What is a frequency distribution?

A table that shows classes (intervals) of data entries with a count of the number of entries in each class Frequency (f) – the number of data

entries in the class

How do you create a frequency

distribution?

1. Choose how many classes (you will be given this information)

2. Calculate class width:highest entry – lowest entry

# of classes

3. Find each class’s lower and upper limits

4. Sort entries into classes (tallies)5. Count tallies to find f for each class

Example 1 The following sample data lists the number

of minutes 50 Internet subscribers spent on the Internet during their most recent session. Construct a frequency distribution that has seven classes.

50 40 41 17 11 7 22 44 28 21 19 23 37 51 54 42 88

41 78 56 72 56 17 7 69 30 80 56 29 33 46 31 39 20

18 29 34 59 73 77 36 39 30 62 54 67 39 31 53 44

Example 1 (cont’d)

1. Number of classes is given to you (7)

2. Class width: 88 – 7 = 11.57 ≈ 12 7

3. Since the lower limit of the first class will be 7, the lower limit of the second class will be 7+12 = 19, and so on.

Example 1 - Frequency Distribution

Class Tally f 7-18 19-30 31-42 43-54

55-6667-7879-90

Σf=50

6

10

13

8

5

62

What else can be done in a frequency distribution?

Midpoint=lower class limit+upper class limit

2 Relative Frequency: portion of the data

set is in a classRF = class frequency = f

sample size n Cumulative Frequency: sum of the

frequency for that class plus all previous classes

Example 2 Using the frequency distribution

constructed for Example 1, find the midpoint, relative frequency, and cumulative frequency for each class.

Example 2 (cont’d)

Class f Mdpt RelFreq CumFreq

7-18 6

19-30 10

31-42 13

43-54 8

55-66 5

67-78 6

79-90 2

Σf = 50

12.5

24.5

36.5

48.5

60.5

72.5

84.5

.12

.2

.26

.16

.1

.12

.04

Σf/n = 1.00

6

16

29

37

42

48

50

HOMEWORK

Worksheet 2-1#3, 4, 5, 6, 15, 16

What is a frequency histogram? Bar graph showing the frequency

distribution of a data set Horizontal scale (x-axis) is quantitative

and measures data values Vertical scale (y-axis) measures frequency

of classes Bars MUST touch each other (no gaps) Use MIDPOINTS as x-values Bars should be drawn to straddle each

midpoint line

Example 3 Draw a frequency histogram for

the frequency distribution in Example 2.

Time online (minutes)

Freq

uen

cy (

# o

f su

bsc

rib

ers

)

12.5 24.5 36.5 48.5 60.5 72.5 84.5

2

4

6

8

10 1

2 1

4

What is a frequency polygon? Line graph to show CHANGE in

frequencies USES MIDPOINTS as x-values

Example 4 Draw a frequency polygon for the

frequency distribution in Example 2.

Time online (minutes)

Freq

uen

cy (

# o

f su

bsc

rib

ers

)

12.5 24.5 36.5 48.5 60.5 72.5 84.5 96.5

2

4

6

8

10 1

2 1

4

HOMEWORK

Worksheet 2-1#17, 18, 29, 30

What is a relative frequency histogram?

Same as a frequency histogram, but shows RELATIVE frequencies

Use UPPER CLASS BOUNDARIES as x-values

Have one more decimal place than the data Eliminates any gaps between classes Example: If the class LIMITS are 10-15, the

class BOUNDARIES will be 9.5 to 15.5 Use relative frequencies as y-values Bars should be drawn to span from the lower

class boundary to upper class boundary (between vertical lines, not straddling the lines)

Example 5 Draw a relative frequency

histogram for the frequency distribution in Example 2.

Time online (minutes)

Rela

tive F

req

uen

cy

(Po

rtio

n o

f su

bsc

rib

ers

)

6.5 18.5 30.5 42.5 54.5 66.5 78.5 90.5

.0

4 .0

8 .1

2 .1

6 .2

.2

4.2

8

What is an ogive? Also known as cumulative

frequency graph Line graph Use UPPER CLASS

BOUNDARIES as x-values Use cumulative frequencies as y-

values Points are placed on the upper

class boundary lines

Example 6 Draw an ogive for the frequency distribution in

Example 2. Estimate how many subscribers spent less than 60 minutes during their last session.

Time online (minutes)

Cu

mu

lati

ve F

req

uen

cy

(#

of

sub

scri

bers

)

6.5 18.5 30.5 42.5 54.5 66.5 78.5 90.5

10 2

0 3

0 4

0 5

0

In conclusion… How do you create a frequency

distribution?

Draw a quick sketch of each: Frequency histogram Frequency polygon Relative frequency histogram Ogive

HOMEWORK

Worksheet 2-1#21, 22, 25, 26