Answer
The mean, median, mode, variance, standard deviation, and the range for letter’s word lengths are 4.5,4, 3, 4.68, 2.163, and 11, respectively.
The following is the set of data, which consists of the length of every word that is used in the letter signed by A MOURNER:
Work Step by Step
Here, the number of words are 132 and the sum of data set is 594. Mean value of the above data set can be calculated as follows:
\[\begin{align}
& \bar{x}=\frac{\sum x}{n} \\
& =\frac{594}{132} \\
& =4.5
\end{align}\]
Hence, the mean is 4.5.
The total value in the data is 132. So, the median will be the average of 66th and 67th data values of the ordered data set, which lies in the row of “Length of Word 4” if see the column with “Cumulative Number of Words”. So, the median of the data set is 4.
The mode of the data set is the data value that occurs most. So, the mode of the data set will be 3, as 3 occurs most of the time among others, i.e., 33 times.
Now, sample variance is calculated as follows:
\[\begin{align}
& {{s}^{2}}=\frac{\sum {{\left( x-\bar{x} \right)}^{2}}}{n-1} \\
& =\frac{{{\left( 2-4.5 \right)}^{2}}+{{\left( 44-4.5 \right)}^{2}}+\cdots +{{\left( 12-4.5 \right)}^{2}}}{131} \\
& =\frac{41345}{131} \\
& =315.61
\end{align}\]
Hence, the sample variance is 315.61. Sample standard deviation can be calculated as follows:
\[\begin{align}
& s=\sqrt{{{s}^{2}}} \\
& =\sqrt{315.61} \\
& =17.76
\end{align}\]
Hence, the standard deviation is 17.76.
The minimum value of the data is 1 and the maximum value of the data set is 12. Range of the data can be calculated as follows:
\[\begin{align}
& \text{Range}=\max -min \\
& =12-1 \\
& =11
\end{align}\]
Hence, range of the data set is 11.
Summary statistics found above about “A MOURNER” are close to the summary statistics of Tom sturdy.
