The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
| Runs scored | Number of batsmen |
|---|---|
| 3000 - 4000 | 4 |
| 4000 - 5000 | 18 |
| 5000 - 6000 | 9 |
| 6000 - 7000 | 7 |
| 7000 - 8000 | 6 |
| 8000 - 9000 | 3 |
| 9000 - 10000 | 1 |
| 10000 - 11000 | 1 |
Find the mode of the data.
Mode = 4608.7 runs (approximately)
Explanation
This question requires finding the mode for grouped data using the standard formula. The student must first identify the modal class (the class with maximum frequency), then apply the formula Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)] × h. The modal class is 4000-5000 with frequency 18, which is the highest among all classes.
Solution Steps
Step 1: Identify the modal class. The maximum frequency is 18, corresponding to the class 4000 - 5000. So, modal class = 4000 - 5000.
Step 2: Identify the values for the formula. Lower limit (l) = 4000, Class size (h) = 1000, Frequency of modal class (f₁) = 18, Frequency of preceding class (f₀) = 4, Frequency of succeeding class (f₂) = 9.
Step 3: Apply the formula. Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)] × h = 4000 + [(18 - 4)/( - 4 - 9)] × 1000
Step 4: Calculate. Mode = 4000 + [14/(36 - 13)] × 1000 = 4000 + [14/23] × 1000 = 4000 + 608.7 = 4608.7
Step 5: Therefore, the mode of the given data is approximately 4608.7 runs.