Question

here are the shopping times (in minutes) for a sample of 6 shoppers at a particular computer store.
39, 32, 37, 30, 28, 32
send data to calculator
find the standard deviation of this sample of shopping times. round your answer to two decimal places.
(if necessary, consult a list of formulas.)

Explanation:

Step1: Calculate the mean

First, find the mean (\(\bar{x}\)) of the data set. The formula for the mean is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 6\) and \(x_{i}\) are the data points.
\(\sum_{i=1}^{6}x_{i}=39 + 32+37 + 30+28 + 32=198\)
\(\bar{x}=\frac{198}{6}=33\)

Step2: Calculate the squared differences

For each data point \(x_{i}\), calculate \((x_{i}-\bar{x})^{2}\):

• For \(39\): \((39 - 33)^{2}=6^{2}=36\)
• For \(32\): \((32 - 33)^{2}=(- 1)^{2}=1\)
• For \(37\): \((37 - 33)^{2}=4^{2}=16\)
• For \(30\): \((30 - 33)^{2}=(-3)^{2}=9\)
• For \(28\): \((28 - 33)^{2}=(-5)^{2}=25\)
• For \(32\): \((32 - 33)^{2}=(-1)^{2}=1\)

Step3: Calculate the sum of squared differences

Sum these squared differences: \(36+1 + 16+9+25 + 1=88\)

Step4: Calculate the sample variance

The formula for sample variance (\(s^{2}\)) is \(s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}\). Here, \(n=6\), so \(n - 1 = 5\)
\(s^{2}=\frac{88}{5}=17.6\)

Step5: Calculate the sample standard deviation

The sample standard deviation (\(s\)) is the square root of the sample variance: \(s=\sqrt{17.6}\approx4.20\)

Answer:

\(4.20\)