Question

a. By hand, make an ordered stemplot of the distribution of the variable MothersAge for the female students. Show both your rough and final version of the stemplot. Use stems of five (See the Notes for an explanation of what stems of five are). There are 63 female students.

Mother's age 18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,51

Female 1, 0, 2, 2, 3, 4, 7, 3, 2, 4, 7, 1, 6, 4, 5, 3, 1, 4, 0, 1, 1, 1, 0, 1, 0

Use the stem and leaf plots that you previously created to help you draw and label histograms on your scratch paper with bin width of 2 for mothers's age at birth of female students and for mother's age at birth of male students. Make the lower bound of your first bin 16.

Comment: Bin width of 2 is not a typo. Yes, your stem and leaf plot has bins of 5 so some thinking is required, but at least your stem and leaf plot has the values in order for you.

Answer 1

The stem and leaf plot is obtained in following steps,

Step 1: Sort the data values from smallest to largest (The given data values are already sorted).

Step 2: Make a stem of tens' digit as shown below (taking bin of size 5),

Stem
1
1
2
2
3
3
4
4
5

Where, the first 1 takes the unit digit 0 to 4 and second 1 takes the unit digit 5 to 9. Similar for tens digit 2, 3 and 5.

Step 3: Now write the unit digit for corresponding tens digit. The plot is shown below,

Stem	Leaf
1
1	8
2	0	0	1	1	2	2	3	3	3	3	4	4	4	4	4	4	4
2	5	5	5	6	6	7	7	7	7	8	8	8	8	8	8	8	9
3	0	0	0	0	0	0	1	1	1	1	2	2	2	2	2	3	3	3	4
3	5	5	5	5	7	8	9
4	1
4
5

Explanation of stem:

Stem

1 (takes values 1.0 to 1.4, width = 5)

1 (takes values 1.5 to 1.9, width = 5)

2 (takes values 2.0 to 2.4, width = 5)

2 (takes values 2.5 to 2.9, width = 5)

3 (takes values 3.0 to 3.4, width = 5)

3 (takes values 3.5 to 3.9, width = 5)

4 (takes values 4.0 to 4.4, width = 5)

4 (takes values 4.5 to 4.9, width = 5)

Since the bin size = 5 we have to take each unit digit twice as stem.