$A$ scientist weighs $30$ fish. Their mean weight is $30 \text{ g}$ and the standard deviation is $2 \text{ g}$. Later,it is discovered that the weighing scale was not calibrated correctly and every fish's weight was recorded $2 \text{ g}$ less than the actual weight. What are the correct mean and standard deviation (in grams) of the fish weights,respectively?
- A$28, 4$
- B$32, 2$
- C$32, 4$
- D$28, 2$
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An analysis of monthly wages paid to workers in two firms $A$ and $B$,belonging to the same industry,gives the following results:
\text{Particulars} \text{Firm } $A$ \text{ and Firm } $B$ \text{No. of wage earners} $A: 586, B: 648$ \text{Mean of monthly wages} $A: Rs. 5253, B: Rs. 5253$ \text{Variance of wages} $A: 100, B: 121$
Which firm,$A$ or $B,$ shows greater variability in individual wages?
| \text{Particulars} | \text{Firm } $A$ \text{ and Firm } $B$ |
| \text{No. of wage earners} | $A: 586, B: 648$ |
| \text{Mean of monthly wages} | $A: Rs. 5253, B: Rs. 5253$ |
| \text{Variance of wages} | $A: 100, B: 121$ |
Which firm,$A$ or $B,$ shows greater variability in individual wages?
Medium
View SolutionThe standard deviation of the following distribution is:
Class interval $0-10$ $10-20$ $20-30$ $30-40$ Frequency $1$ $3$ $4$ $2$
| Class interval | $0-10$ | $10-20$ | $20-30$ | $30-40$ |
| Frequency | $1$ | $3$ | $4$ | $2$ |
Statement-$1$: The variance of the first $n$ even natural numbers is $\frac{n^2 - 1}{4}$.
Statement-$2$: The sum of the first $n$ natural numbers is $\frac{n(n + 1)}{2}$ and the sum of the squares of the first $n$ natural numbers is $\frac{n(n + 1)(2n + 1)}{6}$.
Statement-$2$: The sum of the first $n$ natural numbers is $\frac{n(n + 1)}{2}$ and the sum of the squares of the first $n$ natural numbers is $\frac{n(n + 1)(2n + 1)}{6}$.
Easy
View SolutionIf the standard deviation of $0, 1, 2, 3, \dots, 9$ is $K$,then the standard deviation of $10, 11, 12, 13, \dots, 19$ is
Medium
View SolutionIf the mean of the frequency distribution is $28$,then its variance is $........$.
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ Frequency $2$ $3$ $x$ $5$ $4$
| Class | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ |
| Frequency | $2$ | $3$ | $x$ | $5$ | $4$ |
DifficultJEE MAIN 2023
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