
a.
Construct the histogram for body mass of the 50 difference bird species based on the class intervals.
Identify whether transformation of the data is desirable or not.
a.

Answer to Problem 92E
The histogram for body mass of the 50 difference bird species based on the class intervals is given below:
The transformation of the data is desirable.
Explanation of Solution
Calculation:
It is given that the body mass of the 50 different bird species.
Software procedure:
Step-by-step procedure to construct the histogram using the MINITAB software:
- Choose Graph > Histogram.
- Select Simple, and then click OK.
- In Graph variables, enter the corresponding column of Body mass.
- Click OK.
- Double click on x axis and select Binning.
- Choose Cutpoint and enter Number of intervals as 9.
- Enter 5 10 15 20 25 30 40 50 100 500 under Midpoint/Cutpoint positions.
- Click Ok.
From the histogram, it can be observed that most of the data values fall towards the left of the distribution extending the tail towards the right indicating that the distribution of body mass is positively skewed. Thus, for making the data symmetric a transformation is needed.
Hence, the transformation of the data is desirable.
b.
Construct the histogram by transforming the data using logarithms.
Identify whether the log transformation was successful in producing a more symmetric distribution or not.
b.

Answer to Problem 92E
The histogram by transforming the data using logarithms is given below:
Yes, the log transformation was successful in producing a more symmetric distribution.
Explanation of Solution
Calculation:
It is given that the body mass of the 50 different bird species. The log for the data values is obtained as shown below:
Body Mass | Log (Body Mass) | Transformed values |
7.7 | log (7.7) | 0.88649 |
10.1 | log (10.1) | 1.00432 |
21.6 | log (21.6) | 1.33445 |
8.6 | log (8.6) | 0.93450 |
12 | log (12) | 1.07918 |
11.4 | log (11.4) | 1.05690 |
16.6 | log (16.6) | 1.22011 |
9.4 | log (9.4) | 0.97313 |
11.5 | log (11.5) | 1.06070 |
9 | log (9) | 0.95424 |
8.2 | log (8.2) | 0.91381 |
20.2 | log (20.2) | 1.30535 |
48.5 | log (48.5) | 1.68574 |
21.6 | log (21.6) | 1.33445 |
26.1 | log (26.1) | 1.41664 |
6.2 | log (6.2) | 0.79239 |
19.1 | log (19.1) | 1.28103 |
21 | log (21) | 1.32222 |
28.1 | log (28.1) | 1.44871 |
10.6 | log (10.6) | 1.02531 |
31.6 | log (31.6) | 1.49969 |
6.7 | log (6.7) | 0.82607 |
5 | log (5) | 0.69897 |
68.8 | log (68.8) | 1.83759 |
23.9 | log (23.9) | 1.37840 |
19.8 | log (19.8) | 1.29667 |
20.1 | log (20.1) | 1.30320 |
6 | log (6) | 0.77815 |
99.6 | log (99.6) | 1.99826 |
19.8 | log (19.8) | 1.29667 |
16.5 | log (16.5) | 1.21748 |
9 | log (9) | 0.95424 |
448 | log (448) | 2.65128 |
21.3 | log (21.3) | 1.32838 |
17.4 | log (17.4) | 1.24055 |
36.9 | log (36.9) | 1.56703 |
34 | log (34) | 1.53148 |
41 | log (41) | 1.61278 |
15.9 | log (15.9) | 1.20140 |
12.5 | log (12.5) | 1.09691 |
10.2 | log (10.2) | 1.00860 |
31 | log (31) | 1.49136 |
21.5 | log (21.5) | 1.33244 |
11.9 | log (11.9) | 1.07555 |
32.5 | log (32.5) | 1.51188 |
9.8 | log (9.8) | 0.99123 |
93.9 | log (93.9) | 0.97267 |
10.9 | log (10.9) | 1.03743 |
19.6 | log (19.6) | 1.29226 |
14.5 | log (14.5) | 1.16137 |
Software procedure:
Step-by-step procedure to obtain histogram using MINITAB:
- Choose Graph > Histogram.
- Choose Simple, and then click OK.
- In Graph variables, enter the corresponding column of Logarithm of Body mass.
- Click OK.
- On graph right click on X axis, select edit X scale.
- Select Binning.
- Under Interval Type, Choose cut point.
- Click OK.
Justification: It can be observed that the histogram of the transformed data (using logarithms) is more near to symmetrical shape when compared to the untransformed data. This shows that using the transformation of logarithms produce a more symmetrical distribution for body mass.
Hence, the log transformation was successful in producing a more symmetric distribution.
c.
Construct the histogram by transforming the data using
Identify whether the transformation
c.

Answer to Problem 92E
The histogram by transforming the data using
Yes, the transformation
Explanation of Solution
Calculation:
The transformation for the data values using
Body Mass | Transformed values | |
7.7 | 0.360375 | |
10.1 | 0.314658 | |
21.6 | 0.215166 | |
8.6 | 0.340997 | |
12 | 0.288675 | |
11.4 | 0.296174 | |
16.6 | 0.245440 | |
9.4 | 0.326164 | |
11.5 | 0.294884 | |
9 | 0.333333 | |
8.2 | 0.349215 | |
20.2 | 0.222497 | |
48.5 | 0.143592 | |
21.6 | 0.215166 | |
26.1 | 0.195740 | |
6.2 | 0.401610 | |
19.1 | 0.228814 | |
21 | 0.218218 | |
28.1 | 0.188646 | |
10.6 | 0.307148 | |
31.6 | 0.177892 | |
6.7 | 0.386334 | |
5 | 0.447214 | |
68.8 | 0.120561 | |
23.9 | 0.204551 | |
19.8 | 0.224733 | |
20.1 | 0.223050 | |
6 | 0.408248 | |
99.6 | 0.100201 | |
19.8 | 0.224733 | |
16.5 | 0.246183 | |
9 | 0.333333 | |
448 | 0.017546 | |
21.3 | 0.216676 | |
17.4 | 0.239732 | |
36.9 | 0.164622 | |
34 | 0.171499 | |
41 | 0.156174 | |
15.9 | 0.250785 | |
12.5 | 0.282843 | |
10.2 | 0.313112 | |
31 | 0.179605 | |
21.5 | 0.215666 | |
11.9 | 0.289886 | |
32.5 | 0.175412 | |
9.8 | 0.319438 | |
93.9 | 0.103197 | |
10.9 | 0.302891 | |
19.6 | 0.225877 | |
14.5 | 0.262613 |
Software procedure:
Step-by-step procedure to obtain histogram using MINITAB:
- Choose Graph > Histogram.
- Choose Simple, and then click OK.
- In Graph variables, enter the corresponding column of 1/sqrt(Body mass).
- Click OK.
- On graph right click on X axis, select edit X scale.
- Select Binning.
- Under Interval Type, Choose cut point.
- Click OK.
Justification: It can be observed that the histogram of the transformed data (using
Hence, the transformation
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Chapter 7 Solutions
Introduction to Statistics and Data Analysis
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