How to build frequency tables

For Categorical and Numerical data

Frequency Tables: Categorical

• Rows are called classes• Each categorical (discrete) value

occupies its own class• Then frequency is counted for each

class in absolute (#) and in relative (%) terms.

Example

• Variable: Gender• Nature: Categorical, Nominal.• Values: Male, Female• Raw Data: {M, M, F, M, M, F, F, F,

F, F, M, M, F, F, F, F, M, M, F, F}

Gender Frequency Distribution

Gender AbsoluteFrequency

RelativeFrequency

Male 8 8/20 = 40%

Female 12 12/20 = 60%

Total 20 20/20 = 100%

Frequency Tables: Numerical

• Rows are called classes• The number of classes, c, is a

function of the number of observations, n:C = 1 + 3.3*LOG(n) –Sturge’s law

If n = 50, then c ≈ 6.6

Frequency Tables: Numerical• Each class consists of a range of values

know as the “class width”, w. • The class width must be the same for

all classes.• W = Range ÷ c, where Range = MAX-MIN

• If MIN = 82 and MAX = 213 for n=50 observations, then:

W = (213 – 82) / 6.6 ≈ 20

Frequency Tables: Lower Class Limits

• To build classes, we then start measuring class widths FROM a “nice” (round) number smaller than MIN.

• The LOWER CLASS LIMITS are “c” numbers that are 1 class width, “w”, greater than the previous one.

Frequency Tables: Upper Class Limits

• UPPER CLASS LIMITS mark ending values for each class.

• They are smaller in value than the LOWER CLASS LIMITS of the previous classes.

Frequency Tables: Value Classes Example• Example: 2.12 on

page 57, UTILITY• Data: n=50, MIN=82,

MAX=213• Range = 213 – 82 =

131• C = 1 + 3.3*LOG(50)

≈ 7• W = 131 / 7 ≈ 20

• Frequency Table Class Limits:

From To <

80 100

100 120

120 140

140 160

160 180

180 200

200 220

Frequency Table: absolute and % counts

• To complete a frequency table we then tally how many observations in a data set fall in each of the previously formed class ranges.

• These tallies can be accounted for in units or in % of the total number of observations, n.

Frequency Table

From To < Absolutef Relative%

80 100 4 8%

100 120 7 14 %

120 140 9 18 %

140 160 13 26 %

160 180 9 18 %

180 200 5 10 %

200 220 3 6 %

Frequency Tables: using PhStat• To count frequencies, all you do is let

PhStat do the tallying for you, using the command sequence:→PhStat

→Descriptive Statistics→ Frequency Distribution …

• Then, you input the proper cell ranges in the dialog box for the procedure:• Variable cell range: range of cells for data.• Bins cell range: class limits for classifying

data.