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

(D) Given: $n = 100$,$\bar{x} = 40$,$\sigma = 5.1$.We know that $	ext{Variance} = \sigma^2 = (5.1)^2 = 26.01$.The formula for variance is $\sigma^2 =

Vedclass · Accepted Answer

$161701$

Vedclass · Answer

(D) Given: $n = 100$,$\bar{x} = 40$,$\sigma = 5.1$.We know that $	ext{Variance} = \sigma^2 = (5.1)^2 = 26.01$.The formula for variance is $\sigma^2 = \frac{\sum x_i^2}{n} - (\bar{x})^2$.Substituting the values: $26.01 = \frac{\sum x_i^2}{100} - (40)^2$.$26.01 = \frac{\sum x_i^2}{100} - 1600$.$\frac{\sum x_i^2}{100} = 1626.01$.$\sum x_i^2 = 162601$ (This is the incorrect sum of squares).To find the correct sum of squares,we subtract the square of the incorrect observation and add the square of the correct observation:$	ext{Correct } \sum x_i^2 = 162601 - (50)^2 + (40)^2$.$	ext{Correct } \sum x_i^2 = 162601 - 2500 + 1600$.$	ext{Correct } \sum x_i^2 = 161701$.

List-$I$	List-$II$
$(P)$ The mean of the above data is	$(1) 2.5$
$(Q)$ The median of the above data is	$(2) 5$
$(R)$ The mean deviation about the mean of the above data is	$(3) 6$
$(S)$ The mean deviation about the median of the above data is	$(4) 2.7$
	$(5) 2.4$

The mean and standard deviation of $100$ observations were calculated as $40$ and $5.1$ respectively. Later on,it was found that one of the observations was taken as $50$ in place of $40$. If the wrong entry is replaced by the correct one,then the sum of the squares of all the observations is:

Similar Questions

The coefficients of variation of two distributions are $60$ and $70$,and their standard deviations are $21$ and $16$,respectively. What are their arithmetic means?

The weighted mean of the first $n$ natural numbers,where the weights are equal to the squares of the corresponding numbers,is:

In a frequency distribution,if $d_i$ is the deviation of observations from $a$,and the mean is given by $\text{Mean} = a + \frac{\Sigma f_i d_i}{\Sigma f_i}$,then what is $a$?

The mean and variance of $7$ observations are $8$ and $16$ respectively. If five of the observations are $2, 4, 10, 12, 14$,find the remaining two observations.

Vedclass Test Series

Exam Paper Generator

Online Exam Module