/*! 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 13 The following data represent the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 13

The following data represent the miles per gallon for a 2013 Ford Fusion for six randomly selected vehicles. Compute the mean, median, and mode miles per gallon. $$34.0,33.2,37.0,29.4,23.6,25.9$$

Short Answer

Expert verified
Mean = 30.52, Median = 31.3, and No Mode.

Step by step solution

01

- Arrange Data

First, arrange the data in ascending order: 23.6, 25.9, 29.4, 33.2, 34.0, 37.0
02

- Compute the Mean

To find the mean, sum all the data points and then divide by the number of data points. Sum: \[23.6 + 25.9 + 29.4 + 33.2 + 34.0 + 37.0 = 183.1\]Number of data points: 6 Mean: \[\frac{183.1}{6} = 30.5167 \approx 30.52\]
03

- Compute the Median

Since there is an even number of data points, the median is the average of the two middle numbers in the ordered list. Middle values: 29.4 and 33.2Median: \[\frac{29.4 + 33.2}{2} = 31.3\]
04

- Compute the Mode

The mode is the number that appears most frequently. Here, each number appears only once.Hence, there is no mode.

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 called the average, is a measure of central tendency. It tells us about the overall level of the data. Calculating the mean involves adding all the values together and dividing by the number of values.

To find the mean for the provided data set: 34.0, 33.2, 37.0, 29.4, 23.6, and 25.9, follow these steps:
  • First, add all data values: \(23.6 + 25.9 + 29.4 + 33.2 + 34.0 + 37.0 = 183.1\).
  • Next, divide the sum by the number of data values: \[ \frac{183.1}{6} \approx 30.52 \].

The mean for this set of miles per gallon is approximately 30.52.
Median Calculation
The median is the middle value in an ordered list of numbers and it provides a different measure of central tendency. It separates the higher half from the lower half of your data set.

To find the median:
  • First, arrange your data in ascending order: 23.6, 25.9, 29.4, 33.2, 34.0, 37.0.
  • Next, if you have an odd number of data points, the median is the middle number. However, because there are six data points (an even number), we find the middle two numbers: 29.4 and 33.2.
  • Finally, take the average of these two middle numbers: \[ \frac{29.4 + 33.2}{2} = 31.3 \].

Thus, the median of the data set is 31.3 miles per gallon.
Mode Determination
The mode is the value that appears most frequently in a data set. It can give insight into the most common value.

Determining the mode is straightforward:
  • Look at the frequency of each number in the data set.

For the given data set: 23.6, 25.9, 29.4, 33.2, 34.0, 37.0, every number appears only once and no number repeats.

Hence, we can say that this data set has no mode.

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

True or False: When comparing two populations, the larger the standard deviation, the more dispersion the distribution has. provided that the variable of interest from the two populations has the same unit of measure.

A random sample of 25 college students was asked, "How many hours per week typically do you work outside the home?" Their responses were as follows: $$ \begin{array}{rrrrr} \hline 0 & 0 & 15 & 20 & 30 \\ \hline 40 & 30 & 20 & 35 & 35 \\ \hline 28 & 15 & 20 & 25 & 25 \\ \hline 30 & 5 & 0 & 30 & 24 \\ \hline 28 & 30 & 35 & 15 & 15 \\ \hline \end{array} $$ Determine the shape of the distribution of hours worked by drawing a frequency histogram. Find the mean and median. Which measure of central tendency better describes hours worked?

Find the population variance and standard deviation or the sample variance and standard deviation as indicated. $$ \text { Sample: } 83,65,91,87,84 $$

A certain type of concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The strength of concrete is measured by pouring the mix into casting cylinders after it is allowed to set up for 28 days. The following data represent the strength of nine randomly selected casts. Compute the range and sample standard deviation for the strength of the concrete (in psi). $$ 3960,4090,3200,3100,2940,3830,4090,4040,3780 $$

The following data represent the hemoglobin (in \(\mathrm{g} / \mathrm{dL}\) ) for 20 randomly selected cats. $$ \begin{array}{lllll} \hline 5.7 & 8.9 & 9.6 & 10.6 & 11.7 \\ \hline 7.7 & 9.4 & 9.9 & 10.7 & 12.9 \\ \hline 7.8 & 9.5 & 10.0 & 11.0 & 13.0 \\ \hline 8.7 & 9.6 & 10.3 & 11.2 & 13.4 \\ \hline \end{array} $$ (a) Compute the \(z\) -score corresponding to the hemoglobin of Blackie, \(7.8 \mathrm{~g} / \mathrm{dL}\). Interpret this result. (b) Determine the quartiles. (c) Compute and interpret the interquartile range, IQR. (d) Determine the lower and upper fences. Are there any outliers?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

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.