Math

StatisticsEssentials Of StatisticsSOC As the head of a social services agency, you believe that your staff of 20 social workers is very much overworked compared with 10 years ago. The case loads for each worker are reported below for each of the two years in question. Has the average caseload increased? Which measure of central tendency is most appropriate to answer this question? Why? 2002 2012 52 55 42 82 50 49 75 50 57 50 69 52 49 52 65 50 45 59 58 55 65 60 64 65 60 65 69 60 55 68 60 60 42 60 50 60 50 42 60 60BuyFind*arrow_forward*

4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 3, Problem 3.10P

Textbook Problem

*SOC**As the head of a social services agency, you believe that your staff of 20 social workers is very much overworked compared with 10 years ago. The case loads for each worker are reported below for each of the two years in question. Has the average caseload increased? Which measure of central tendency is most appropriate to answer this question? Why?*

2002 | 2012 | ||

52 | 55 | 42 | 82 |

50 | 49 | 75 | 50 |

57 | 50 | 69 | 52 |

49 | 52 | 65 | 50 |

45 | 59 | 58 | 55 |

65 | 60 | 64 | 65 |

60 | 65 | 69 | 60 |

55 | 68 | 60 | 60 |

42 | 60 | 50 | 60 |

50 | 42 | 60 | 60 |

Expert Solution

To determine

**To find:**

The most appropriate measures of central tendency for each variable.

**Description:**

When the variables measured have non-numerical scores or categories, they are said to have a nominal level of measurement.

When the variables measured have non-numerical scores or categories that could be ranked from high to low, they are said to have an ordinal level of measurement.

When the variables measured have numerical scores and can be used for further statistical analysis, they are said to have an interval ratio level of measurement.

From the given information, the variable **Caseload** has a numeric value; therefore, the level of measurement of this variable is interval-ratio.

**Choosing a Measures of Central Tendency:**

When the data is Nominal type — Mode

When the data is Ordinal type — Median

When the data is Interval ratio type — Mean

For the variable **Case load, the measure of central tendency is: Mean.**

**Formula Used:**

The formula to calculate mean is given by,

**For year 2002:**

Substitute 20 for

Essentials Of Statistics

Show all chapter solutions

Ch. 3 - SOCA variety of information has been gathered from...Ch. 3 - A variety of information has been collected for...Ch. 3 - You have been observing the local Democratic Party...Ch. 3 - The following table presents the annual...Ch. 3 - SOC Data have been gathered on four variables for...Ch. 3 - SOC The following tables list the median family...Ch. 3 - Find the appropriate measure of central tendency...Ch. 3 - SOC The accompanying table gives scores on four...Ch. 3 - SOC The college administration is considering a...Ch. 3 - SOC As the head of a social services agency, you...

Find more solutions based on key concepts

Show solutions For the following set of scores, find the value of each expression: a. X b. (X)2 c. X2 d. (X +3)

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Use a calculator to evaluate the line integral correct to four decimal places. 23. C F dr, where F(x,y)=x+yi+(...

Multivariable Calculus

(a) Show that f(x) = x + ex is one-to-one. (b) What is the value of f1(1)? (c) Use the formula from Exercise 77...

Single Variable Calculus: Early Transcendentals, Volume I

Rationalize Numerator Rationalize the numerator. 94. xx+hhxx+h

Precalculus: Mathematics for Calculus (Standalone Book)

In Exercises 1-6, simplify the expression. 5(1)26(1)+9

Calculus: An Applied Approach (MindTap Course List)

Prove, without graphing, that the graph of the function has at least two x-intercepts in the specified interval...

Calculus: Early Transcendentals

Testing for Symmetry In Exercises 29-40, test for symmetry with respect to each axis and to the origin. y=x54x2

Calculus: Early Transcendental Functions

Solve the equations in Exercises 112 for x (mentally, if possible). 7x+55=98

Finite Mathematics and Applied Calculus (MindTap Course List)

Let a=log2,b=log3, and c=log7. In Exercises 2946, use the logarithm identities to express the given quantity in...

Applied Calculus

13. A normal distribution has a mean .of µ=30 and a standard deviation of =12.For each ,of the following core i...

Statistics for The Behavioral Sciences (MindTap Course List)

4548 Find the foci and vertices and sketch the graph. 6y2+x36y+55=0

Calculus (MindTap Course List)

One of the assumptions underlying the theory of control charting (see Chapter 16) is that successive plotted po...

Probability and Statistics for Engineering and the Sciences

Ecology: Wetlands Government agencies carefully monitor water quality and its effect on wetlands (Reference: En...

