For a statistical data $x_1, x_2, \ldots, x_{10}$ of $10$ values,a student obtained the mean as $5.5$ and $\sum_{i=1}^{10} x_i^2 = 371$. He later found that he had noted two values in the data incorrectly as $4$ and $5$,instead of the correct values $6$ and $8$,respectively. The variance of the corrected data is
- A$7$
- B$4$
- C$9$
- D$5$
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Similar Questions
The following table shows the information about marks obtained in Physics,Chemistry,Mathematics,and Biology by $100$ students in a class. Which subject shows the highest variability in marks?
Physics Chemistry Mathematics Biology Mean $20$ $25$ $23$ $27$ $S$.$D$. $3$ $2$ $4$ $5$
| Physics | Chemistry | Mathematics | Biology | |
|---|---|---|---|---|
| Mean | $20$ | $25$ | $23$ | $27$ |
| $S$.$D$. | $3$ | $2$ | $4$ | $5$ |
The diameters of circles (in mm) drawn in a design are given below:
Diameters $33-36$ $37-40$ $41-44$ $45-48$ $49-52$ No. of circles $15$ $17$ $21$ $22$ $25$
Calculate the standard deviation and mean diameter of the circles.
[ Hint : First make the data continuous by making the classes as $32.5-36.5, 36.5-40.5, 40.5-44.5, 44.5-48.5, 48.5-52.5$ and then proceed.] (in $\text{ mm}$)
| Diameters | $33-36$ | $37-40$ | $41-44$ | $45-48$ | $49-52$ |
| No. of circles | $15$ | $17$ | $21$ | $22$ | $25$ |
Calculate the standard deviation and mean diameter of the circles.
[ Hint : First make the data continuous by making the classes as $32.5-36.5, 36.5-40.5, 40.5-44.5, 44.5-48.5, 48.5-52.5$ and then proceed.] (in $\text{ mm}$)
Medium
View SolutionThe variance of the first $50$ even natural numbers is
The arithmetic mean of the observations $10, 8, 5, a, b$ is $6$ and their variance is $6.8$. Then $ab$ is equal to:
Find the mean and variance for the following frequency distribution.
Classes $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ Frequencies $5$ $8$ $15$ $16$ $6$
| Classes | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ |
| Frequencies | $5$ | $8$ | $15$ | $16$ | $6$ |
Difficult
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