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 Data161 182 191 194 202 205 213 215 231 232233 257 264 266 267 269 270 283 284 298304 307 309 318 320 320 324 328 331 355375 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 limits161214267320373426

Make the distribution

Upper class limits213266319372425478

• 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 7214 266 IIIIIII 7267 319 IIIIIIIIII 10320 372 IIIIII 6373 425 IIIIIII 7426 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 2142 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

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Make a frequency distribution and histogram for the following

use 7 classes12 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