[PDF] Lecture 2 – Grouped Data Calculation





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1.

Mean, Median and Mode

2.

First Quantile, third Quantile

and

Interquantile

Range.

Lecture 2 - Grouped Data

Calculation

Mean - Grouped Data

Number

of orderf

10 - 12

13 - 15

16 - 18

19 - 214

12 20 14 n = 50

Number

of orderfxfx

10 - 12

13 - 15

16 - 18

19 - 214

12 20

141114

17 2044
168
340
280
n = 50= 832 fx832 x = = =16.64 n50 Example: The following table gives the frequency distribution of the nu mber of orders received each day during the past 50 days at the office of a m ail-order company. Calculate the mean.

Solution:

X is the midpoint of the

class. It is adding the class limits and divide by 2.

Median and Interquartile Range -Grouped Data

Step 1:

Construct the cumulative frequency distribution.

Step 2:

Decide the class that contain the median.

Class Median

is the first class with the value of cumulative frequency equal at least n/2.

Step 3:

Find the median by using the following formula:

Median

m m n-F2=L +if m L m f

Where:

n = the total frequency F = the cumulative frequency before class median i = the class width = the lower boundary of the class median= the frequency of the class median

Time to travel to workFrequency

1 - 10

11 - 20

21 - 30

31 - 40

41 - 508

14 12 9 7 Example: Based on the grouped data below, find the median:

Solution:

Time to travel

to workFrequencyCumulative

Frequency

1 - 10

11 - 20

21 - 30

31 - 40

41 - 508

14 12 9 78
22
34
43
50
25250
2n m f m L 1 st Step: Construct the cumulative frequency distribution class median is the 3 rd class So,

F = 22, = 12, = 20.5 and i = 10

Therefore,

2 25 22

2151012

24

Median

m m n-F =L if Thus, 25 persons take less than 24 minutes to travel to work and another 25 persons take more than 24 minutes to travel to work. 1 1 1Q Q n-F4QL+ if 3 3 3Q Q

3n-F4QL+ if

QuartilesUsing the same method of calculation as in the Median, we can get Q 1 and Q 3 equation as follows:

Time to travel to workFrequency

1 - 10

11 - 20

21 - 30

31 - 40

41 - 508

14 12 9 7 Example: Based on the grouped data below, find the Interquartile Range

Time to travel

to workFrequencyCumulative

Frequency

1 - 10

11 - 20

21 - 30

31 - 40

41 - 508

14 12 9 78
22
34
43
50
1 n50Class Q12 544. 1 1 1 4 125 8

105 1014

137143

Q Q n-F QL if

Solution:

1 st Step: Construct the cumulative frequency distribution

Class Q

1 is the 2 nd class

Therefore,2

nd

Step: Determine the Q

1 and Q 3 3

3503nClass Q37 544.

3 3 3 4

375 34

305109

343889

Q Q n-Fquotesdbs_dbs11.pdfusesText_17
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