/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 15 Watch out for these little bugge... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 15

Watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, \((d)\) midrange, and then answer the given question. Listed below are foot lengths in inches of randomly selected Army women measured in the 1988 Anthropometric Survey (ANSUR). Are the statistics representative of the current population of all Army women? $$\begin{array}{ccccccccccc}10.4 & 9.3 & 9.1 & 9.3 & 10.0 & 9.4 & 8.6 & 9.8 & 9.9 & 9.1 & 9.1\end{array}$$

Short Answer

Expert verified
(a) Mean 鈮� 9.45, (b) Median = 9.3, (c) Mode = 9.1, (d) Midrange = 9.5. The statistics may not represent the current population of all Army women due to changes over time.

Step by step solution

01

Arrange the Data in Ascending Order

First, it is important to arrange the provided foot lengths in ascending order to make calculating the statistics easier. The arranged data is: 8.6, 9.1, 9.1, 9.1, 9.3, 9.3, 9.4, 9.8, 9.9, 10.0, 10.4
02

Calculate the Mean

Add all the foot lengths together and divide by the number of data points to find the mean. Sum = 8.6 + 9.1 + 9.1 + 9.1 + 9.3 + 9.3 + 9.4 + 9.8 + 9.9 + 10.0 + 10.4 = 104 Number of data points = 11 Mean = Sum / Number of data points Mean = 104 / 11 鈮� 9.45 inches
03

Calculate the Median

The median is the middle value of the ordered data set. With 11 data points, the median is the 6th value. Median = 9.3 inches
04

Determine the Mode

The mode is the value(s) that appear most frequently in the data set. In this data set, 9.1 appears three times. Mode = 9.1 inches
05

Calculate the Midrange

The midrange is the value midway between the maximum and minimum values. Minimum value = 8.6, Maximum value = 10.4 Midrange = (Minimum value + Maximum value) / 2 Midrange = (8.6 + 10.4) / 2 = 9.5 inches
06

Answer the Given Question

Determine if these statistics are representative of the current population of all Army women. It鈥檚 important to consider that the data is from 1988; so there may be differences in the current population due to changes over time, recruitment practices, and demographic shifts.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Mean Calculation
The mean, often referred to as the average, is a measure of central tendency that gives us an idea of the 'typical' value in a dataset. It's calculated by summing all the values and then dividing by the number of values. To find the mean of our dataset of foot lengths:
- First, we need to add all the foot lengths together: 8.6 + 9.1 + 9.1 + 9.1 + 9.3 + 9.3 + 9.4 + 9.8 + 9.9 + 10.0 + 10.4 = 104 inches.
- Next, divide the sum by the number of data points: 104 / 11 鈮� 9.45 inches.
So, the mean foot length for this sample is approximately 9.45 inches. This value gives us a central point around which the rest of the data is distributed.
Median Determination
The median is another measure of central tendency and helps to find the middle value in an ordered dataset. Unlike the mean, the median isn't affected by extreme values (outliers). To find the median:
- First, arrange the data in ascending order: 8.6, 9.1, 9.1, 9.1, 9.3, 9.3, 9.4, 9.8, 9.9, 10.0, 10.4.
- Next, identify the middle value. With 11 data points, the median is the 6th value, which is 9.3.
Thus, the median foot length in this dataset is 9.3 inches. This reflects a value where half the measurements are below and half are above.
Mode Identification
The mode is the value that appears most frequently in a dataset. It gives us a sense of the most common value. To identify the mode in our dataset:
- We look at each value and count its occurrences. In this dataset, 9.1 inches appears three times, more than any other value.
Hence, the mode of this dataset is 9.1 inches. The mode is particularly useful when we want to know the most typical case in a group.
Midrange Computation
The midrange provides a measure of central tendency by averaging the maximum and minimum values in a dataset. It's easy to calculate and gives insight into the range's midpoint. To compute the midrange:
- Identify the minimum value: 8.6 inches.
- Identify the maximum value: 10.4 inches.
- Apply the midrange formula: \[ \text{Midrange} = \frac{\text{Minimum Value} + \text{Maximum Value}}{2} \] So, the midrange is: \[ \text{Midrange} = \frac{8.6 + 10.4}{2} = 9.5 \text{ inches} \] Thus, the midrange for our dataset is 9.5 inches. This simple average of extremes gives a quick estimation of the dataset's center.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as "minutes") in your results. (The same data were used in Section 3-I, where we found measures of center. Here we find measures of variation.) Then answer the given questions. Listed below are foot lengths in inches of randomly selected Army women measured in the 1988 Anthropometric Survey (ANSUR). Are the statistics representative of the current population of all Army women? $$\begin{array}{ccccccccccc} 10.4 & 9.3 & 9.1 & 9.3 & 10.0 & 9.4 & 8.6 & 9.8 & 9.9 & 9.1 & 9.1 \end{array}$$

Find the coefficient of variation for each of the two samples; then compare the variation. (The same data were used in Section 3-I.) Listed below are amounts (in millions of dollars) collected from parking meters by Brinks and others in New York City during similar time periods. A larger data set was used to convict five Brinks employees of grand larceny. The data were provided by the attorney for New York City, and they are listed on the DASL Website. Do the two samples appear to have different amounts of variation? $$\begin{array}{lcccccccccc} \text { Collection Contractor Was Brinks } & 1.3 & 1.5 & 1.3 & 1.5 & 1.4 & 1.7 & 1.8 & 1.7 & 1.7 & 1.6 \\ \text { Collection Contractor Was Not Brinks } & 2.2 & 1.9 & 1.5 & 1.6 & 1.5 & 1.7 & 1.9 & 1.6 & 1.6 & 1.8 \end{array}$$

Find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as "minutes") in your results. (The same data were used in Section 3-I, where we found measures of center. Here we find measures of variation.) Then answer the given questions. Listed below in dollars are the annual costs of tuition and fees at the 10 most expensive colleges in the United States for a recent year (based on data from \(U . S .\) News \& World Report). The colleges listed in order are Columbia, Vassar, Trinity, George Washington, Carnegie Mellon, Wesleyan, Tulane, Bucknell, Oberlin, and Union. What does this "top 10" list tell us about the variation among costs for the population of all U.S. college tuition? $$\begin{array}{rlllllllll} 49,138 & 47,890 & 47,510 & 47,343 & 46,962 & 46,944 & 46,930 & 46,902 & 46,870 & 46,785 \end{array}$$

Use z scores to compare the given values. Tallest and Shortest Men The tallest living man at the time of this writing is Sultan Kosen, who has a height of \(251 \mathrm{cm}\). The shortest living man is Chandra Bahadur Dangi, who has a height of \(54.6 \mathrm{cm}\). Heights of men have a mean of \(174.12 \mathrm{cm}\) and a standard deviation of 7.10 cm. Which of these two men has the height that is more extreme?

Find the coefficient of variation for each of the two samples; then compare the variation. (The same data were used in Section 3-I.) Listed below are pulse rates (beats per minute) from samples of adult males and females (from Data Set 1 "Body Data" in Appendix B). Does there appear to be a difference? $$\begin{array}{llllllllllllllll} \text { Male: } & 86 & 72 & 64 & 72 & 72 & 54 & 66 & 56 & 80 & 72 & 64 & 64 & 96 & 58 & 66 \\ \text { Female: } & 64 & 84 & 82 & 70 & 74 & 86 & 90 & 88 & 90 & 90 & 94 & 68 & 90 & 82 & 80 \end{array}$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.