/*! 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 1 \(\\{15,9,23,8,42,6,35,8\\}\) ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 1

\(\\{15,9,23,8,42,6,35,8\\}\) What is the arithmetic mean (average) of the data set?

Short Answer

Expert verified
Answer: The arithmetic mean of the data set is 18.25.

Step by step solution

01

Add up all the values

First, we need to find the sum of all the values in the data set. We can do this by adding each number together: \(15 + 9 + 23 + 8 + 42 + 6 + 35 + 8 = 146\)
02

Count the number of values

Next, we need to determine how many values there are in the data set. In this case, there are 8 values: \(\\{15, 9, 23, 8, 42, 6, 35, 8\\}\).
03

Divide the sum by the number of values

To find the arithmetic mean, we will now divide the sum from step 1 by the total number of values from step 2: \(\text{Mean} = \frac{\text{Sum}}{\text{Number of values}} = \frac{146}{8} = 18.25\) The arithmetic mean (average) of the data set is 18.25.

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
Calculating the mean, often referred to as the "average," is a fundamental concept in statistics. It involves finding the central value of a set of numbers.
To calculate the mean, you perform the following steps:
  • First, add all the numbers together to get the total sum.
  • Then, count how many numbers are in the set. This count gives you the divisor.
  • Finally, divide the sum by this count to get the mean.
For example, consider the data set \(\{15, 9, 23, 8, 42, 6, 35, 8\}\).
Add the numbers: \(15 + 9 + 23 + 8 + 42 + 6 + 35 + 8 = 146\).
Count the numbers, which is 8 in this set.
Then, divide the sum by 8: \(\frac{146}{8} = 18.25\).
The mean of the set is 18.25, representing the average value of all numbers combined.
Data Set Analysis
Analyzing a data set is essential to understand the information it holds. A data set is simply a collection of numbers, each representing a piece of information.
When analyzing a data set, like \(\{15, 9, 23, 8, 42, 6, 35, 8\}\), consider the following steps:
  • Identify any patterns or trends. For instance, notice repeated numbers like 8.
  • Determine the range by subtracting the smallest value from the largest value, in this case, \(42 - 6 = 36\).
  • Categorize the numbers if in context, such as grouping by size or frequency.
By performing data set analysis, you can make deductions about trends, variability, and the overall spread of your data, providing deeper insights beyond just mean calculation.
Average in Statistics
The term "average" is used in statistics to describe the central point of a data set, usually referring to the arithmetic mean. It provides a quick summary of the entire dataset.
The mean, which was calculated as 18.25 in our example, is one of the most common types of averages.
There are other forms of averages, including the median and mode.
  • The median is the middle number in a sorted data set.
  • The mode is the number that appears most frequently in the set.
Understanding averages helps to compare different datasets and observe general tendencies in statistical data. Each type of average gives unique insights, highlighting different aspects of the data set's structure.

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

In a study of 100 children, the children were asked to choose among three types of toy: a doll, a toy car, or a stuffed animal. Use the probability model below to determine the probability of a child choosing either a stuffed animal or a doll. $$ \begin{array}{|c|c|c|} \hline \text { Type of Toy } & \text { Number of Children } & \text { Probability } \\ \hline \text { doll } & 33 & \\ \hline \text { toy car } & 26 & \\ \hline \text { stuffed animal } & 41 & \\ \hline \text { total } & \mathbf{1 0 0} & \mathbf{1} \\ \hline \end{array} $$

The host of the popular podcast Trivial asked listeners to call in and vote for their favorite podcast. Of the callers, \(78 \%\) said Trivial is their favorite podcast. What type of bias is present in this survey?

$$ \begin{array}{|c|c|c|c|c|c|} \hline \text { Student } & \text { Test } 1 & \text { Test } 2 & \text { Test } 3 & \text { Test } 4 & \text { Test } 5 \\ \hline \text { Bradley } & 85 & 87 & 91 & 89 & 92 \\ \hline \text { Audree } & 96 & 73 & 86 & 90 & 75 \\ \hline \end{array} $$ What is Audree's average test score?

How many possible groups of three people can be formed from a class of 20 people?

There is a \(72 \%\) probability of snow on Tuesday. What is the percent probability that it will not snow on Tuesday?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

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.