in the calculation of the variance and standard deviation.
Variance ( $\sigma^2$ )
- Variance is the average of the squared differences from the mean.
- It is calculated as $\sigma^2 = \frac{1}{N}\sum_{i=1}^{N}(x_i - \mu)^2$ .
- The standard deviation is the square root of the variance.

List – I (Population Mean (μ) and	List - II (Population Standard Deviation (σ))
A.	I.	8
B.	II.	7
C.	III.	6
D.	IV.	5