Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Calculate the A.M. and S.D. for the following distribution: Class: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Frequency: 18 16 15 12 10 5 2 1 - Mathematics

Calculate the A.M. and S.D. for the following distribution:

Class: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency: 18 16 15 12 10 5 2 1
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Solution

Class
 

\[f_i\]
Midpoint
\[\left( x_i \right)\]
 

\[u_i = \frac{x_i - 35}{10}\]
 

\[f_i u_i\]
 

\[f_i {u_i}^2\]
0−10 18 5
 
-3
- 54
162
10−20 16 15
-2
- 32
64
20−30 15 25
-1
 
- 15
15
30−40 12 35 0 0 0
40−50 10 45 1 10 10
50−60 5 55 2 10 20
60−70 2 65 3 6 18
70−80 1 75 4 4 16
 
 

\[\sum f_i = 79\]
   
 

\[\sum f_i u_i = - 71\]
 

\[\sum f_i {u_i}^2 = 305\]
\[\bar{X} = a + h\left( \frac{\sum f_i u_i}{N} \right) = 35 + 10\left( \frac{- 71}{79} \right) = 26 . 01\]

AM = 26.01

\[\sigma^2 = h^2 \left[ \frac{\sum f_i {u_i}^2}{N} - \left( \frac{\sum f_i u_i}{N} \right)^2 \right] = 100\left[ \frac{305}{79} - \frac{5041}{6241} \right] = 305 . 20\]

\[\sigma = \sqrt{305 . 20} = 17 . 47\]

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.6 | Q 3 | Page 42
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