A publisher receives a copy of a 500-page textbook from a...

A publisher receives a copy of a 500-page textbook from a printer. The page proofs are carefully read and the number of errors on each page is recorded, producing the data in the following table: $$ \begin{array}{ccccccc} \hline \text { Number of errors } & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Number of pages } & 102 & 138 & 140 & 79 & 33 & 8 \\ \hline \end{array} $$ Find the mean and standard deviation in number of errors per page.

A publisher receives a copy of a 500-page textbook from a printer. The page proofs are carefully read and the number of errors on each page is recorded, producing the data in the following table:
$$
\begin{array}{ccccccc}
\hline \text { Number of errors } & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline \text { Number of pages } & 102 & 138 & 140 & 79 & 33 & 8 \\
\hline
\end{array}
$$
Find the mean and standard deviation in number of errors per page.

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Key Concepts

Frequency Distribution

A frequency distribution organizes data by listing each distinct value or range of values along with the number of observations (frequency) for each. It provides a summary that makes it easier to understand the overall pattern in the data, such as which values occur most frequently and how spread out the data is.

Mean (Weighted Average)

The mean is a measure of central tendency that represents the average value in the data set. In the context of a frequency distribution, the mean is calculated by multiplying each value by its corresponding frequency, summing these products, and then dividing by the total number of observations. This weighted approach accounts for the varying number of occurrences for each data value.

Standard Deviation

The standard deviation quantifies the amount of variability or spread in the data relative to the mean. It is computed by taking the square root of the variance, where the variance is the average of the squared differences between each value and the mean. In a frequency distribution, these squared differences are also weighted by their frequencies before averaging.

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