For the following distribution, calculate first four central moments using recurrence
relations. Also find the coefficients of skewness and kurtosis.
| Marks: | 2.7- 7.5 | 7.5- 12.5 | 12.5- 17.5 | 17.5- 22.5 | 22.5- 27.5 | 27.5- 32.5 | 32.5- 37.5 |
| Frequency: | 06 | 13 | 23 | 39 | 19 | 15 | 05 |
To calculate the first four central moments using recurrence relations, you can follow these steps:
Step 1: Calculate the mean (µ) and the total number of data points (N).
Mean (µ) = Σ [Midpoint × Frequency] / N
N = Σ Frequency
Given the data:
Midpoints: 5.1, 10, 15, 20, 25, 30, 35
Frequencies: 6, 13, 23, 39, 19, 15, 5
Calculate N:
N = 6 + 13 + 23 + 39 + 19 + 15 + 5 = 120
Now, calculate the mean (µ):
µ = (5.1*6 + 10*13 +
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The sum of deviations of 15 value from their main is 15.
For the following distribution, calculate first four central moments using recurrence
relations. Also find the coefficients of skewness and kurtosis.
| Marks: | 2.7- 7.5 | 7.5- 12.5 | 12.5- 17.5 | 17.5- 22.5 | 22.5- 27.5 | 27.5- 32.5 | 32.5- 37.5 |
| Frequency: | 06 | 13 | 23 | 39 | 19 | 15 | 05 |
What do you mean by measures of central tendency? Also find the missing frequency for the following frequency distribution if median is given 25:
If each value of X is multiplied by 10 and each value of Y is multiplied by 20, then the modified regression coefficient 
would be the half of previous.
Why are two different lines of regression used to obtain the optimum values of two
variables X and Y. The marks of lo students of a class in Mathematics and Statistics are given below:
| Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Mathematics | 40 | 46 | 42 | 30 | 35 | 28 | 39 | 43 | 25 | 45 |
| Statistics | 35 | 41 | 36 | 32 | 42 | 48 | 29 | 38 | 28 | 40 |