Question

Find the standard deviation for the following group of data items .
23 26 26 32

Answer 1

To find the standard deviation of the given data set \(23, 26, 26, 32\), we can follow these steps:

1. **Calculate the mean**:
\[
\text{Mean} = \frac{(23 + 26 + 26 + 32)}{4} = \frac{107}{4} = 26.75
\]

2. **Calculate the squared differences from the mean**:
- For \(23\): \((23 - 26.75)^2 = (-3.75)^2 = 14.0625\)
- For \(26\): \((26 - 26.75)^2 = (-0.75)^2 = 0.5625\)
- For \(26\): \((26 - 26.75)^2 = (-0.75)^2 = 0.5625\)
- For \(32\): \((32 - 26.75)^2 = (5.25)^2 = 27.5625\)

3. **Sum the squared differences**:
\[
14.0625 + 0.5625 + 0.5625 + 27.5625 = 42.25
\]

4. **Calculate the variance**:
Since this is a sample of the population (4 data points), we divide by \(n - 1\) (which is 3):
\[
\text{Variance} = \frac{42.25}{3} \approx 14.0833
\]

5. **Calculate the standard deviation**:
\[
\text{Standard deviation} = \sqrt{14.0833} \approx 3.75
\]

So, the standard deviation for the given data set \(23, 26, 26, 32\) is approximately **3.75**.