/*! 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 43 For each set of data in Exercise... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 43

For each set of data in Exercises 2.43 to 2.46: (a) Find the mean \(\bar{x}\). (b) Find the median \(m\). (c) Indicate whether there appear to be any outliers. If so, what are they? \(\begin{array}{lllll}& 8, & 12, & 3, & 18 & 15\end{array}\)

Short Answer

Expert verified
The mean \(\bar{x}\) is 11.2, the median \(m\) is 12, and there is one outlier, which is 3.

Step by step solution

01

Calculate the Mean

To calculate the mean \(\bar{x}\), add up all the values and divide by the number of values. Hence, \(\bar{x} = \frac{8+12+3+18+15}{5} = 11.2\)
02

Calculate the Median

To find the median, first order the values in ascending order. Then, select the middle value. Here, the ordered values are: 3, 8, 12, 15, 18. The median (m) is the middle value, which is 12.
03

Identify Potential Outliers

To find outliers, we need to ascertain if any values are significantly different than the others. In this data set, 3 appears to be significantly lower than the others. Thus, 3 is deemed an outlier.

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 of a data set is simply the average of all the values. It provides a central or typical value of the data. To calculate the mean, you add up all the numbers in the set, and then divide that total by the count of numbers in the set. This process can be thought of as distributing the total sum equally among all values.

For instance, if you have the numbers 8, 12, 3, 18, and 15, start by adding them together to get 56. Then, count the numbers, which is 5 in this case. Next, divide 56 by 5, resulting in a mean value of 11.2. This number represents the average of the data set.
  • Add: 8 + 12 + 3 + 18 + 15 = 56
  • Count: 5 numbers
  • Divide: 56 梅 5 = 11.2
Median Determination
The median offers a measure of the "middle" value within a data set. It is especially useful in reflecting the central tendency when data is skewed or contains outliers. Finding the median involves rearranging all values in ascending order and selecting the one in the middle.

For the data set 8, 12, 3, 18, and 15, start by ordering the numbers: 3, 8, 12, 15, 18. Since there are five data points, the median will be the third number after ordering, which is 12. If there was an even number of points, you would take the average of the two central numbers.
  • Order: 3, 8, 12, 15, 18
  • Select Middle: 12
Outlier Identification
Outliers are values that appear significantly different from others in a data set. They can skew results and provide misleading insights if not handled properly. Identifying outliers typically involves looking for numbers that are much higher or lower than the rest of the data.

In the data set 8, 12, 3, 18, and 15, the value 3 might be considered an outlier because it is noticeably lower than the others. To systematically determine outliers, statistical tests or calculation of data points falling outside 1.5 times the interquartile range (IQR) from the quartiles may be used. However, visually or intuitively identifying them can also work for small data sets.
  • Value Analyzed: 3
  • Outlier Conclusion: 3 is significantly lower than other values

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 and interpret the \(z\) -score for the data value given. The value 88 in a dataset with mean 96 and standard deviation 10

Sketch a curve showing a distribution that is symmetric and bell-shaped and has approximately the given mean and standard deviation. In each case, draw the curve on a horizontal axis with scale 0 to 10 . Mean 5 and standard deviation 0.5

In Exercises 2.11 and 2.12, cases are classified according to one variable, with categories \(\mathrm{A}\) and \(\mathrm{B},\) and also classified according to a second variable with categories \(1,2,\) and 3 . The cases are shown, with the first digit indicating the value of the first variable and the second digit indicating the value of the second variable. (So "A1" represents a case in category \(\mathrm{A}\) for the first variable and category 1 for the second variable.) Construct a two-way table of the data. Twenty cases: \(\begin{array}{llllllllll}\mathrm{A} 1 & \mathrm{~A} 1 & \mathrm{~A} 1 & \mathrm{~A} 2 & \mathrm{~A} 3 & \mathrm{~A} 3 & \mathrm{~A} 3 & \mathrm{~A} 3 & \mathrm{~A} 3 & \mathrm{~A} 3 \\ \mathrm{~A} 3 & \mathrm{~A} 3 & \mathrm{~B} 1 & \mathrm{~B} 1 & \mathrm{~B} 1 & \mathrm{~B} 1 & \mathrm{~B} 2 & \mathrm{~B} 2 & \mathrm{~B} 2 & \mathrm{~B} 3\end{array}\)

What's Wrong with the Statement? A researcher claims to have evidence of a strong positive correlation \((r=0.88)\) between a person's blood alcohol content \((\mathrm{BAC})\) and the type of \(\mathrm{alco-}\) holic drink consumed (beer, wine, or hard liquor). Explain, statistically, why this claim makes no sense.

Each describe a sample. The information given includes the five number summary, the sample size, and the largest and smallest data values in the tails of the distribution. In each case: (a) Clearly identify any outliers. (b) Draw a boxplot. Five number summary: (15,42,52,56,71)\(;\) \(n=120\) Tails: \(15,20,28,30,31, \ldots, 64,65,65,66,71\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Decision Maths

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.