Question

use the display of data to find the standard deviation.
the standard deviation is .
(type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Calculate the mean

From the histogram, the data is \(8\) with frequency \(8\).
The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}\). Here \(x = 8\), \(f=8\). So \(\bar{x}=\frac{8\times8}{8}=8\)

Step2: Calculate the variance

The formula for variance \(s^{2}=\frac{\sum_{i = 1}^{n}f_{i}(x_{i}-\bar{x})^{2}}{\sum_{i = 1}^{n}f_{i}-1}\)
Substitute \(x = 8\), \(\bar{x}=8\), \(f = 8\) into the formula: \((x_{i}-\bar{x})^{2}=(8 - 8)^{2}=0\)
\(s^{2}=\frac{8\times0}{8 - 1}=0\)

Step3: Calculate the standard deviation

The formula for standard deviation \(s=\sqrt{s^{2}}\)
Since \(s^{2}=0\), then \(s=\sqrt{0}=0\)

Answer:

\(0\)