Unformatted text preview: 1020
2030
3040
4050
5060
interval
Frequency
5
8
12
7
5
3
132 ∴ M0 = 20 + Solution:
HISTOGRAM
14 12 Frequency 10 8 6 4 2 0 10 20 Mode 30 40 50 60 Class Interval Daily Wages (in Rs.) Merits of Mode:
1. It is easy to calculate and in some cases it can be located
mere inspection
2. Mode is not at all affected by extreme values.
3. It can be calculated for openend classes.
4. It is usually an actual value of an important part of the
series.
5. In some circumstances it is the best representative of data.
Demerits of mode:
1. It is not based on all observations.
2. It is not capable of further mathematical treatment.
3. Mode is illdefined generally, it is not possible to find mode
in some cases.
133 4. As compared with mean, mode is affected to a great extent,
by sampling fluctuations.
5. It is unsuitable in cases where relative importance of items
has to be considered.
EMPIRICAL RELATIONSHIP BETWEEN AVERAGES
In a symmetrical distribution the three simple averages
mean = median = mode. For a moderately asymmetrical
distribution, the relationship between them are brought by Prof.
Karl Pearson as mode = 3median  2mean.
Example 34:
If the mean and median of a moderately asymmetrical series
are 26.8 and 27.9 respectively, what would be its most probable
mode?
Solution:
Using the empirical formula
Mode = 3 median − 2 mean
= 3 × 27.9 − 2 × 26.8
= 30.1
Example 35:
In a moderately asymmetrical distribution the values of
mode and mean are 32.1 and 35.4 respectively. Find the median
value.
Solution:
Using empirical Formula
1
Median = [2mean+mode]
3
1
= [2 × 35.4 + 32.1]
3
= 34.3
Exercise  6
I Choose the correct answer:
1. Which of the following represents median?
a) First Quartile
b) Fiftieth Percentile
c) Sixth decile
d) Third quartile
134 2. 3. 4. 5. 6. 7. 8. 9.
10. 11.
12.
13. If the grouped data has openend classes, one can not
calculate.
a)median b) mode
c) mean
d) quartile
1
4
Geometric mean of two numbers and is 16 25 1
1
a) b) c) 10
d) 100 10 100 In a symmetric distr...
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 Winter '08
 Moshiri
 Business, Statistics

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