   Chapter 3, Problem 1P Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912

Solutions

Chapter
Section Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912
Textbook Problem

Find the mean, median, and mode for the following sample of scores: 4, 5, 2, 7, 1, 3, 5

To determine

Find the mean, median and mode for the given sample of scores.

Solution:

Mean=4 Median=4.5 Mode=5

Explanation

Given:

The sample of scores:

5, 4, 5, 2, 7, 1, 3, 5

Here n=8 is even.

Formula used:

M= x n

Median= ( n 2 ) th score+ ( n 2 +1 ) th score 2

Calculations:

To find mean, add all scores and divide the sum by number of scores in the sample.

M= x n = 5+4+5+2+7+1+3+5 8 = 32 8 =4

To find median, first arrange data in ascending order as shown below and then find the middle score.

 1 2 3 4 5 5 5 7

For eight scores, the median would be average of ( n 2 ) th = ( 8 2 ) th = 4 th score and ( n 2 +1 ) th = ( 8 2 +1 ) th = 5 th score of the sorted data.

Median= ( n 2 ) th score+ ( n 2 +1 ) th score 2 = 4 th score+ 5 th score 2 = 4+5 2 =4.5

The mode is most occurred score in the sample. In this sample, 5 occurred most of the times. Therefore:

Mode=5

The mean is the average of scores. To find mean, add all scores and divide the sum by number of scores in the sample.

The median is the middle most score (in case when n is odd) or average of two middle scores (in case when n is even) when data is arranged from the smallest to the largest score.

Case 1:

When n is odd:

Median= ( n+1 2 ) th score

Case 2:

When n is even:

Median= ( n 2 ) th score+ ( n 2 +1 ) th score 2

The mode is most occurred score in the sample. There can be more than one mode.

Conclusion:

Mean=4 Median=4.5 Mode=5

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