/*! 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 65 Which is the greatest, the mean,... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Which is the greatest, the mean, the mode, or the median of the data set? 11; 11; 12; 12; 12; 12; 13; 15; 17; 22; 22; 22

Short Answer

Expert verified
The greatest is the mean, approximately 15.08.

Step by step solution

01

Calculate the Mean

To find the mean, sum up all the numbers in the data set and divide by the total number of values. The total sum is \(11 + 11 + 12 + 12 + 12 + 12 + 13 + 15 + 17 + 22 + 22 + 22 = 181\). There are 12 numbers in the set. Therefore, the mean is \( \frac{181}{12} \approx 15.08 \).
02

Identify the Mode

The mode is the number that appears most frequently in the data set. Here, the number 12 appears 4 times, which is more frequent than any other number. Thus, the mode is 12.
03

Find the Median

To find the median, arrange the numbers in order and identify the middle value(s). Since there are 12 numbers, the median is the average of the 6th and 7th numbers. Counting through the data set, the 6th and 7th numbers are 12 and 13, respectively. So the median is \( \frac{12 + 13}{2} = 12.5 \).
04

Compare Mean, Mode, and Median

Now we compare all the calculated values: the mean is approximately 15.08, the mode is 12, and the median is 12.5. The greatest value among these is the mean, 15.08.

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 91Ó°ÊÓ!

Key Concepts

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

Mean Calculation
The mean is a fundamental concept in mathematics, specifically in the study of statistics. When you calculate the mean, you are essentially finding the average of a set of numbers.

To determine the mean of a data set, follow these steps:
  • Add all the numbers in the data set together to get the total sum.
  • Count the number of values in the data set.
  • Divide the total sum by the number of values.
For instance, in the provided data set: 11, 11, 12, 12, 12, 12, 13, 15, 17, 22, 22, 22, the total sum is 181. Since there are 12 numbers, the mean is calculated as: \[\text{Mean} = \frac{181}{12} \approx 15.08\]This average gives a sense of what is the typical value in our data set, however, it is crucial to remember that the mean can be skewed by extremely high or low values.
Mode Identification
The mode is one of the simplest descriptors of a data set and can offer unique insights, especially when the data set contains repeated values. The mode represents the most frequently occurring value in a data set.

Here's how to identify the mode in a set of numbers:
  • List all numbers in the data set.
  • Count the frequency of each number.
  • The number with the highest frequency is the mode.
In the example data set 11, 11, 12, 12, 12, 12, 13, 15, 17, 22, 22, 22, the number 12 appears four times, more than any other number. Thus, the mode is 12.

This measurement can be particularly useful when analyzing data sets where certain values appear more frequently, hinting at a trend or significant occurrence.
Median Finding
Finding the median involves arranging the data in order and pinpointing the middle value, offering a central point that isn't influenced by extreme values. It is considered a robust measure of central tendency.

To find the median:
  • Arrange the data set in ascending order.
  • If the set has an odd number of observations, the median is the middle number.
  • If the set has an even number, the median is the average of the two central numbers.
In our data set of 11, 11, 12, 12, 12, 12, 13, 15, 17, 22, 22, 22, there are 12 numbers.

The 6th and 7th numbers are 12 and 13, respectively. So, the median is computed as:\[\text{Median} = \frac{12 + 13}{2} = 12.5\]This value effectively bisects the data set, ensuring that half the numbers are less and half are more, providing valuable insight into the distribution of values in the data set.

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

\text… # Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows: $$\begin{array}{|l|l|}\hline \\# \text { of movies } & {\text { Frequency }} \\\ \hline 0 & {5} \\ \hline 1 & {9} \\ \hline 2 & {6} \\ \hline 3 & {4} \\\ \hline 4 & {1} \\ \hline\end{array}$$ a. Find the sample mean \(\overline{x}\) . b. Find the approximate sample standard deviation, s.

Use the following information to answer the next two exercises. X = the number of days per week that 100 clients use a particular exercise facility. $$\begin{array}{|l|l|}\hline x & {\text { Frequency }} \\ \hline 0 & {3} \\\ \hline 1 & {12} \\ \hline 2 & {33} \\ \hline 3 & {28} \\ \hline 4 & {11} \\\ \hline 5 & {9} \\ \hline 6 & {4} \\ \hline\end{array}$$ The \(80^{\text { th }}\) percentile is ____ a. 5 b. 80 c. 3 d. 4

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of a representative sample of 12 of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The 12 change scores are as follows: 3; 8; –1; 2; 0; 5; –3; 1; –1; 6; 5; –2 a. What is the mean change score? b. What is the standard deviation for this population? c. What is the median change score? d. Find the change score that is 2.2 standard deviations below the mean.

For the next three exercises, use the data to construct a line graph. In a survey, 40 people were asked how many times they visited a store before making a major purchase. The results are shown in Table 2.37. $$\begin{array}{|l|l|}\hline \text { Number of times in store } & {\text { Frequency }} \\ \hline 1 & {4} \\ \hline\end{array}$$ $$\begin{array}{|l|l|}\hline \text { Number of times in store } & {\text { Frequency }} \\ \hline 2 & {10} \\ \hline 3 & {16} \\ \hline 4 & {6} \\\ \hline 5 & {4} \\ \hline\end{array}$$

For each of the following data sets, create a stem plot and identify any outliers. The height in feet of 25 trees is shown below (lowest to highest). 25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54

See all solutions

Recommended explanations on Math Textbooks

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.