Question

Prepare a frequency table of the following scores obtained by 50 students in a test:

42	51	21	42	37	37	42	49	38	52
7	33	17	44	39	7	14	27	39	42
42	62	37	39	67	51	53	53	59	41
29	38	27	31	54	19	53	51	22	61
42	39	59	47	33	34	16	37	57	43

Answer 1

Hint: To prepare the frequency table, we will create a table with two columns, one column will be of the observations, in the case of this questions, the scores of the students and the other column will have the frequency or in simple words, the number of times observation has occurred in the given data set. The sum of the frequencies of each observation must be equal to the number of elements in the data set.

Complete step by step answer:
The data set given to us is as follows:

42	51	21	42	37	37	42	49	38	52
7	33	17	44	39	7	14	27	39	42
42	62	37	39	67	51	53	53	59	41
29	38	27	31	54	19	53	51	22	61
42	39	59	47	33	34	16	37	57	43

We will now create a table. It is a general practice to start the table with the smallest observation. The smallest observation in our data is 7. We can also see that it has occurred 2 times in the total data set. Thus, the table will be as follows:

Observations	Frequency
7	2

The remaining data set is as follows:

42	51	21	42	37	37	42	49	38	52
_	33	17	44	39	_	14	27	39	42
42	62	37	39	67	51	53	53	59	41
29	38	27	31	54	19	53	51	22	61
42	39	59	47	33	34	16	37	57	43

The second smallest number is 14 and it occurs only once in the data set.

Observations	Frequency
7	2
14	1

42	51	21	42	37	37	42	49	38	52
_	33	17	44	39	_	_	27	39	42
42	62	37	39	67	51	53	53	59	41
29	38	27	31	54	19	53	51	22	61
42	39	59	47	33	34	16	37	57	43

The next value is 16.

Observations	Frequency
7	2
14	1
16	1

42	51	21	42	37	37	42	49	38	52
_	33	17	44	39	_	_	27	39	42
42	62	37	39	67	51	53	53	59	41
29	38	27	31	54	19	53	51	22	61
42	39	59	47	33	34	_	37	57	43

We will continue to create the table in a similar way.
The final answer will be as follows:

Observations	Frequency
7	2
14	1
16	1
17	1
19	1
21	1
22	1
27	2
29	1
31	1
33	2
34	1
37	4
38	2
39	4
41	1
42	6
43	1
44	1
47	1
49	1
51	3
52	1
53	3
54	1
57	1
59	2
61	1
62	1
67	1
Sum:	50

Note: Another column of tally can be added in the frequency table. The tally column shows the counting of the observations. Students are advised to be careful while dealing with such a massive frequency table as there are many observations. It is always a good practice to cross-check your solution.