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Find the mean and variance of frequency distribution given below:
| xi: | 1 ≤ x < 3 | 3 ≤ x < 5 | 5 ≤ x < 7 | 7 ≤ x < 10 |
| fi: | 6 | 4 | 5 | 1 |
Concept: undefined >> undefined
The weight of coffee in 70 jars is shown in the following table:
| Weight (in grams): | 200–201 | 201–202 | 202–203 | 203–204 | 204–205 | 205–206 |
| Frequency: | 13 | 27 | 18 | 10 | 1 | 1 |
Determine the variance and standard deviation of the above distribution.
Concept: undefined >> undefined
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Mean and standard deviation of 100 observations were found to be 40 and 10 respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.
Concept: undefined >> undefined
Two plants A and B of a factory show following results about the number of workers and the wages paid to them
| Plant A | Plant B | |
| No. of workers | 5000 | 6000 |
| Average monthly wages | Rs 2500 | Rs 2500 |
| Variance of distribution of wages | 81 | 100 |
In which plant A or B is there greater variability in individual wages?
Concept: undefined >> undefined
The means and standard deviations of heights ans weights of 50 students of a class are as follows:
| Weights | Heights | |
| Mean | 63.2 kg | 63.2 inch |
| Standard deviation | 5.6 kg | 11.5 inch |
Which shows more variability, heights or weights?
Concept: undefined >> undefined
Coefficient of variation of two distributions are 60% and 70% and their standard deviations are 21 and 16 respectively. What are their arithmetic means?
Concept: undefined >> undefined
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 | Chemistry |
| 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?
Concept: undefined >> undefined
From the data given below state which group is more variable, G1 or G2?
| Marks | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| Group G1 | 9 | 17 | 32 | 33 | 40 | 10 | 9 |
| Group G2 | 10 | 20 | 30 | 25 | 43 | 15 | 7 |
Concept: undefined >> undefined
Find the coefficient of variation for the following data:
| Size (in cms): | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 |
| No. of items: | 2 | 8 | 20 | 35 | 20 | 15 |
Concept: undefined >> undefined
If X and Y are two variates connected by the relation
Concept: undefined >> undefined
In a series of 20 observations, 10 observations are each equal to k and each of the remaining half is equal to − k. If the standard deviation of the observations is 2, then write the value of k.
Concept: undefined >> undefined
If each observation of a raw data whose standard deviation is σ is multiplied by a, then write the S.D. of the new set of observations.
Concept: undefined >> undefined
If v is the variance and σ is the standard deviation, then
Concept: undefined >> undefined
\[\lim_{x \to a} \frac{\log x - \log a}{x - a}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{\log \left( a + x \right) - \log \left( a - x \right)}{x}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{\log \left( 2 + x \right) + \log 0 . 5}{x}\]
Concept: undefined >> undefined
The standard deviation of the data:
| x: | 1 | a | a2 | .... | an |
| f: | nC0 | nC1 | nC2 | .... | nCn |
is
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{x\left( 2^x - 1 \right)}{1 - \cos x}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{\sqrt{1 + x} - 1}{\log \left( 1 + x \right)}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{\log \left| 1 + x^3 \right|}{\sin^3 x}\]
Concept: undefined >> undefined
