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Statistics for People Who (Think T...

5th Edition
Neil J. Salkind
ISBN: 9781452277714

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Chapter
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BuyFindarrow_forward

Statistics for People Who (Think T...

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

The mean, median and mode for the given data.

Answer

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.

31324342
24342544
23432436
25412328
14212417
25234421
13262332
12261442
14315212
23423234

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. NoValuesS. NoValuesS. NoValuesS. NoValues
112112321263136
212122322263241
313132323283342
414142324313442
514152425313542
614162426323643
717172427323743
821182528323844
921192529343944
1023202530344052

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:

ValueFrequencyValueFrequency
122312
131323
143342
171361
212411
235423
243432
253442
262521
281--

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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