Making a frequency
distribution and histogram
The Data
• Make sure the data is quantitative
• Sort the data from smallest to largest
• Count how many
The Data
161
182
191
194
202
205
213
215
231
232
233
304
375
257
307
379
264
309
381
266
318
392
267
320
403
269
320
414
270
324
425
283
328
446
284
331
467
298
355
478
The data is sorted, quantitative, and
there are 40 elements
Find the range and class width
• Range is found by subtracting the smallest
from the largest
• Class width is found by dividing the range
by the number of class.
• Always round the class width up to the
same number of decimal places as the
original data.
Range and class width
• Range = 478-161 = 317
• For 6 class the class width would by
– 317÷6 = 52.833 round up to 53
Make the distribution
• Start with the smallest value
as the lower class limit of
the first class.
• The class width will be
added to a lower class limit
to find the next lower class
limit
Lower class
limits
161
214
267
320
373
426
Make the distribution
• Look at the second classes lower
Upper class
limit and find the largest value that
limits
the data could be and not be in the
213
second class. (usually one less
than the second classes lower
266
limit )
319
• The class width will be added to a
372
upper class limit to find the next
425
lower class limit (look at how these
compare to the lower class limit of
478
the next class)
Tallies and frequency
• If the data is not in order you will want to
do a tally to keep count for each class
• Frequency is the number of time an
element is in each class
Tallies and frequency
Lower Upper
class
class
limits
limits
161
213
214
266
267
319
320
372
373
425
426
478
Tally
IIIIIII
IIIIIII
IIIIIIIIII
IIIIII
IIIIIII
III
Frequency
7
7
10
6
7
3
Cumulative frequency, relative
frequency, and class marks
• Cumulative frequency is the running total.
– It is found by adding a classes frequency to the
Cumulative frequency of the class before
• Relative frequency is a ratio of the classes
frequency to the number of elements in the
sample.
• Class marks are the middle value of each class.
– It is found by adding the upper and lower class limit
together and then dividing by two.
Complete Frequency Distribution
Lower Upper
class class
limits limits
Tally
Cumulative Relative
Frequency frequency frequency
Class
marks
161
213
IIIIIII
7
7
0.1750
187
214
266
IIIIIII
7
14
0.1750
240
267
319
IIIIIIIIII
10
24
0.2500
293
320
372
IIIIII
6
30
0.1500
346
373
425
IIIIIII
7
37
0.1750
399
426
478
III
3
40
0.0750
452
Class Bounds
• These are the points between each class
– To find the class bound add the upper class
limit of one class to the lower class limit of the
next class and divide by 2
• You will also have to find the lower and
upper bound
– Look at the pattern and find the one below the
first and also one above the last class
These are found by averaging the upper
and lower class limits
160.5
213  214
2
266  267
2
213.5
266.5
319  320
2
319.5
372  373
2
372.5
425  426
2
425.5
Found by adding or subtracting 53 (the class width)
from the end and beginning
478.5
10
9
8
7
6
5
4
3
2
1
160.5
213.5
266.5
319.5
372.5
425.5
478.5
Make a frequency distribution
and histogram for the following
use 7 classes
12
13
15
18
20
21
23
23
25
27
29
33
34
35
36
36
38
39
39
40
40
42
43
44
44
44
45
47
49
50
50
51
53
53
54
55
55
57
59
60
60
61
63
64
65
65
66
67
68
69