Last updated at March 9, 2017 by Teachoo

Transcript

Misc 3 The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations. Let the observations be 𝑥1, 𝑥2, 𝑥3, ..., 𝑥6 and 𝑥 be their mean. Given that Mean = 𝑥 = 8, Standard deviation = 4 If each observation is multiplied by 3 , we get new observations, Let the new observations be 𝑦1, 𝑦2, 𝑦3, ..., 𝑦6 where 𝑦𝑖 = 3( 𝑥𝑖) Calculating new mean New mean = 1𝑛 𝑦𝑖 𝑦 = 16 3𝑥𝑖 𝑦 = 3 × 16 𝑥𝑖 𝑦 = 3 𝑥 𝑦 = 3 × 8 𝑦 = 24 So, New Mean = 24 Calculating new standard deviation First we find variance of the new observations i.e. New Variance = 1n ( 𝑦𝑖− 𝑦)2 Given Old Standard deviation = 4 So, Old Variance = 42 = 16 Now, Old Variance = 1𝑛 ( 𝑥𝑖− 𝑥)2 16 = 16 ( 𝑥𝑖− 𝑥)2 16 × 6 = ( 𝑥𝑖− 𝑥)2 96 = ( 𝑥𝑖− 𝑥)2 ( 𝑥𝑖− 𝑥)2 = 96 ( 13 𝑦𝑖− 13 𝑦)2 = 96 ( 13 (𝑦𝑖− 𝑦))2 = 96 132 ( 𝑦𝑖− 𝑦)2 = 96 19 ( 𝑦𝑖− 𝑦)2 = 96 ( 𝑦𝑖− 𝑦)2 = 96 × 9 ( 𝑦𝑖− 𝑦)2 = 864 So, New Variance = 1𝑛 ( 𝑦𝑖− 𝑦)2 = 16 × 864 = 144 Hence, New standard deviation = 𝑁𝑒𝑤 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 144 = 12

Indirect questions - Multiplication of observation

Chapter 15 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
- Indirect questions - Multiplication of observation
- Indirect questions - finding remaining observations
- Indirect questions - Incorrect observation

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.