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

Class 11

Important Question for exams Class 11

- Chapter 1 Class 11 Sets
- Chapter 2 Class 11 Relations and Functions
- Chapter 3 Class 11 Trigonometric Functions
- Chapter 4 Class 11 Mathematical Induction
- Chapter 5 Class 11 Complex Numbers
- Chapter 6 Class 11 Linear Inequalities
- Chapter 7 Class 11 Permutations and Combinations
- Chapter 8 Class 11 Binomial Theorem
- Chapter 9 Class 11 Sequences and Series
- Chapter 10 Class 11 Straight Lines
- Chapter 11 Class 11 Conic Sections
- Chapter 12 Class 11 Introduction to Three Dimensional Geometry
- Chapter 13 Class 11 Limits and Derivatives
- Chapter 14 Class 11 Mathematical Reasoning
- Chapter 15 Class 11 Statistics
- Chapter 16 Class 11 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.