 # Compute the range and standard deviation of the following 10 test scores. 66 , 75 , 69 , 72 , 84 , 90 , 96 , 70 , 55 , 45 ### 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 4.2P
Textbook Problem
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## Compute the range and standard deviation of the following 10 test scores. 66 , 75 , 69 , 72 , 84 , 90 , 96 , 70 , 55 , 45

Expert Solution
To determine

To find:

The range and standard deviation of the given scores

### Explanation of Solution

The given scores are,

66,75,69,72,84,90,96,70,55,45

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,

45,55,66,69,70,72,75,84,90,96

The highest score is 96 and the lowest score is 45.

The range is given by,

Range=High ScoreLow score

Substitute 96 for high score and 45 for low score in the above mentioned formula,

Range=9645=51

The size of the population is 10.

The mean is given by,

X¯=i=1NXiN

Substitute 10 for N, 66 for X1, 75 for X2 and so on in the above mentioned formula of mean.

X¯=66+75+69+72+84+90+96+70+55+4510=72210=72.2 ……(1)

Consider the following table of sum of squares,

 Scores (Xi) (Xi−X¯) (Xi−X¯)2 66 −6.2 38.44 75 2.8 7.84 69 −3.2 10.24 72 −0.2 0.04 84 11.8 139.24 90 17.8 316.84 96 23.8 566.44 70 −2.2 4.84 55 −17.2 295.84 45 −27.2 739.84 ∑(Xi−X¯)=0 ∑(Xi−X¯)2=2119

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