Q. 2.158 - Elementary Statistics

Question

Class Project: Number of Siblings. This exercise is a class project and works best in relatively large classes.

a. Determine the number of siblings for each student in the class.

b. Obtain a relative-frequency histogram for the number of siblings. Use single-value grouping.

c. Obtain a simple random sample of about one-third of the students in the class.

d. Find the number of siblings for each student in the sample.

e. Obtain a relative-frequency histogram for the number of siblings for the sample. Use single-value grouping.

f. Repeat parts (c)-(e) three more times.

g. Compare the histograms for the samples to each other and to that for the entire population. Relate your observations to key Fact 2.1

Step-by-Step Solution

Answer

Ans:  

(a)  

3	0	0	0	3	4	4	0
3	0	3	0	1	2	4	1
3	4	3	2	4	4	3	1
0	1	2	4	1	1	4	4
1	1	0	4	3	0	0	3

(b)  

(c)   We should make one sample of three data from your siblings' number of classmates. We have 40 students, so choose $14 students (40/3=13.33)$. Selected readers for word numbers are displayed as follows.

(d)  

0	3	4	1	0
4	4	3	0	1
4	2	3	1

(e)  

(f)  Repeat parts (c)-(e) three more times. 

(g)  All sample histograms are similar but not identical. Although the first sample looks less than half (e) it is similar to a human histogram. 

Step 1. Given information.

given,

     Number of Siblings. This exercise is a class project and works best in relatively large classes. 

Step 2. The number of students in the class should be 40.

 The number of siblings 40 students do not have as shown in the following table.

3	0	0	0	3	4	4	0
3	0	3	0	1	2	4	1
3	4	3	2	4	4	3	1
0	1	2	4	1	1	4	4
1	1	0	4	3	0	0	3

Step 3. (b) We need to find the frequency distribution relative to the number of siblings. Here we have to consider how to collect a single value.

We can count the number of zeros, one, two, and three. Four from the data provided will provide the distribution frequency. The related frequency table is obtained by dividing each frequency by the total number of observations, 40, we find the related frequencies (circled in three places) in the third column of the following table. The related frequency table is shown below.

Number of           siblings	Frequency	Relative F-       quency
0	10	0.25
1	8	0.2
2	3	0.075
3	9	0.225
4	10	0.25
Total	40	1

Step 4. The histogram for relative frequency distribution obtained in part (b) is drawn using EXCEL software as follows:

Step 5. (c) Now,

 We should make one sample of three data from your siblings' number of classmates. We have 40 students, so choose $14 students (40/3 = 13.33)$. Selected readers for word numbers are displayed as follows.

Step 6. (d) The sample number of observations is shown in the following table.

0	3	4	1	0
4	4	3	0	1
4	2	3	1

Step 7. (e) The relative frequency is shown in the following table,

Siblings	Frequency	Relative frequency
0	3	0.214
1	3	0.214
2	1	0.071
3	3	0.214
4	4	0.286
Total	14	1.000

A related sample histogram of 14 sibling values is drawn using EXCEL software as follows. 

Step 8. (f) Let us consider another sample of 14 students from a class and note the number of siblings each student selected.

The following table shows the sample comments.

1	0	4	2	0
2	3	3	2	0
2	4	0	2

Step 9. The relative frequency is shown in the following table.

Siblings	Frequency	Relative frequency
0	6	0.428571
1	1	0.071429
2	2	0.142857
3	1	0.071429
4	4	0.285714
Total	14	1

A related sample histogram of 14 sibling values is drawn using the EXCEL software as follows.

Let us consider another sample of 14 students from a class and note the number of siblings each student selected.

The following table shows the sample comments.

4	4	2	1	1
1	2	1	3	4
0	0	4	4

Step 10. The relative frequency is shown in the following table.

Siblings	Frequency	Relative frequency
0	2	0.28571
1	4	0.07143
2	2	0.35714
3	1	0.14286
4	5	0.14286
Total	14	1

The relative frequency histogram for the sample of 14 siblings' values is drawn using EXCEL software as follows.

Let us consider another sample of 14 students from a class and note the number of siblings each student selected.

The following table shows the sample comments.

4	4	2	1	1
1	2	1	3	4
0	0	4	4

Step 11. The relative frequency is shown in the following table.

Siblings	Frequency	Relative frequency
0	2	0.14286
1	4	0.28571
2	2	0.14286
3	1	0.07143
4	5	0.35714
Total	14	1

A related sample histogram of 14 sibling values is drawn using the EXCEL software as follows:

Step 12. (g) Compare the histograms for the samples to each other and to that for the entire population.

All sample histograms are similar but not identical. Although the first sample looks less than half (e) it is similar to a human histogram.