The mean and standard deviation of marks obtained by $50$ students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
Subject
Mathematics
Physics
Chemistty
Mean
$42$
$32$
$40.9$
Standard deviation
$12$
$15$
$20$
Which of the three subjects shows the highest variability in marks and which shows the lowest?
The mean and standard deviation of marks obtained by $50$ students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
| Subject | Mathematics | Physics | Chemistty |
| Mean | $42$ | $32$ | $40.9$ |
| Standard deviation | $12$ | $15$ | $20$ |
Which of the three subjects shows the highest variability in marks and which shows the lowest?
Standard deviation of Mathematics $=12$
Standard deviation of Physics $=15$
Standard deviation of Chemistry $=20$
The coefficient of variation $( C.V. )$ is given by $\frac{\text { Standard deviation }}{\text { Mean }} \times 100$
$C.V.$ (in Mathematics) $=\frac{12}{42} \times 100=28.57$
$C.V.$ (in Physics) $=\frac{15}{32} \times 100=46.87$
$C.V.$ (in Chemistry) $=\frac{20}{40.9} \times 100=48.89$
The subject with greater $C.V.$ is more variable than others.
Therefore, the highest variability in marks is in Chemistry and the lowest variability in marks is in Mathematics.
Similar Questions
Let $x_1, x_2, x_3, x_4, .......... , x_n$ be $n$ observations and let $\bar x$ be their arithmetic mean and $\sigma ^2$ be their variance.
Statement $-1$ : Variance of observations $2x_1, 2x_2, 2x_3, ......, 2x_n$ is $4\sigma ^2$ .
Statement $-2$ : Arithmetic mean of $2x _1, 2x_2, 2x_3, ......, 2x_n$ is $4\bar x$ .
Let $x_1, x_2, x_3, x_4, .......... , x_n$ be $n$ observations and let $\bar x$ be their arithmetic mean and $\sigma ^2$ be their variance.
Statement $-1$ : Variance of observations $2x_1, 2x_2, 2x_3, ......, 2x_n$ is $4\sigma ^2$ .
Statement $-2$ : Arithmetic mean of $2x _1, 2x_2, 2x_3, ......, 2x_n$ is $4\bar x$ .
The variance of $20$ observations is $5 .$ If each observation is multiplied by $2,$ find the new variance of the resulting observations.
The variance of $20$ observations is $5 .$ If each observation is multiplied by $2,$ find the new variance of the resulting observations.
The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7 hours. Find the overall standard deviation.
The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7 hours. Find the overall standard deviation.
Find the mean and variance for the following frequency distribution.
Classes
$0-30$
$30-60$
$60-90$
$90-120$
$120-150$
$50-180$
$180-210$
$f_i$
$2$
$3$
$5$
$10$
$3$
$5$
$2$
Find the mean and variance for the following frequency distribution.
| Classes | $0-30$ | $30-60$ | $60-90$ | $90-120$ | $120-150$ | $50-180$ | $180-210$ |
| $f_i$ | $2$ | $3$ | $5$ | $10$ | $3$ | $5$ | $2$ |
Let $x_1, x_2,........,x_n$ be $n$ observations such that $\sum {{x_i}^2 = 300} $ and $\sum {{x_i} = 60} $ on value of $n$ among the following is
Let $x_1, x_2,........,x_n$ be $n$ observations such that $\sum {{x_i}^2 = 300} $ and $\sum {{x_i} = 60} $ on value of $n$ among the following is