JAMIA 2024 — Mathematics PYQ

The values are: $4.2,4.3,4,4.1$

Total number of observations ($n$) = $4$

Step 1: Calculate the Mean ($\bar{x}$)

The mean is the sum of all observations divided by the total number of observations:

Step 2: Find the Squared Deviations from the Mean

Variance is based on how much each value deviates from the mean ($x_i-\bar{x}$). We then square these values:

1. $(4.2-4.15{)}^2=(0.05{)}^2=0.0025$

2. $(4.3-4.15{)}^2=(0.15{)}^2=0.0225$

3. $(4-4.15{)}^2=(-0.15{)}^2=0.0225$

4. $(4.1-4.15{)}^2=(-0.05{)}^2=0.0025$

Step 3: Calculate the Variance (${\sigma }^2$)

The formula for variance is the average of these squared deviations:

Final Answer

The variance of the given observation values is: