Frequency Distribution Lec

8/3/2019 Frequency Distribution Lec

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Construction of a Frequency Distribution (Relative / Cumulative)

Sample Data: Calories per Serving for different Brands of Ready to Eat Cereals

57 88 89 89 107 112 114 125

95 101 103 110 107 110 113 113

77 96 105 99 107 109 116 110

96 97 105 96 102 108 112 112

97 95 89 104 105 109 105 113

97 86 94 102 121 112 110 115

99 84 96 97 111 107 113 112

106 97 95 103 107 110 105 110

53 89 104 103 103 106 119 111

73 74 96 112 101 108 109


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Construction of a Frequency Distribution (Relative / Cumulative)

Ready to Eat Cereals

Calories per

Serving Number

of Brandsfrom up to

50 60 260 70 0

70 80 3

80 90 7

90 100 16

100 110 33

110 120 16

120 130 2

Questions:

How many points of concentration?

Where is it (are they) located?

What is the shape of the distribution?

Referred to as ClassesReferred to as Frequencies or Counts


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Construction of a Frequency Distribution

Step #1: Determine the class width (CW).

Step #2: Determine Lowest Lower Limit.

Step #3: Determine Lowest and subsequent Upper Limits.Step #4: Determine the class frequencies using a tally.

As required

Step #5: Compute relative and cumulative relative frequencies.

and/or

Step #6: Compute cumulative (less than) relative frequencies.


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Calories per Serving

57 88 89 89 107 112 114 125

95 101 103 110 107 110 113 113

77 96 105 99 107 109 116 11096 97 105 96 102 108 112 112

97 95 89 104 105 109 105 113

97 86 94 102 121 112 110 115

99 84 96 97 111 107 113 112

106 97 95 103 107 110 105 110

53 89 104 103 103 106 119 111

73 74 96 112 101 108 109

Step #1: Determine the class width (CW):

- Choose between 5 and 20 classes (low end for small data sets, higher for large data sets)

- Round to a "nice" value. ie. 1, 5, 2.5, 10, 50, 25, .1, .5, .25 etc.

CWRange

NumberofClasses

Highest Lowest

ofClasses

#

.125 53

7

103 10


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Construction of a Frequency DistributionCalories per Serving

57 88 89 89 107 112 114 125

95 101 103 110 107 110 113 113

77 96 105 99 107 109 116 110

96 97 105 96 102 108 112 112

97 95 89 104 105 109 105 113

97 86 94 102 121 112 110 115

99 84 96 97 111 107 113 112

106 97 95 103 107 110 105 110

53 89 104 103 103 106 119 111

73 74 96 112 101 108 109

Step #2: Determine Lowest Lower Limit :

At or just below the Lowest Value in the data such that It is a multiple of the class width It is a nice number with few none 0 digits and minimum # of digits in total. ie: 50 is better than 51 It is a is less than 25% of a class width fro the lowest value.

ie: if CW is 10 then it should be within 2.5 of the lowest value.

For this example 50 is the best choice (even though the last criteria is not met)

Other Lower Limits are determined by repeatedly adding the CW to this limit.

50, 60 (50+10), 70 , 80, 90, 100, 110, 12050 -

60 -

70 -80 -90 -

100

110 -

120 -


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Step #3: Determine Lowest [and subsequent Upper Limit.]

Continuous Data: use closed and open limits, [....)

Use next lower limit. under 60"

ie: 50-under 6060-under 70

Optional

Discrete Data: use the largest value that might have occurred which is less than the next Lower Limit, [ ], when data is exact or

rounded.ie: largest value less than 60 that might have occurred .. 59

50 - 59

60 - 69


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Step #1: Determine the class width (CW): 10

Step #2: Determine Lower Limits.

Step #3: Determine Lowest and subsequent Upper Limit.

Step #4: Determine the class frequencies using a tally.

CLASSES TALLY FREQ

50 under 60 // 2

60 under 70 0

70 under 80 /// 3

80 under 90 ///// // 7

90 under 100 ///// ///// ///// / 16100 under 110 ///// .... /// 33

110 under 120 ///// ///// ///// / 16

120 under 130 // 2

Frequency Distribution

Cold Cereals

Calories/Serving Number of Brands

50 to under 60 2

60 to under 70 0

70 to under 80 3

80 to under 90 7

90 to under 100 16100 to under 110 33

110 to under 1202 16

120 to under 130 2


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If you are planning to compare two or more distributions than a relative frequence distribution may be required to discount

different data sizes.

Step #5: Construct relative frequencies distributions.

- Compute relative frequencies by dividing each

frequency by the total frequency.

Freq Relative Frequency

2 2/79= .0253 or 2.53%

0 0/79 = 0 or 0% ......... ........

- Avoid doing computations with rounded values. ie:

The total % of brands might be incorrect if you sum

the rounded class %s .

Relative Frequency Distribution

Cold Cereals

Calories/Serving Percent of Brands

50 to under 60 2.53%

60 to under 70 0.00

70 to under 80 3.80

80 to under 90 8.8690 to under 100 20.25

100 to under 110 41.77110 to under 120 20.25

120 to under 130 2.53

100.0%


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If you are planning to construct one or more Ogive(s).

Step #6: Construct cumulative (less than) relative frequencies distribution(s).

- Cumulative less than percentages are associated with upper

limits. Compute cumulative relative frequencies by successively

summing unrounded relative frequencies.

Cumulative Cumulative RelativeFrequency Frequency Frequency

2 2 2/79*100 = 2.5316%

0 2 2/79*100 = 2.5316%

3 5 5/79*100 = 6.3291%7 12 12/79*100 = 15.1899%

16 28 28/79*100 = 35.4430%27 61 61/79*100 = 69.6203%

22 77 77/79*100 = 97.4684%

2 79 79/79*100 = 100.0000%

- Avoid doing computations with rounded values. ie: Using the rounded relative frequencies may cause cumulative percentages to be

incorrect.

Ogive

Cold Cereals

Cumulative (less than)

Calories/Serving Percent of Brands

up to 50 0.0 %

60 2.53

70 2.53

80 6.33

90 15.19

100 35.44

110 77.22

120 97.47

130 100.00

Frequency Distribution Lec

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