1 Mean, Median and Mode 2 First Quantile, third Quantile and Interquantile Range Lecture 2 – Grouped Data Calculation
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[PDF] Lecture 2 – Grouped Data Calculation
1 Mean, Median and Mode 2 First Quantile, third Quantile and Interquantile Range Lecture 2 – Grouped Data Calculation
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1.
Mean, Median and Mode
2.First Quantile, third Quantile
andInterquantile
Range.
Lecture 2 - Grouped Data
Calculation
Mean - Grouped Data
Number
of orderf10 - 12
13 - 15
16 - 18
19 - 214
12 20 14 n = 50Number
of orderfxfx10 - 12
13 - 15
16 - 18
19 - 214
12 20141114
17 2044168
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 fWhere:
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 medianTime 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 workFrequencyCumulativeFrequency
1 - 10
11 - 20
21 - 30
31 - 40
41 - 508
14 12 9 7822
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 222151012
24Median
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 Q3n-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 RangeTime to travel
to workFrequencyCumulativeFrequency
1 - 10
11 - 20
21 - 30
31 - 40
41 - 508
14 12 9 7822
34
43
50
1 n50Class Q12 544. 1 1 1 4 125 8