Question

find the mean and standard deviation of the data set.
number of books read
sylvester 218 edmund 224
rashin 217 treya 217
mean: 220; standard deviation: 4.9
mean: 219; standard deviation: 4.9
mean: 219; standard deviation: 3.4
mean: 220; standard deviation: 3.4

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}$ of a data set $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
Here, $n = 4$, $x_1=218$, $x_2 = 217$, $x_3=224$, $x_4=217$.
$\sum_{i=1}^{4}x_i=218 + 217+224+217=876$.
$\bar{x}=\frac{876}{4}=219$.

Step2: Calculate the variance

The formula for the variance $s^{2}$ of a sample data set is $s^{2}=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^{2}}{n - 1}$.
For $x_1 = 218$: $(218 - 219)^{2}=(-1)^{2}=1$.
For $x_2 = 217$: $(217 - 219)^{2}=(-2)^{2}=4$.
For $x_3 = 224$: $(224 - 219)^{2}=5^{2}=25$.
For $x_4 = 217$: $(217 - 219)^{2}=(-2)^{2}=4$.
$\sum_{i = 1}^{4}(x_i-\bar{x})^{2}=1 + 4+25+4=34$.
$s^{2}=\frac{34}{4-1}=\frac{34}{3}\approx11.33$.

Step3: Calculate the standard deviation

The standard deviation $s=\sqrt{s^{2}}$.
$s=\sqrt{\frac{34}{3}}\approx3.4$.

Answer:

Mean: 219; Standard Deviation: 3.4 (the third option)