Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Need explanation for: - If mean and standard deviation of 5 observation are 10 and 3, respectively, then the variance of 6 - Statistics and Probability - JEE Main

If mean and standard deviation of 5 observation x_{1},x_{2},x_{3},x_{4},x_{5} are 10 and 3, respectively, then the variance of 6 obeservation x_{1},x_{2},--------,x_{5}and -50 is equal to:

 

  • Option 1)

    586.5

  • Option 2)

    582.5

  • Option 3)

    507.5

  • Option 4)

    509.5

Answers (1)

best_answer

 

ARITHMETIC Mean -

The arithmetic mean is defined as the sum of items divided by the number of items.

-

 

 

ARITHMETIC Mean -

For the values x1, x2, ....xn of the variant x the arithmetic mean is given by 

\bar{x}= \frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}

in case of discrete data.

-

 

 

Standard Deviation -

If x1, x2...xn are n observations then square root of the arithmetic mean of 

\sigma = \sqrt{\frac{\sum \left ( x_{i}-\bar{x} \right )^{2}}{n}}

\bar{}

- wherein

where \bar{x} is mean

 

 

Variance -

In case of discrete data 

\dpi{100} \sigma ^{2}= \left ( \frac{\sum x_{i}^{2}}{n} \right )-\left ( \frac{\sum x_{i}}{n} \right )^{2}

-

 

  As we have learnt from the concept 

mean =\bar{x}=\frac{\sum x_{i}}{5}=10

\sum_{i=1}^{5}x_{i}=50

S.D. =\sqrt{\frac{\sum_{i=1}^{5}x_{i}^{2}}{5}-(\bar{x})^{2}}=8

=>\sum_{i=1}^{5}(x_{i})^{2}=109

Variance = \frac{\sum_{i=1}^{5}(x_{i})^{2}+(-50)^{2}}{6}-(\sum_{i=1}^{5}\frac{x_{i}-50}{6})^{2}

              = 507.5

 


Option 1)

586.5

Option 2)

582.5

Option 3)

507.5

Option 4)

509.5

Posted by

admin

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025: BTech CSE cut-offs for PwD candidates at NITs make entry easy; top institutes still selective
anam-khan

73 or 99 percentile? JEE Main result questioned, J-K candidate says, ‘Don’t create hype’
anam-khan

JEE Main 2025: 11 from Kota coaching centres among 24 students with 100 percentile

Latest Question