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2. How many workers produced less than 23 tools? Solution:
Using sturges formula for determining the number of class
intervals, we have
Number of class intervals = 1+ 3.322 log10N
= 1+ 3.322 log10100
= 7.6
Sizes of class interval = Range
Number of class interval 46  13
7.6
5
Hence taking the magnitude of class intervals as 5, we have 7
classes 1317, 1822… 4347 are the classes by inclusive type.
Using tally marks, the required frequency distribution is obtain in
the following table
= 58 Class
Interval Tally Marks 1317
1822
2327
2832
3337
3842
4347
Total Number of
tools produced
(Frequency)
6
11
18
25
22
11
7
100 4.7 Percentage frequency table:
The comparison becomes difficult and at times impossible
when the total number of items are large and highly different one
distribution to other. Under these circumstances percentage
frequency distribution facilitates easy comparability. In percentage
frequency table, we have to convert the actual frequencies into
percentages. The percentages are calculated by using the formula
given below:
Actual Frequency
Frequency percentage =
× 100
Total Frequency
It is also called relative frequency table:
An example is given below to construct a percentage
frequency table.
Marks
010
1020
2030
3040
4050
5060
Total No. of
students
3
8
12
17
6
4
50
59 Frequency
percentage
6
16
24
34
12
8
100 4.8 Cumulative frequency table:
Cumulative frequency distribution has a running total of the
values. It is constructed by adding the frequency of the first class
interval to the frequency of the second class interval. Again add
that total to the frequency in the third class interval continuing
until the final total appearing opposite to the last class interval will
be the total of all frequencies. The cumulative frequency may be
downward or upward. A downward cumulation results in a list
presenting the number of frequencies “less than” any given amount
as revealed by the lower limit of succeeding class interval and the
upward cumulative results in a list presenting the number of
frequencies “more than” and given amount is revealed by the upper
limit of a preceding class...
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 Winter '08
 Moshiri
 Business, Statistics

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