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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
233 257 264 266 267 269 270 283 284 298
304 307 309 318 320 320 324 328 331 355
375 379 381 392 403 414 425 446 467 478
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 limits161
214
267
320
373
426
Make the distribution
Upper class limits213
266
319
372
425
478
• Look at the second classes lower limit and find the largest value that the data could be and not be in the second class. (usually one less than the second classes lower limit )
• The class width will be added to a upper class limit to find the next lower class limit (look at how these compare to the lower class limit of 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 class limits
Upper class limits Tally Frequency
161 213 IIIIIII 7
214 266 IIIIIII 7
267 319 IIIIIIIIII 10
320 372 IIIIII 6
373 425 IIIIIII 7
426 478 III 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 class limits
Upper class limits Tally Frequency
Cumulative frequency
Relative 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
160.5 213.5 266.5 319.5 372.5 425.5 478.5
213 214
2
266 267
2
319 320
2
372 373
2
425 426
2
These are found by averaging the upper and lower class limits
Found by adding or subtracting 53 (the class width) from the end and beginning
160.5 213.5 266.5 319.5 372.5 425.5 478.5
10
9
8
7
6
5
4
3
2
1
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