Question

The graph shows a distribution of data.

Answer 1

Answer: The variance of the data is 0.25, therefore second option is correct.

Explanation:

From the given graph it is noticed that the graph is symmetric along x = 4 or it is a bell shaped graph. So, the data follows the normal distribution.

The graph of normal distribution is bell shaped graph symmetric along the mean. The graph of normal distribution is shown below.

Since the given graph is symmetric along x = 4 therefore the mean of the data is 4.

Let the variance be $\sigma ^2$. So, the given data follows normal distribution with mean 4 and variance $\sigma ^2$.

In the below graph the point immediate left to the mean is $\mu-\sigma$ and in the given graph it 3.5

$\mu-\sigma=3.5$

$4-\sigma=3.5$

$\sigma=0.5$

$\sigma^2=0.25$

Therefore, the variance of the data is 0.25, therefore second option is correct.

Answer 2

The curve is bell shaped, the distribution of data is equal on both sides , that is from mid point called mean.

50% of Data lies on both side of mean.

So,Equation 1.→ Mean - 2 × standard deviation=3.5

or,Equation 2. →Mean + 2 × standard deviation=4.5

x -2 a= 3.5

4 -2 a=3.5

4-3.5=2 a

2 a=0.5

$a=\frac{0.5}{2}=0.25$

Using equation (2)

→ 4 +2 a=4.5

2 a=4.5-4

2 a=0.5

$a=\frac{0.5}{2}=0.25$

So, Standard Deviation = 0.25

→Variance =(Standard deviation)²=a²=(0.25)²=0.0625

Option (A)→0.0625