Question

question 5 using your calculator, find the standard deviation and variance of the sample data shown below. x 1.3 6.5 5.5 5.6 18.8 10 25.8 standard deviation, s: round to two decimal places. variance, s²: round to one decimal place.

Explanation:

Step1: Enter data into calculator

Enter the data points 1.3, 6.5, 5.5, 5.6, 18.8, 10, 25.8 into a statistical - capable calculator.

Step2: Calculate standard deviation

Use the calculator's function to find the sample standard deviation. Let the data set be \(x_1,x_2,\cdots,x_n\). The formula for the sample standard deviation \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}\), where \(\bar{x}\) is the sample mean and \(n\) is the number of data points. Here \(n = 7\). After calculation, \(s\approx8.34\).

Step3: Calculate variance

The variance \(s^{2}\) is the square of the standard deviation. Since \(s\approx8.34\), then \(s^{2}=s\times s\approx69.6\).

Answer:

Standard deviation, \(s\): 8.34
Variance, \(s^{2}\): 69.6