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Chapter 12: Problem 67

What is the midrange and how is it obtained?

Short Answer

Expert verified
The midrange is a type of average obtained by adding the highest and the lowest number in a data set and then dividing by 2. For example, for the set {1, 2, 10}, midrange is 5.5.

Step by step solution

01

Definition of Midrange

Midrange is a type of average, or mean, which is calculated by adding the highest and the lowest number in a data set and then dividing by 2.
02

Procedure to obtain midrange

To calculate the midrange of a set of numbers, first find the minimum and maximum number in the set. Then, add these two numbers together and divide the sum by 2
03

Example

Suppose the set of numbers is {1, 2, 10}. The minimum number is 1 and the maximum number is 10. Therefore, midrange is calculated as: \[\frac{(1+10)}{2} = 5.5\]

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Most popular questions from this chapter

An advertisement for a speed-reading course claimed that the "average" reading speed for people completing the course was 1000 words per minute. Shown below are the actual data for the reading speeds per minute for a sample of 24 people who completed the cours茅. $$ \begin{array}{|c|c|c|c|c|c|} \hline 1000 & 900 & 800 & 1000 & 900 & 850 \\ \hline 650 & 1000 & 1050 & 800 & 1000 & 850 \\ \hline 700 & 750 & 800 & 850 & 900 & 950 \\ \hline 600 & 1100 & 950 & 700 & 750 & 650 \\ \hline \end{array} $$ a. Find the mean, median, mode, and midrange. (If you prefer, first organize the data in a frequency distribution.) b. Which measure of central tendency was given in the advertisement? c. Which measure of central tendency is the best indicator of the "average" reading speed in this situation? Explain your answer.

A set of data items is normally distributed with a mean of 400 and a standard deviation of 50. Find the data item in this distribution that corresponds to the given z-score. \(z=1.5\)

Intelligence quotients (IQs) on the Stanford-Binet intelligence test are normally distributed with a mean of 100 and a standard deviation of 16. Use the 68-95-99.7 Rule to find the percentage of people with IQs between 68 and 100 .

Use the data \(0,1,3,4,4,6\). Add 2 to each of the numbers. How does this affect the mean? How does this affect the standard deviation?

A random sample of 40 college professors is selected from all professors at a university. The following list gives their ages: $$ \begin{aligned} &63,48,42,42,38,59,41,44,45,28,54,62,51,44,63,66,59,46, \\ &51,28,37,66,42,40,30,31,48,32,29,42,63,37,36,47,25,34, \\ &49,30,35,50 \end{aligned} $$ Construct a stem-and-leaf plot for the data. What does the shape of the display reveal about the ages of the professors?
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