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 for the class where the cumulative frequency exceeds 17.5. The cumulative
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