Find the range, mean, variance, and standard deviation of...

Find the range, mean, variance, and standard deviation of the sample data set. The durations (in days) of pregnancies for a random sample of mothers $\begin{array}{ccccc}295 & 280 & 268 & 278 & 291\end{array}$ $277 \quad 291$ $\begin{array}{rrrrr}279 & 296 & 285 & 269 & 293\end{array}$ $277 \quad 282$ $\begin{array}{rrrr}267 & 281 & 286 & 269\end{array}$ $264 \quad 299$

Find the range, mean, variance, and standard deviation of the sample data set.
The durations (in days) of pregnancies for a random sample of mothers
$\begin{array}{ccccc}295 & 280 & 268 & 278 & 291\end{array}$
$277 \quad 291$
$\begin{array}{rrrrr}279 & 296 & 285 & 269 & 293\end{array}$
$277 \quad 282$
$\begin{array}{rrrr}267 & 281 & 286 & 269\end{array}$
$264 \quad 299$

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Key Concepts

Mean

The mean, also known as the average, is calculated by summing all the values in a data set and then dividing by the number of values. It serves as a central measure that summarizes the typical value in the data.

Variance

Variance measures how far the data values are spread out from the mean; it is computed as the average of the squared differences from the mean. In a sample, this is typically adjusted by dividing by one less than the number of observations to provide an unbiased estimate of the population variance.

Standard Deviation

Standard deviation is the square root of the variance and provides a measure of dispersion in the same units as the original data. It indicates, on average, how much the individual data values deviate from the mean, making it a useful tool to assess data variability.

Range

The range is a measure of dispersion that is calculated as the difference between the largest and smallest values in a data set. It provides a quick sense of the spread of the data, although it can be heavily influenced by outliers.

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