Understanding Basic Statistics

Keeping with the Traffic Flow By driving at a speed to match the prevailing traffic speed, you decrease the cha...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Rewrite by completing the square. (a) x2 + x + 1 (b) 2x2 12x + 11

Single Variable Calculus

For Problems 51-78, simplify each of the numerical expressions. Objective 3 (3421)(5267)

Intermediate Algebra

By any method, determine all possible real solutions of each equation in Exercises 1330. Check your answers by ...

Finite Mathematics

Use the method of Example 4 to find the equation of the line that describes all points equidistant from the poi...

Elementary Geometry For College Students, 7e

Change 3.2 km to m.

Elementary Technical Mathematics

Loan Payment Time Nominal Kate Present Value Payment Frequency Period (years) (%) (Amount of Loan) 19. $3,756.6...

Contemporary Mathematics for Business & Consumers

Use the recursive definition for Fibonacci numbers and deductive reasoning to verify that, for Fibonacci number...

Mathematical Excursions (MindTap Course List)

Let z1=2+3i, z2=23i, and z3=4+5i, and find z1z2

Trigonometry (MindTap Course List)

In Exercises 1- 9, let be the given group. Write out the elements of a group of permutations that is isomorphi...

Elements Of Modern Algebra

55. Course grades To earn an A in a course, a student must get at least a 90 average on four tests and a final ...

Mathematical Applications for the Management, Life, and Social Sciences

Evaluate the integral. 15. 0ax2a2x2dx

Single Variable Calculus: Early Transcendentals

In Exercise 5 and 6, find X2 the probability distribution of the system after two observations for the distribu...

Finite Mathematics for the Managerial, Life, and Social Sciences

Conjecture Use Newtons Law of Universal Gravitation to make a conjecture about what happens to the force of att...

Calculus of a Single Variable

Work In Exercises 25-28, use Greens Theorem to calculate the work done by the force F on a particle that is mov...

Calculus: Early Transcendental Functions (MindTap Course List)

Refer to Exercise 6.116, but now suppose that two viewers are randomly selected (without replacement). Let R1 a...

Introduction To Statistics And Data Analysis

The fourth term of {an} defined by a1 = 3, and for n = 1, 2, 3, … is:

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercises 33 to 38, use algebra to find the point of intersection of the two lines whose equations are provi...

Elementary Geometry for College Students

The graph of x = 2 + 3t, y = 4 − t is a:
circle
ellipse
line
parabola

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Repeat exercise 11 for the acceptance sampling plan with n = 20 and c = 1. What pens to the producers risk as t...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

A social science researcher would like to determine the characteristics of people who live and work in small to...

Research Methods for the Behavioral Sciences (MindTap Course List)

Each of the following research studies uses a survey as a method for collecting data. However, not all of the s...

Research Methods for the Behavioral Sciences (MindTap Course List)

Nielsen Research provides weekly ratings of nationally broadcast television programs. The ratings of the 84 pri...

Statistics for Business & Economics, Revised (MindTap Course List)

Think About It The price P (in dollars) of q used car is a function of its initial cost C (in dollars) and its ...

Multivariable Calculus

Investigation Determine the value of c such that the work done by the force field F(x,y)=15[ (4x2y)ixyj ] on an...

Calculus (MindTap Course List)

Add the terms in the following expressions. 2.06gh3+(0.85gh3)

Mathematics For Machine Technology

Let N = the set of natural numbers. W = the set of whole number Z = the set of integers Q = the set of rational...

College Algebra (MindTap Course List)

Cincinnati, Ohio, also known as the Queen City, has a population of approximately 298,000 and is the third larg...

Essentials Of Statistics For Business & Economics

40. The prior probabilities for events A1, A2, and A3 are P(A1) = .20, P(A2) = .50, and P(A3) = .30. The condit...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

62. Two coins are tossed. Using ordered pairs, give the following. a. The sample space. b. The event E that exa...

Mathematics: A Practical Odyssey

For each of 5-21 prove each statement that I true and find a counterexample for each statement that is false. A...

Discrete Mathematics With Applications

Reminder Round all answers to two decimal places unless otherwise indicated. Wages A worker is reviewing his pa...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

The right-circular conical tank shown in Figure 1.3.13 loses water out of a circular hole at its bottom. Determ...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Use the following information to answer the next two exercises. An experiment is conducted to show that blood p...

Introductory Statistics

Finding an Equation of a Line: In Exercises 113-116, use a determinant to find an equation of the line passing ...

College Algebra