The mean and standard deviation of $100$ observations $x_1, x_2, \ldots, x_{100}$ were calculated as $40$ and $5.1$ respectively by a student who took by mistake $50$ instead of $40$ for one observation. Then the correct value of $\sum_{i=1}^{100} x_i^2=$
- A$3990$
- B$161701$
- C$162601$
- D$4000$
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Consider the following data:
Daily wage (Rs.) $30$-$40$ $40$-$50$ $50$-$60$ $60$-$70$ $70$-$80$ $80$-$90$ No. of workers $17$ $28$ $21$ $15$ $13$ $6$
The coefficient of variation of the above distribution of wages,if its standard deviation is $14.72$,is
| Daily wage (Rs.) | $30$-$40$ | $40$-$50$ | $50$-$60$ | $60$-$70$ | $70$-$80$ | $80$-$90$ |
| No. of workers | $17$ | $28$ | $21$ | $15$ | $13$ | $6$ |
The coefficient of variation of the above distribution of wages,if its standard deviation is $14.72$,is
Let the mean and variance of four numbers $3, 7, x$ and $y$ $(x > y)$ be $5$ and $10$ respectively. Then the mean of four numbers $3+2x, 7+2y, x+y$ and $x-y$ is ..... .
DifficultJEE MAIN 2021
View Solution$x_1, x_2, \ldots, x_n$ are $n$ observations with mean $\bar{x}$ and standard deviation $\sigma$. Match the items of List-$I$ with those of List-$II$:
List-$I$ List-$II$ $(a) \sum_{i=1}^n(x_i-\bar{x})$ $(i) \text{ Median}$ $(b) \text{ Variance } (\sigma^2)$ $(ii) \text{ Coefficient of variation}$ $(c) \text{ Mean deviation}$ $(iii) \text{ Zero}$ $(d) \text{ Measure used to find the homogeneity of given two series}$ $(iv) \text{ Mean of the absolute deviations from any measure of central tendency}$ $(v) \text{ Mean of the squares of the deviations from mean}$
| List-$I$ | List-$II$ |
|---|---|
| $(a) \sum_{i=1}^n(x_i-\bar{x})$ | $(i) \text{ Median}$ |
| $(b) \text{ Variance } (\sigma^2)$ | $(ii) \text{ Coefficient of variation}$ |
| $(c) \text{ Mean deviation}$ | $(iii) \text{ Zero}$ |
| $(d) \text{ Measure used to find the homogeneity of given two series}$ | $(iv) \text{ Mean of the absolute deviations from any measure of central tendency}$ |
| $(v) \text{ Mean of the squares of the deviations from mean}$ |
DifficultTS EAMCET 2018
View SolutionThe mean and the variance of five observations are $4$ and $5.20,$ respectively. If three of the observations are $3, 4,$ and $4,$ then the absolute value of the difference of the other two observations is
DifficultJEE MAIN 2019
View SolutionLet $a$ and $b$ be two real numbers. If the arithmetic mean and the variance of $a, b, 8, 5$ and $10$ are respectively $6$ and $6.8$,then an ordered pair $(a, b) =$
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