QuestionFollowing are heights, in inches, for a sample of college basketball players.
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Find the sample standard deviation for the heights of the basketball players.
80.4
6.0
18.0
5.8
Studdy Solution
STEP 1
1. We have a sample of 20 heights of college basketball players.
2. We need to calculate the sample standard deviation.
3. The sample standard deviation formula is used:
$ s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}
\]
where \( n \) is the number of data points, \( x_i \) are the data points, and \( \bar{x} \) is the sample mean.
STEP 2
1. Calculate the sample mean.
2. Calculate the squared deviations from the mean.
3. Sum the squared deviations.
4. Divide by and take the square root to find the sample standard deviation.
STEP 3
Calculate the sample mean ():
List the heights:
Calculate the sum of the heights:
Calculate the sample mean:
STEP 4
Calculate the squared deviations from the mean:
Calculate each squared deviation:
\begin{align*}
(84 - 80.85)^2 & = 9.9225 \\
(88 - 80.85)^2 & = 51.0225 \\
(86 - 80.85)^2 & = 26.6225 \\
(85 - 80.85)^2 & = 17.2225 \\
(70 - 80.85)^2 & = 117.7225 \\
(75 - 80.85)^2 & = 34.2225 \\
(72 - 80.85)^2 & = 78.7225 \\
(86 - 80.85)^2 & = 26.6225 \\
(78 - 80.85)^2 & = 8.1225 \\
(81 - 80.85)^2 & = 0.0225 \\
(86 - 80.85)^2 & = 26.6225 \\
(78 - 80.85)^2 & = 8.1225 \\
(81 - 80.85)^2 & = 0.0225 \\
(72 - 80.85)^2 & = 78.7225 \\
(73 - 80.85)^2 & = 61.9225 \\
(76 - 80.85)^2 & = 23.5225 \\
(77 - 80.85)^2 & = 14.8225 \\
(87 - 80.85)^2 & = 37.8225 \\
(88 - 80.85)^2 & = 51.0225 \\
(84 - 80.85)^2 & = 9.9225 \\
\end{align*}
STEP 5
Sum the squared deviations:
STEP 6
Calculate the sample standard deviation:
Divide by :
Take the square root:
The sample standard deviation is approximately:
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