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Find the Mean and Variance of Frequency Distribution Given Below:Xi:1 ≤ X < 33 ≤ X < 55 ≤ X < 77 ≤ X < 10fi:6451 - Mathematics

Find the mean and variance of frequency distribution given below:

xi: 1 ≤ < 3 3 ≤ < 5 5 ≤ < 7 7 ≤ < 10
fi: 6 4 5 1
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Solution

xi Mid-Values(yi) yi2 fi fi yi fyi2
1–3 2 4 6 12 24
3–5 4 16 4 16 64
5–7 6 36 5 30 180
7–10 8.5 72.25 1 8.5 72.25
      `sum f_i = 16`
 

\[\sum_{} f_i y_i = 66 . 5\]
 

\[\sum_{}$ f_i {y_i}^2 = 340 . 25\]

Therefore,

Mean =

\[\frac{\sum_{} f_i y_i}{\sum_{} f_i} = \frac{66 . 5}{16} = 4 . 16\]
Variance =\[\left( \frac{1}{N} \sum_{} f_i y_i^2 \right) - \left( \frac{1}{N} \sum_{} f {}_i y {}_i \right)^2 = \frac{1}{16} \times 340 . 25 - \left( \frac{1}{16} \times 66 . 5 \right)^2 = 21 . 26 - 17 . 22 = 4 . 04\]
 

 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.6 | Q 6 | Page 42
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