Mean, Median, Mode, Quartiles for continuous series data, Worked out example Question, See Questions with Answers
Mean (Arithmetic Mean)
The mean (or average) is the sum of all data values divided by the number of values. It is represented by \(\bar{X}\). The mean can be calculated by two methods.
1. Direct Method
Formula for Continuous Data:
\(\begin{aligned}
& \bar{X} = \frac{\sum f m}{N}
\end{aligned}\)
where:
- \( m \) = Midpoint of each class interval
- \( f \) = Frequency of each class
- \( \sum f m \) = Sum of the product of midpoints and frequencies
- \( \sum f = N \) = Total frequency
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2. Indirect Method
Formula for Continuous Data:
\(\begin{aligned}
\bar{X} = A + \frac{\sum fd}{N}
\end{aligned}\)
where:
- \( A \) = Assumed Mean
- \( d = m - A \) = Difference of Midpoint and Assumed mean
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Example Questions
Q. Find the mean of the following data.
Marks
10-20
20-30
30-40
40-50
50-60
60-70
No. of Students
3
5
6
7
4
2
Solution:
Marks
Students (\( f \))Â
Mid-Point (\( m \))Â
\( f \times m \)Â
10-20
3
15
45
20-30
5
25
125
30-40
6
35
210
40-50
7
45
457
50-60
4
55
220
60-70
2
65
130
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\(\sum f = N =27\)
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\(\sum fm =1187 \)
Now, we have,
\(\bar{X} = \frac{\sum f m}{N}\)
\(or, \bar{X} = \frac{1187}{27}\)
\(\therefore \bar{X} = 43.96\) (Answer)
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Median
The median is the middle value when the data is arranged in order. It is represented by \(M_d\).
- \( cf \) = Cumulative frequency before the median class
- \( f \) = Frequency of the median class
- \( h \) = Class width
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Mode
The mode of a data set is the data with the highest frequency. For continuous data, the mode is the most frequently occurring class. It is represented by \(M_o\).
Class 10: Mathematics
