Question

in the next training session, rajhanur made four throws as shown in the table 7. given the mean of the distance is 10.5. calculate the variance of the data.

Explanation:

Step1: Recall variance formula

The formula for variance $s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n}$, where $x_{i}$ are the data - points, $\bar{x}$ is the mean and $n$ is the number of data - points. Here, $n = 4$ and $\bar{x}=10.5$.

Step2: Calculate $(x_{i}-\bar{x})^{2}$ for each data - point

For $x_1 = 10.6$: $(10.6 - 10.5)^{2}=(0.1)^{2}=0.01$.
For $x_2 = 10.7$: $(10.7 - 10.5)^{2}=(0.2)^{2}=0.04$.
For $x_3 = 10.4$: $(10.4 - 10.5)^{2}=(-0.1)^{2}=0.01$.
For $x_4 = 10.3$: $(10.3 - 10.5)^{2}=(-0.2)^{2}=0.04$.

Step3: Calculate the sum of $(x_{i}-\bar{x})^{2}$

$\sum_{i = 1}^{4}(x_{i}-\bar{x})^{2}=0.01 + 0.04+0.01 + 0.04=0.1$.

Step4: Calculate the variance

$s^{2}=\frac{\sum_{i = 1}^{4}(x_{i}-\bar{x})^{2}}{4}=\frac{0.1}{4}=0.025$.

Answer:

$0.025$