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Example 13 - Chapter 13 Class 11 Statistics
Last updated at May 8, 2024 by Teachoo
Indirect questions - Multiplication of observation
Chapter 13 Class 11 Statistics
Concept wise
- Mean deviation about mean - Ungrouped
- Mean deviation about mean - Discrete Frequency
- Mean deviation about mean - Continuous frequency distibution
- Mean deviation about median - Ungrouped
- Mean deviation about median - Discrete Frequency
- Mean deviation about median - Continuous frequency distibution
- Standard deviation and variance - Ungrouped data
- Standard deviation and variance - Discrete frequency (grouped data)
- Standard deviation and variance - Continuous frequency (grouped data)
- Co-efficient of variation
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Indirect questions - Multiplication of observation
- Indirect questions - finding remaining observations
- Indirect questions - Incorrect observation
Transcript
Example 13 The variance of 20 observations is 5. If each observation is multiplied by 2, find the new variance of the resulting observations. Let the observations be 1 , 2 , 3 , ..., 20 and be their mean. Given that Variance = 5 and n = 20. We know that Variance = 1 n ( ) 2 5 = 1 20 ( ) 2 5 20 = ( ) 2 100 = ( ) 2 ( ) 2 = 100 If each observation is multiplied by 2 , we get new observations, Let the new observations be 1 , 2 , 3 , ..., 20 where = 2 ( ) We need to find variance of the new observations i.e. New Variance = 1 n ( ) 2 Now, We know = 2 ( ) Calculating in terms of = 1 = 1 20 2 = 2 ( 1 20 ) = 2 From (1) ( ) 2 = 100 ( 1 2 1 2 ) 2 = 100 ( 1 2 ( )) 2 = 100 1 2 2 ( ) 2 = 100 1 2 2 ( ) 2 = 100 ( ) 2 = 100 4 ( ) 2 = 400 Now, New Variance = 1 n ( ) 2 = 1 20 400 = 20
