Question

calculate the sample standard deviation (round to two decimal places): 2,3,4,5,6. remember that the equation for the sample standard deviation is:
(sqrt{\frac{sigma (x - \bar{x})^2}{n - 1}})

5.56
1.62
1.58
3.45

Explanation:

Step1: Calculate the mean ($\bar{X}$)

The data set is \(2, 3, 4, 5, 6\). The mean is calculated as the sum of the data points divided by the number of data points (\(N\)).
\(\bar{X}=\frac{2 + 3 + 4 + 5 + 6}{5}=\frac{20}{5} = 4\)

Step2: Calculate \((X - \bar{X})^2\) for each data point

• For \(X = 2\): \((2 - 4)^2=(-2)^2 = 4\)
• For \(X = 3\): \((3 - 4)^2=(-1)^2 = 1\)
• For \(X = 4\): \((4 - 4)^2=(0)^2 = 0\)
• For \(X = 5\): \((5 - 4)^2=(1)^2 = 1\)
• For \(X = 6\): \((6 - 4)^2=(2)^2 = 4\)

Step3: Calculate \(\sum(X - \bar{X})^2\)

Sum the values from Step 2: \(4 + 1 + 0 + 1 + 4=10\)

Step4: Calculate the sample standard deviation

Using the formula \(s=\sqrt{\frac{\sum(X - \bar{X})^2}{N - 1}}\), where \(N = 5\) (so \(N-1 = 4\)) and \(\sum(X - \bar{X})^2=10\).
\(s=\sqrt{\frac{10}{4}}=\sqrt{2.5}\approx1.58\)

Answer:

1.58