Calculate the first, second and third quartile for following data:
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 05 | 15 | 30 | 12 | 08 |
Also find the quartile deviation and coefficient of quartile deviation.
To calculate the first, second, and third quartiles (Q1, Q2, Q3) for the given data, we will first find the cumulative frequency and use it to locate the quartiles.
Step 1: Data Table
| Class | Frequency (f) | Cumulative Frequency (CF) |
|---|---|---|
| 0-10 | 5 | 5 |
| 10-20 | 15 | 20 |
| 20-30 | 30 | 50 |
| 30-40 | 12 | 62 |
| 40-50 | 8 | 70 |
Step 2: Total Frequency (N)
Total frequency (N) = 5 + 15 + 30 + 12 + 8 = 70.
Step 3: Calculate the Quartiles
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First Quartile (Q1): This corresponds to the 25th percentile, so Q1 is located at:
Q1=(14×N)=14×70=17.5Q1 = \left(\frac{1}{4} \times N \right) = \frac{1}{4} \times 70 = 17.5We look
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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 |
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 |
If the regression coefficients 
of a data are 1.6 and 0.4, respectively, then the value of r(X, Y) is 0.8.
The sum of deviations of 15 value from their main is 15.
Describe the various types of measures of skewness. If the first four raw moments are 10, 100, 200 and 250 for given data then calculate the coefficients Of skewness and kurtosis.