The mean and standard deviation of 100 observ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given that number of observations $(n) = 100$.Incorrect mean $(\bar{x}) = 40$.Incorrect standard deviation $(\sigma) = 5.1$.We know that $\bar{x}

Vedclass · Accepted Answer

$39.9, 5$

Vedclass · Answer

(A) Given that number of observations $(n) = 100$.Incorrect mean $(\bar{x}) = 40$.Incorrect standard deviation $(\sigma) = 5.1$.We know that $\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$.$40 = \frac{1}{100} \sum_{i=1}^{100} x_i \implies \sum_{i=1}^{100} x_i = 4000$.Incorrect sum of observations $= 4000$.Correct sum of observations $= 4000 - 50 + 40 = 3990$.Correct mean $= \frac{3990}{100} = 39.9$.Also,standard deviation $\sigma = \sqrt{\frac{1}{n} \sum x_i^2 - (\bar{x})^2}$.$5.1 = \sqrt{\frac{1}{100} \sum x_i^2 - (40)^2}$.$26.01 = \frac{1}{100} \sum x_i^2 - 1600$.Incorrect $\sum x_i^2 = 100(26.01 + 1600) = 162601$.Correct $\sum x_i^2 = 162601 - (50)^2 + (40)^2 = 162601 - 2500 + 1600 = 161701$.Correct standard deviation $= \sqrt{\frac{161701}{100} - (39.9)^2} = \sqrt{1617.01 - 1592.01} = \sqrt{25} = 5$.

The mean and standard deviation of $100$ observations were calculated as $40$ and $5.1$,respectively,by a student who took by mistake $50$ instead of $40$ for one observation. What are the correct mean and standard deviation?

Similar Questions

The mean and variance of $5$ observations are $4$ and $5.2$ respectively. If three of these observations are $1, 2,$ and $6,$ find the other two observations.

The mean and standard deviation of the marks of $10$ students were found to be $50$ and $12$ respectively. Later,it was observed that two marks $20$ and $25$ were wrongly read as $45$ and $50$ respectively. Then the correct variance is $............$.

The coefficients of variation of two distributions are $60$ and $70$. The standard deviations are $21$ and $16$ respectively. Find their means.

The mean and variance of the data $4, 5, 6, 6, 7, 8, x, y$ where $x < y$ are $6$ and $\frac{9}{4}$ respectively. Then $x^{4} + y^{2}$ is equal to

The average age of a group of men and women is $30$ years. If the average age of men is $32$ years and that of women is $27$ years,what is the percentage of women in the group?

Vedclass Test Series

Exam Paper Generator

Online Exam Module