# Chapter 2, Problem 1TP

### Statistics for People Who (Think T...

5th Edition
Neil J. Salkind
ISBN: 9781452277714

Chapter
Section

### Statistics for People Who (Think T...

5th Edition
Neil J. Salkind
ISBN: 9781452277714
To determine

The mean, median and mode for the given data.

The mean of the given data is 28.375, the median is 25.5 and the mode is 23.

Explanation

Given info:

The below table shows the set of 40 reading scores.

 31 32 43 42 24 34 25 44 23 43 24 36 25 41 23 28 14 21 24 17 25 23 44 21 13 26 23 32 12 26 14 42 14 31 52 12 23 42 32 34

Calculation:

The formula for mean is given below:

Mean=1nXnn

140Xn=31+24+23+...+42+12+34=1,135

Substitute 1,135 for 140Xn and 40 for n in the above equation as follows:

Mean=1,13540=28.375

Thus, the mean of the given data is 28.375.

Arrange the given data in ascending order, to find the median of the given data.

 S. No Values S. No Values S. No Values S. No Values 1 12 11 23 21 26 31 36 2 12 12 23 22 26 32 41 3 13 13 23 23 28 33 42 4 14 14 23 24 31 34 42 5 14 15 24 25 31 35 42 6 14 16 24 26 32 36 43 7 17 17 24 27 32 37 43 8 21 18 25 28 32 38 44 9 21 19 25 29 34 39 44 10 23 20 25 30 34 40 52

The total number of terms is 40, which is an even number.

The formula for median when n is even is given below:

Median=n2thterm+(n2+1)thterm2

Substitute 40 for n in the above equation as follows:

Median=402thterm+(402+1)thterm2=20thterm+(20+1)thterm2=20thterm+21stterm2

The 20th term is 25 and 21st term is 26 when the data is arranged in the ascending order.

Substitute 25 for 20thterm and 26 for 21stterm in the above equation as follows:

Median=25+262=512=25.5

Thus, the median of the given data is 25.5.

Mode:

The value in data set which occurs maximum times is called mode.

The frequency of the data is tabulated below:

 Value Frequency Value Frequency 12 2 31 2 13 1 32 3 14 3 34 2 17 1 36 1 21 2 41 1 23 5 42 3 24 3 43 2 25 3 44 2 26 2 52 1 28 1 - -

From the above table, it is noticed that the highest frequency is 5 for 23.

Thus, the mode of the given data is 23.

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