Statistics for People Who (Think They) Hate Statistics
Statistics for People Who (Think They) Hate Statistics
6th Edition
ISBN: 9781506333830
Author: Neil J. Salkind
Publisher: SAGE Publications, Inc
Question
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Chapter 4, Problem 1TP

1

To determine

To construct: The frequency distribution and histogram for a data of set of 50 comprehension score.

1

Expert Solution
Check Mark

Answer to Problem 1TP

The frequency distribution of given table is

Class-interval Class Boundaries Width Frequency Cumulative Frequency
2-11 1.5-11.5 9 5 5
12-21 11.5-21.5 9 9 14
22-31 21.5-31.5 9 8 22
32-41 31.5-41.5 9 5 27
42-51 41.5-51.5 9 12 39
52-61 51.5-61.5 9 11 50
Total     50 157

The sketch of histogram is,

Statistics for People Who (Think They) Hate Statistics, Chapter 4, Problem 1TP , additional homework tip  1

Explanation of Solution

Given info:

The data shows the comprehension of 50 scores

12 22 54 43 56
15 26 55 31 57
11 27 51 12 59
16 36 56 14 54
21 34 53 15 56
25 33 57 16 43
21 38 49 22 44
8 42 45 29 41
6 44 45 29 42
2 47 47 54 7

Calculation:

The class boundaries for any class are given by:

Upperclassboundary=Upperclasslimit+d2Lowerclassboundary=Lowerclasslimitd2

Where d is the gap between the upper limit of any class and the lower limit of the succeeding class.

The grouped frequency distribution is as follows:

Class-interval Class Boundaries Frequency
2-11 1.5-11.5 5
12-21 11.5-21.5 9
22-31 21.5-31.5 8
32-41 31.5-41.5 5
42-51 41.5-51.5 12
52-62 51.5-61.5 11

The histogram is a graph that displays the data by using contiguous vertical bars of various heights to represent the frequencies of the classes.

Upper Bound Frequency
11.5 5
21.5 9
31.5 8
41.5 5
51.5 12
61.5 11

Construction steps for a histogram:

  • Press [Ctrl]-N for a new workbook.
  • Enter the data in column A, one number per cell.
  • Enter the upper boundaries into column B.
  • From the toolbar, select the Data tab, then select Data Analysis.
  • In Data Analysis, select Histogram and click [OK].
  • In the Histogram dialog box, select relative column in the Input Range box and select upper limit column in the Bin Range box.
  • Select New Worksheet Ply and Chart Output. Click [OK].

The screen will show the histogram as shown below.

Statistics for People Who (Think They) Hate Statistics, Chapter 4, Problem 1TP , additional homework tip  2

2

To determine

To explain: The selection of class interval for frequency distribution table.

2

Expert Solution
Check Mark

Answer to Problem 1TP

The class width is 9 then the class interval is 1.5-11.5, 11.5-21.5 and so on upto 7 class interval.

Explanation of Solution

Step for constructing class intervals

  • The largest value is 59 and the smallest value is 2.

    Range=largestvaluesmallestvalue=59-2=57

  • Let the class interval is 7.

    Classwidth=Rangeclassinterval=577=8.14[Roundingup]=9

  • Let the starting point be 1.5.
  • Now, the 1st class interval has lower limit 1.5 and upper limit is 11.5 because the class width is 9 and for 2nd class interval the lower limit is the upper limit of 1st class interval after adding class width then get the upper limit of 2nd class interval.
  • After adding 7 times the class width in preceding upper limit of class interval to get the 7 class interval that are constructed.

3.

To determine

To explain: The skewness of the distribution.

3.

Expert Solution
Check Mark

Answer to Problem 1TP

The distribution of 50 score comprehension is almost negatively skewed.

Explanation of Solution

If the most of the data is on the right with few smaller values showing up on the left side of the histogram then data are positively skewed and if most of the data is on the left with few smaller values showing up on the right side of the histogram then data are negatively skewed.

Here the distribution of the 50 score comprehensions on the histogram has more fluctuation from both the side.

Hence, on resulting the data are negatively skewed.

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