Question
Calculate mean, median and mode from the following data.
| Class Interval | Frequency |
|---|---|
| 3 - 4 | 3 |
| 4 - 5 | 7 |
| 5 - 6 | 22 |
| 6 - 7 | 60 |
| 7 - 8 | 85 |
| 8 - 9 | 32 |
| 9 - 10 | 8 |
Calculate the coefficient of variation from the data given above.
Answer :
Word Count : 910
To solve this problem, we are given a grouped frequency distribution and need to calculate: 1. Mean 2. Median 3. Mode 4. Coefficient of Variation (C.V.) --- ### Step 1: Create a frequency table with class midpoints and cumulative frequencies | Class Interval | Frequency (f) | Midpoint (x) | f × x | Cumulative Frequency (CF) | | -------------- | ------------- | ------------ | ----- | ------------------------- | | 3 - 4 | 3 | 3.5 | 10.5 | 3 | | 4 - 5 | 7 | 4.5 | 31.5 | 10 | | 5 - 6 | 22 | 5.5 | 121.0 | 32 | | 6 - 7 | 60 | 6.5 | 390.0 | 92 | | 7 - 8 | 85 | 7.5 | 637.5 | 177 | | 8 - 9 | 32 | 8.5 | 272.0 | 209 | | 9 - 10 | 8 | 9.5 | 76.0 | 217 | Total Frequency (N) = 217 Total f × x = Σ(fx) = 1538.5 --- ### Step 2: Calculate the Mean $$ \text{Mean} = \frac{\Sigma f \cdot x}{\Sigma f} = \frac{1538.5}{217} \approx 7.088 $$ --- ### Step 3: Calculate the Median Median formula for grouped data: $$ \text{Median} = L + \left( \frac{\frac{N}{2} - CF}{f} \right) \cdot h $$ Where: * L = lower boundary of the median __________ __________ ______ _________ ________ _____.
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To solve this problem, we are given a grouped frequency distribution and need to calculate: 1. Mean 2. Median 3. Mode 4. Coefficient of Variation (C.V.) --- ### Step 1: Create a frequency table with class midpoints and cumulative frequencies | Class Interval | Frequency (f) | Midpoint (x) | f × x | Cumulative Frequency (CF) | | -------------- | ------------- | ------------ | ----- | ------------------------- | | 3 - 4 | 3 | 3.5 | 10.5 | 3 | | 4 - 5 | 7 | 4.5 | 31.5 | 10 | | 5 - 6 | 22 | 5.5 | 121.0 | 32 | | 6 - 7 | 60 | 6.5 | 390.0 | 92 | | 7 - 8 | 85 | 7.5 | 637.5 | 177 | | 8 - 9 | 32 | 8.5 | 272.0 | 209 | | 9 - 10 | 8 | 9.5 | 76.0 | 217 | Total Frequency (N) = 217 Total f × x = Σ(fx) = 1538.5 --- ### Step 2: Calculate the Mean $$ \text{Mean} = \frac{\Sigma f \cdot x}{\Sigma f} = \frac{1538.5}{217} \approx 7.088 $$ --- ### Step 3: Calculate the Median Median formula for grouped data: $$ \text{Median} = L + \left( \frac{\frac{N}{2} - CF}{f} \right) \cdot h $$ Where: * L = lower boundary of the median __________ __________ ______ _________ ________ _____.
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