Worked Problem.....Frequency Distribution.....Psyc205/Soc205.....Vernoy

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Creating A Grouped Frequency Distribution
(A worked Problem: Procedure explained in more detail in Chapter 2)

Problem: Create a grouped frequency distribution for the following 15 scores:

46, 48, 54, 58, 59, 64, 65, 77, 77, 79, 84, 89, 89, 91, 97

I. Compute the Range

Range = 97 - 46 = 51

II. Choose an interval size ( i )

i = 5

III. Check that the number of intervals is between 10 and 20

Number of class intervals = Range / i

Number of class intervals = 51 / 5 = 10.2

(This will give about 11 class intervals)

IV. Create the Apparent Limits (see class intervals a worked problem)

Real Lim	App Lim	Freq	Mid Pt	Rel F	Cum F	C R F	Cum %
	95 - 99
	90 - 94
	85 - 89
	80 - 84
	75 - 79
	70 - 74
	65 - 69
	60 - 64
	55 - 59
	50 - 54
	45 - 49

V. Create the Real Limits

URL = UAL + .5 units

LRL = LAL - .5 units

Real Lim	App Lim	Freq	Mid Pt	Rel F	Cum F	C R F	Cum %
94.5 - 99.5	95 - 99
89.5 - 94.5	90 - 94
84.5 - 89.5	85 - 89
79.5 - 84.5	80 - 84
74.5 - 79.5	75 - 79
69.5 - 74.5	70 - 74
64.5 - 69.5	65 - 69
59.5 - 64.5	60 - 64
54.5 - 59.5	55 - 59
49.5 - 54.5	50 - 54
44.5 - 49.5	45 - 49

VI. Tally the Frequencies

Real Lim	App Lim	Freq	Mid Pt	Rel F	Cum F	C R F	Cum %
94.5 - 99.5	95 - 99	1
89.5 - 94.5	90 - 94	1
84.5 - 89.5	85 - 89	2
79.5 - 84.5	80 - 84	1
74.5 - 79.5	75 - 79	3
69.5 - 74.5	70 - 74	0
64.5 - 69.5	65 - 69	1
59.5 - 64.5	60 - 64	1
54.5 - 59.5	55 - 59	2
49.5 - 54.5	50 - 54	1
44.5 - 49.5	45 - 49	2

Remember: The sum of the frequencies = n

VII. Compute the Midpoints

Real Lim	App Lim	Freq	Mid Pt	Rel F	Cum F	C R F	Cum %
94.5 - 99.5	95 - 99	1	97
89.5 - 94.5	90 - 94	1	92
84.5 - 89.5	85 - 89	2	87
79.5 - 84.5	80 - 84	1	82
74.5 - 79.5	75 - 79	3	77
69.5 - 74.5	70 - 74	0	72
64.5 - 69.5	65 - 69	1	67
59.5 - 64.5	60 - 64	1	62
54.5 - 59.5	55 - 59	2	57
49.5 - 54.5	50 - 54	1	52
44.5 - 49.5	45 - 49	2	47

VIII. Compute Relative Frequency

n = number of scores = 15

Real Lim	App Lim	Freq	Mid Pt	Rel F	Cum F	C R F	Cum %
94.5 - 99.5	95 - 99	1	97	.067
89.5 - 94.5	90 - 94	1	92	.067
84.5 - 89.5	85 - 89	2	87	.133
79.5 - 84.5	80 - 84	1	82	.067
74.5 - 79.5	75 - 79	3	77	.200
69.5 - 74.5	70 - 74	0	72	.000
64.5 - 69.5	65 - 69	1	67	.067
59.5 - 64.5	60 - 64	1	62	.067
54.5 - 59.5	55 - 59	2	57	.133
49.5 - 54.5	50 - 54	1	52	.067
44.5 - 49.5	45 - 49	2	47	.133

Remember: The sum of the relative frequencies = 1
(Slight differences might occure because of round off error.)

IX. Find the Cumulative frequencies

Add the frequencies from the bottom

Real Lim	App Lim	Freq	Mid Pt	Rel F	Cum F	C R F	Cum %
94.5 - 99.5	95 - 99	1	97	.067	15
89.5 - 94.5	90 - 94	1	92	.067	14
84.5 - 89.5	85 - 89	2	87	.133	13
79.5 - 84.5	80 - 84	1	82	.067	11
74.5 - 79.5	75 - 79	3	77	.200	10
69.5 - 74.5	70 - 74	0	72	.000	7
64.5 - 69.5	65 - 69	1	67	.067	7
59.5 - 64.5	60 - 64	1	62	.067	6
54.5 - 59.5	55 - 59	2	57	.133	5
49.5 - 54.5	50 - 54	1	52	.067	3
44.5 - 49.5	45 - 49	2	47	.133	2

Remember: The Cumulative Frequency in the highest interval = n

X. Compute Cumulative Relative Frequency

Real Lim	App Lim	Freq	Mid Pt	Rel F	Cum F	C R F	Cum %
94.5 - 99.5	95 - 99	1	97	.067	15	1.000
89.5 - 94.5	90 - 94	1	92	.067	14	.933
84.5 - 89.5	85 - 89	2	87	.133	13	.867
79.5 - 84.5	80 - 84	1	82	.067	11	.733
74.5 - 79.5	75 - 79	3	77	.200	10	.667
69.5 - 74.5	70 - 74	0	72	.000	7	.467
64.5 - 69.5	65 - 69	1	67	.067	7	.467
59.5 - 64.5	60 - 64	1	62	.067	6	.400
54.5 - 59.5	55 - 59	2	57	.133	5	.333
49.5 - 54.5	50 - 54	1	52	.067	3	.200
44.5 - 49.5	45 - 49	2	47	.133	2	.133

XI. Compute Cumulative Percent

Real Lim	App Lim	Freq	Mid Pt	Rel F	Cum F	C R F	Cum %
94.5 - 99.5	95 - 99	1	97	.067	15	1.000	100
89.5 - 94.5	90 - 94	1	92	.067	14	.933	93.3
84.5 - 89.5	85 - 89	2	87	.133	13	.867	86.7
79.5 - 84.5	80 - 84	1	82	.067	11	.733	73.3
74.5 - 79.5	75 - 79	3	77	.200	10	.667	66.7
69.5 - 74.5	70 - 74	0	72	.000	7	.467	46.7
64.5 - 69.5	65 - 69	1	67	.067	7	.467	46.7
59.5 - 64.5	60 - 64	1	62	.067	6	.400	40.0
54.5 - 59.5	55 - 59	2	57	.133	5	.333	33.3
49.5 - 54.5	50 - 54	1	52	.067	3	.200	20.0
44.5 - 49.5	45 - 49	2	47	.133	2	.133	13.3

XII. Visual Summary: Creating a Grouped Frequency Distribution

Copyright � 2004 by Mark W. Vernoy