question 5 using your calculator, find the standard deviation and variance of the sample data shown below. x…

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.

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.

Answer

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