The number of annual precipitation days for one-half of the...

The number of annual precipitation days for one-half of the 50 largest U.S. cities is listed below. Find the range, variance, and standard deviation of the data. $\begin{array}{llllllllll}{135} & {128} & {136} & {78} & {116} & {77} & {111} & {79} & {44} & {97} \\ {116} & {123} & {88} & {102} & {26} & {82} & {156} & {133} & {107} & {35} \\ {112} & {98} & {45} & {122} & {125} & {}\end{array}$

The number of annual precipitation days for one-half of the 50 largest U.S. cities is listed below. Find the range, variance, and standard deviation of the data.
$\begin{array}{llllllllll}{135} & {128} & {136} & {78} & {116} & {77} & {111} & {79} & {44} & {97} \\ {116} & {123} & {88} & {102} & {26} & {82} & {156} & {133} & {107} & {35} \\ {112} & {98} & {45} & {122} & {125} & {}\end{array}$

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Key Concepts

Standard Deviation

Standard deviation is the square root of the variance, and it provides a measure of dispersion in the same units as the original data. It indicates how much the individual data points typically differ from the mean, offering insight into the variability within the data set.

Range

The range is a measure of dispersion that is calculated by taking the difference between the maximum and minimum values in a data set. It provides a simple indication of the overall spread of the data, although it can be sensitive to outliers.

Variance

Variance quantifies the spread of a data set by measuring the average squared deviations from its mean. It is calculated by taking each observation's deviation from the mean, squaring it, and then averaging these squared differences. Variance is fundamental in understanding the dispersion of the data points.

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