Question

18 36 23 17 13
send data to excel
the sample variance for the height increase is
the sample standard deviation for the height increase is

Explanation:

Step1: Calculate the mean

Let the data set be \(x = \{18,36,23,17,13\}\). The number of data - points \(n = 5\). The mean \(\bar{x}=\frac{18 + 36+23+17+13}{5}=\frac{107}{5}=21.4\)

Step2: Calculate the squared differences

\((18 - 21.4)^2=(- 3.4)^2 = 11.56\), \((36 - 21.4)^2=(14.6)^2 = 213.16\), \((23 - 21.4)^2=(1.6)^2 = 2.56\), \((17 - 21.4)^2=(-4.4)^2 = 19.36\), \((13 - 21.4)^2=(-8.4)^2 = 70.56\)

Step3: Calculate the sample variance

The formula for the sample variance \(s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}\). \(\sum_{i=1}^{5}(x_{i}-\bar{x})^{2}=11.56 + 213.16+2.56+19.36+70.56=317.2\). Then \(s^{2}=\frac{317.2}{4}=79.3\)

Step4: Calculate the sample standard deviation

The sample standard deviation \(s=\sqrt{s^{2}}\), so \(s=\sqrt{79.3}\approx8.905\)

Answer:

The sample variance for the height increase is \(79.3\).
The sample standard deviation for the height increase is approximately \(8.905\).