Question

find the mean and standard deviation of the data set.

	number of books read
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 data set is \(218, 224, 217, 217\). The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 4\), \(\sum_{i=1}^{4}x_{i}=218 + 224+217+217=876\). So \(\bar{x}=\frac{876}{4}=219\).

Step2: Calculate the variance

The formula for the variance \(s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}\).
\((218 - 219)^{2}=(- 1)^{2}=1\), \((224 - 219)^{2}=5^{2}=25\), \((217 - 219)^{2}=(-2)^{2}=4\), \((217 - 219)^{2}=(-2)^{2}=4\).
\(\sum_{i = 1}^{4}(x_{i}-\bar{x})^{2}=1 + 25+4 + 4=34\).
\(s^{2}=\frac{34}{3}\approx11.33\).

Step3: Calculate the standard - deviation

The standard deviation \(s=\sqrt{s^{2}}\), so \(s=\sqrt{\frac{34}{3}}\approx3.4\).

Answer:

Mean: 219; Standard Deviation: 3.4