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, assume the score \(x = 9\) and frequency \(f=11\).
The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}f_ix_i}{\sum_{i = 1}^{n}f_i}\). Here \(n = 1\), \(f_1=11\), \(x_1 = 9\). So \(\bar{x}=9\).

Step2: Calculate the standard deviation

The formula for the standard deviation of a frequency - distribution is \(s=\sqrt{\frac{\sum_{i = 1}^{n}f_i(x_i-\bar{x})^2}{\sum_{i = 1}^{n}f_i-1}}\).
Since \(x_i=\bar{x} = 9\), then \((x_i-\bar{x})^2=(9 - 9)^2=0\).
Substitute into the formula: \(s=\sqrt{\frac{11\times0}{11 - 1}}=\sqrt{0}=0\)

Answer:

\(0\)