Explanation Definition: 1. If a data set contains n data values, the mean of the data set is μ = ∑ x n . This represents the mean of the whole population. 2. The standard deviation of population of sample of n data values is given by σ = ∑ ( x − μ ) 2 n . 3. For a set of data with mean x ¯ and standard deviation s , we define the coefficient of variation, denoted by CV , as C V = s x ¯ ⋅ 100 % . Calculation: Begin by determining the population standard deviation for the Coffee prices. From the given table understand each data value. X 4.74 4.91 4.83 4.99 4.72 4.69 4.79 4.81 4.67 4.61 4.41 4.49 First find the mean of the given data set. To compute the mean, let us find the sum of given data values. The sum is 4.74 + 4.91 + 4.83 + 4.99 + 4.72 + 4.69 + 4.79 + 4.81 + 4.67 + 4.61 + 4.41 + 4.49 = 56.66. Therefore, ∑ x = 56.66. There are 12 data values. Therefore, n = 12. The mean is then ∑ x n = 56.66 12 = 4.72166666666667. Next find the population standard deviation. To begin with, find the deviation from the mean for each value. For x = 4.74 the deviation from the mean is 0.01833333333333. For x = 4.91 the deviation from the mean is 0.18833333333333. For x = 4.83 the deviation from the mean is 0.10833333333333. For x = 4.99 the deviation from the mean is 0.26833333333333. For x = 4.72 the deviation from the mean is − 0.00166666666667. For x = 4.69 the deviation from the mean is − 0.03166666666667. For x = 4.79 the deviation from the mean is 0.06833333333333. For x = 4.81 the deviation from the mean is 0.08833333333333. For x = 4.67 the deviation from the mean is − 0.05166666666667. For x = 4.61 the deviation from the mean is − 0.11166666666667. For x = 4.41 the deviation from the mean is − 0.31166666666667. For x = 4.49 the deviation from the mean is − 0.23166666666667. Now, square each of the deviation value. For x = 4.74 , ( 0.01833333333333 ) 2 = 0.00033611111111111900. For x = 4.91 , ( 0.18833333333333 ) 2 = 0.03546944444444450000. For x = 4.83 , ( 0.10833333333333 ) 2 = 0.01173611111111110000. For x = 4.99 , ( 0.26833333333333 ) 2 = 0.07200277777777790000. For x = 4.72 , ( − 0.00166666666667 ) 2 = 0.00000277777777777865. For x = 4.69 , ( − 0.03166666666667 ) 2 = 0.00100277777777775000. For x = 4.79 , ( 0.06833333333333 ) 2 = 0.00466944444444445000. For x = 4.81 , ( 0.08833333333333 ) 2 = 0.00780277777777771000. For x = 4.67 , ( − 0.05166666666667 ) 2 = 0.00266944444444445000. For x = 4.61 , ( − 0.11166666666667 ) 2 = 0.01246944444444440000. For x = 4.41 , ( − 0.31166666666667 ) 2 = 0.09713611111111100000. For x = 4.49 , ( − 0.23166666666667 ) 2 = 0.05366944444444440000. Note that each value appears only once. So, their frequency is 1. Hence, the product of the square and the frequency will be same as the square. The sum of these values is 0.29896666666666600000. The population standard deviation is therefore given as follows: σ = ∑ ( x − μ ) 2 n = 0.29896666666666600000 12 = 0.02491388888888890000. Taking square root gives, μ = 0

6th Edition

ISBN: 9780134434681

Author: Tom Pirnot

Publisher: PEARSON

See similar textbooks

Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

Videos

Question

Chapter 14.3, Problem 36E

To determine

To find:

The population standard deviation of each data set given by the following table:

2015 Coffee Prices ($/lb) Gasoline Prices ($/gal)

Jan 4.74 2.11

Feb 4.91 2.25

Mar 4.83 2.48

Apr 4.99 2.49

May 4.72 2.78

Jun 4.69 2.83

Jul 4.79 2.83

Aug 4.81 2.68

Sept 4.67 2.39

Oct 4.61 2.29

Nov 4.41 2.19

Dec 4.49 2.06

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.3, Problem 35E

Chapter 14.3, Problem 37E

Students have asked these similar questions

Help me please

A real estate agent has developed a linear model for the price of a house, P, in dollars in terms of the area, A, in square feet for the homes in a certain neighborhood. The data set had areas ranging from 1,000 square feet to 4,500 square feet. Would predicting the prices of a home that is 4,900 square feet be interpolation or extrapolation? Explain. Using the model to predict the price of a 4,900 square foot home is extrapolation because 4,900 square feet is outside the range of the areas in the data. Using the model to predict the price of a 4,900 square foot home is interpolation because 4,900 square feet is inside the range of the areas in the data. Using the model to predict the price of a 4,900 square foot home is extrapolation because 4,900 square feet is inside the range of the areas in the data. Using the model to predict the price of a 4,900 square foot home is interpolation because 4,900 square feet is outside the range of the areas in the data.

B - Does there appear to be a relationship between income and sadness, hopelessness, and worthlessness? justify your answer in your own word. points Figure 2. Feelings of Worthlessness. Hopelessness, and Sadness All or Most of the Time, by Income. 2011 Percentage of adults 4.6% 3.8% Less than $35.000 3.2% Sadness 2,3% 1.9% $35.000-49.999 Hopelessness 2.3% 1.5% 1.1% $50,000-74,999 Annual family income Worthlessness 1.3% 0.6% 0.6% $75,000-99,999 1.2% 0.5% 0.6% $100,000 or more

Chapter 14 Solutions

Mathematics All Around (6th Edition)

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

2015	Coffee Prices ($/lb)	Gasoline Prices ($/gal)
Jan	4.74	2.11
Feb	4.91	2.25
Mar	4.83	2.48
Apr	4.99	2.49
May	4.72	2.78
Jun	4.69	2.83
Jul	4.79	2.83
Aug	4.81	2.68
Sept	4.67	2.39
Oct	4.61	2.29
Nov	4.41	2.19
Dec	4.49	2.06

The population standard deviation of each data set given by the following table: 2015 Coffee Prices ($/lb) Gasoline Prices ($/gal) Jan 4.74 2.11 Feb 4.91 2.25 Mar 4.83 2.48 Apr 4.99 2.49 May 4.72 2.78 Jun 4.69 2.83 Jul 4.79 2.83 Aug 4.81 2.68 Sept 4.67 2.39 Oct 4.61 2.29 Nov 4.41 2.19 Dec 4.49 2.06

Solution Summary: The author explains that the prices of Coffee were more stable than those of Gasoline.

Concept explainers

Videos

Want to see the full answer?

Chapter 14 Solutions