 # Compute the range and standard deviation of the following 10 scores. (HINT: It will be helpful to organize your computations as in Table 4.4.) 10, 12, 15, 20, 25, 30, 32, 35, 40, 50 ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836 ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

#### Solutions

Chapter
Section
Chapter 4, Problem 4.1P
Textbook Problem
519 views

## Compute the range and standard deviation of the following 10 scores. (HINT: It will be helpful to organize your computations as in Table 4.4.)10, 12, 15, 20, 25, 30, 32, 35, 40, 50

Expert Solution
To determine

To find:

The range and standard deviation of the given scores

Solution:

The range and standard deviation of the given scores is 40 and 12.28 respectively.

### Explanation of Solution

The given scores are,

10,12,15,20,25,30,32,35,40,50

Formula used:

The formula to calculate the range is,

Range=High ScoreLow score

Let the data values be Xi’s.

The formula to calculate the mean is,

X¯=i=1NXiN

The formula to calculate the standard deviation is,

s=(XiX¯)2N

Where, N is the population size.

Calculation:

Arrange the given data in increasing order.

The data in increasing order is given by,

10,12,15,20,25,30,32,35,40,50

The highest score is 50 and the lowest score is 10.

The range is given by,

Range=High ScoreLow score

Substitute 50 for high score and 10 for low score in the above mentioned formula,

Range=5010=40

The range of population is 40.

The size of the population is 10.

The mean is given by,

X¯=i=1NXiN

Substitute 10 for N, 10 for X1, 12 for X2 and so on in the above mentioned formula,

X¯=10+12+15+20+25+30+32+35+40+5010=26910=26.9 ……(1)

Consider the following table of sum of squares,

 Scores (Xi) (Xi−X¯) (Xi−X¯)2 10 −16.9 285.61 12 −14.9 222.01 15 −11.9 141.61 20 −6.9 47.61 25 −1.9 3.61 30 3.1 9.61 32 5.1 26.01 35 8.1 65.61 40 13.1 171.61 50 23.1 533.61 ∑(Xi−X¯)=0 ∑(Xi−X¯)2=1506.9

From equation (1), substitute 10 for X1 and 26.9 for X¯ in (X1X¯).

(X1X¯)=(1026.9)(X1X¯)=16.9

Square both sides of the equation.

(X1X¯)2=(16.9)2(X1X¯)2=285.61

Proceed in the same manner to calculate (XiX¯)2 for all the 1iN for the rest of the values and refer table for the rest of the (XiX¯)2 values calculated. Then the value of (XiX¯)2 is calculated as,

(XiX¯)2=285.61+222.01+..................+171.61+533.61=1506.9 ……(2)

The formula to calculate the standard deviation is given by,

s=(XiX¯)2N

From equation (2), substitute 1506.9 for (XiX¯)2 and 10 for N in the above mentioned formula,

s=1506.910=150.6912.28

Thus, range is 40 and standard deviation is 12.28.

Conclusion:

Therefore, the range and standard deviation of the given scores is 40 and 12.28 respectively.

### Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Get Solutions

### Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Get Solutions

Find more solutions based on key concepts
Show solutions
Convert the expressions in Exercises 8596 radical form. x1/3y3/2

Finite Mathematics and Applied Calculus (MindTap Course List)

Evaluate the indefinite integral. x1+x4dx

Single Variable Calculus: Early Transcendentals, Volume I

Use the definition of the derivative to find the slope of the tangent line to the graph of the function f(x) = ...

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

.

Mathematical Applications for the Management, Life, and Social Sciences

Sketch the curve and find the area that it encloses. 12. r = 2 cos

Single Variable Calculus: Early Transcendentals

True or False: The function whose graph is given at the right is a probability density function.

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

0 1 π It does not exist.

Study Guide for Stewart's Multivariable Calculus, 8th

Define a construct and explain the role that constructs play in theories.

Research Methods for the Behavioral Sciences (MindTap Course List)

The Condé Nast Traveler Gold List provides ratings for the top 20 small cruise ships. The following data shown ...

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

The Shroud of Turin, which shows the negative image of the body of a man who appears to have been crucified, is...

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

Reminder Round all answers to two decimal places unless otherwise indicated. An Investment You have invested mo...

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