Frequency Distribution

Objectives: Create Frequency Distributions

Analyze Frequency Distribution

What is a Frequency Distribution?

• Allows us to understand and interpret the nature of the distribution of a data set.

• Shows how data is partitioned among classes by listing the classes along with the number of data values in each.

PULSE RATES (BEATS PER MINUTE) of FEMALES

76 72 88 60 72 68 80 64 68 68

80 76 68 72 96 72 68 72 64 80

64 80 76 76 76 80 104 88 60 76

72 72 88 80 60 72 88 88 124 64

Creating a Frequency Distribution Table

• Lower Class Limits: smallest numbers that can belong to the different classes

• Upper Class Limits: largest numbers ...• Class Boundaries: numbers used to separate

the classes, but w/out the gaps created by class limits

• Class Midpoints: values in the middle of the classes

• Class width: difference b/w 2 consecutive lower/upper class boundaries

Procedure:

• Determine the number of classes– Will either be given or found by– ALWAYS ROUND UP!

n

n

Calculate the Class Width

• Round up for convenience

classes of #

minimum-maximum width class

Lower Class Limit

• Select either the lowest data value or a convenient value below the minimum as the first lower class limit.

Cont...

• Using the class width and the first lower class limit begin listing the lower class limits in a vertical column by adding the class width.

Adding the upper class limits

• Identify the corresponding upper class limits to each class making sure that the classes do not overlap

Finish by...

• Taking the total values in each class and listing them is column number 2

Things to watch out for:

• Confusing the class width and the class boundaries– Class width is the difference between lower or

upper class limits!• Make sure you include all classes, even

those with 0 data values. • The sum of column 2 should be the # of

values in data set

Example using Female Pulse Rates

• Step 1: Find total # of classes– n=40

• Round up: There are 7 classes

...324.640

Pulse Rate Frequency

Calculate Class Width

•

classes of #

minimum-maximum width class

10...142.97

60-124 width class

Begin filling in table

• Choose 60 as the first lower class limit because it is both the minimum value and a convenient value

• Add the class width and record in following rows

Pulse Rate Frequency

60-

70-

80-

90-

100-

110-

120-

Identify corresponding UCL

• Make sure you leave no gaps where numbers would fit in.

Pulse Rate Frequency

60-69

70-79

80-89

90-99

100-109

110-119

120-129

Finish by...

• Calculating frequency for each class

• All values should be included totals should match up!

Pulse Rate Frequency

60-69 12

70-79 14

80-89 11

90-99 1

100-109 1

110-119 0

120-129 1

Relative Frequency Tables

• Same Classes• Sum must be close to 1

sfrequencie all

frequency classfrequency relative

Relative frequency distribution tables

Pulse Rate Relative Frequency

60-69 30%

70-79 40%

80-89 27.5%

90-99 2.5%

100-109 2.5%

110-119 0

120-129 2.5%

Cumulative Frequency

• Replace lower class limits with “less than...”

• Add each cell to previous cells

Pulse Rate Frequency

Less than 70 12

Less than 80 26

Less than 90 37

Less than 100 38

Less than 110 39

Less than 120 39

Less than 130 40

Interpreting Frequency Distributions

Normal Distribution (Bell Curve) within a frequency distribution table:

Frequencies start low, increase in frequency, then return to low.

Distribution is approximately symmetric

IQ Scores of 1000 Adults

IQ score Freq Normal Dist

50-69 24 frequencies start low...

70-89 228

90-109 490 increase to maximum...

110-129 232

130-149 26 decrease to be come low again.

Relatively symmetric

Last Digits of Female Pulse RatesLast digit

Freq

0 91 02 83 04 65 06 77 08 109 0

Randomly Selected Pennies

Wt. (grams) of pennies Frequency2.40-2.49 182.50-2.59 192.60-2.69 02.70-2.79 02.80-2.89 02.90-2.99 23.00-3.09 253.10-3.19 8