The following values are calculated in respect of heights and weights of the students of a section of Class $\mathrm{XI}:$
Height | Weight | |
Mean | $162.6\,cm$ | $52.36\,kg$ |
Variance | $127.69\,c{m^2}$ | $23.1361\,k{g^2}$ |
Can we say that the weights show greater variation than the heights?
To compare the variability, we have to calculate their coefficients of variation.
Given $\quad$ Variance of height $=127.69 cm ^{2}$
Therefore Standard deviation of height $=\sqrt{127.69} cm =11.3 cm$
Also $\quad$ Variance of weight $=23.1361 kg ^{2}$
Therefore Standard deviation of weight $=\sqrt{23.1361} kg =4.81 kg$
Now, the coefficient of variations $(C.V.)$ are given by
$(C.V.)$ in heights $=\frac{\text { Standard } \text { Deviation }}{\text { Mean }} \times 100$
$=\frac{11.3}{162.6} \times 100=6.95$
and $\quad$ $(C.V.)$ in weights $=\frac{4.81}{52.36} \times 100=9.18$
Clearly $C.V.$ in weights is greater than the $C.V.$ in heights
Therefore, we can say that weights show more variability than heights
Consider three observations $a, b$ and $c$ such that $b = a + c .$ If the standard deviation of $a +2$ $b +2, c +2$ is $d ,$ then which of the following is true ?
If the variance of the frequency distribution is $160$ , then the value of $\mathrm{c} \in \mathrm{N}$ is
$X$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ |
$f$ | $2$ | $1$ | $1$ | $1$ | $1$ | $1$ |
Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of $100$ consecutive positive integers $a _1, a _2, a _3, \ldots ., a _{100}$ is $25$. Then $S$ is
The mean and standard deviation of $15$ observations were found to be $12$ and $3$ respectively. On rechecking it was found that an observation was read as $10$ in place of $12$ . If $\mu$ and $\sigma^2$ denote the mean and variance of the correct observations respectively, then $15\left(\mu+\mu^2+\sigma^2\right)$ is equal to$...................$
Consider the statistics of two sets of observations as follows :
Size | Mean | Variance | |
Observation $I$ | $10$ | $2$ | $2$ |
Observation $II$ | $n$ | $3$ | $1$ |
If the variance of the combined set of these two observations is $\frac{17}{9},$ then the value of $n$ is equal to ..... .