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Chapter 3: Problem 22

Grand Jury indictment data for Gloucester County, New Jersey, are published every week in the Gloucester County Times newspaper (www.nj.com/gloucester). The following data are the number of indictments for a sample of 11 weeks selected from July 2010 through June 2011 : \(\begin{array}{lllllllll}35 & 13 & 17 & 21 & 21 & 29 & 20 & 26 & 24\end{array}\) \(13 \quad 23\) Find the mean, median, and mode for these data.

Short Answer

Expert verified
The mean of the data is 22.45, the median is 21 and the modes are 13 and 21.

Step by step solution

01

- Arrange the data in ascending order

We arrange the data in ascending order to make it easier to find the median and mode. Here are the sorted data: \(13, 13, 17, 20, 21, 21, 23, 24, 26, 29, 35\).
02

- Calculate the mean

The mean is calculated by adding up all the numbers and then dividing by the quantity of numbers. Therefore, the mean of the data is \((13 + 13 + 17 + 20 + 21 + 21 + 23 + 24 + 26 + 29 + 35) / 11 = 22.45\).
03

- Calculate the median

With 11 data points, the median is the 6th value. So, the median of the data set is 21.
04

- Determine the mode

The mode of a dataset is the number that appears most frequently in the series. In this series, the number 13 and 21 appear twice. So, the modes are 13 and 21.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Mean
The mean, often referred to as the average, gives us an idea of the central value of a data set. To calculate the mean, add up all the numbers in the data set. Then, divide this sum by the total number of values present. For example, for the dataset representing Gloucester County indictments, the numbers are:
  • 13, 13, 17, 20, 21, 21, 23, 24, 26, 29, 35.
The sum of these numbers is 247. Since there are 11 numbers, the mean is calculated as follows: \[ \text{Mean} = \frac{247}{11} = 22.45 \] Thus, the mean offering a summary value helps us see what a typical week might closely resemble in terms of the number of indictments.
Grasping the Median
The median is the middle value in a sorted list of numbers. It divides the data into two equal halves. To find the median, order your data from smallest to largest, and then locate the middle number. In our dataset:
  • 13, 13, 17, 20, 21, 21, 23, 24, 26, 29, 35
With 11 numbers in total, the middle, or the 6th number, is 21. Therefore, the median of this dataset is 21. It is important because it provides a central value that is not influenced by extremely high or low values, unlike the mean.
Discovering the Mode
The mode is the number that appears most frequently in your data set. It tells us which value is most common and can sometimes reflect patterns in the data. When we look at the Gloucester County indictment numbers:
  • 13, 13, 17, 20, 21, 21, 23, 24, 26, 29, 35
The numbers 13 and 21 both appear twice, more than any other numbers in the set. Thus, this dataset is bimodal, with both 13 and 21 as its modes. Having more than one mode is quite normal, and it highlights multiple values that could be considered typical within the dataset.

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Most popular questions from this chapter

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The following table gives the frequency distribution of the times (in minutes) that 50 commuter students at a large university spent looking for parking spaces on the first day of classes in the Fall semester of 2012 . \begin{tabular}{lc} \hline \multicolumn{1}{c} { Time } & Number of Students \\ \hline 0 to less than 4 & 1 \\ 4 to less than 8 & 7 \\ 8 to less than 12 & 15 \\ 12 to less than 16 & 18 \\ 16 to less than 20 & 6 \\ 20 to less than 24 & 3 \\ \hline \end{tabular} Find the mean, variance, and standard deviation. Are the values of these summary measures population parameters or sample statistics?
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