13.3 Mode: The Peak of the Data

1. Identify the Modal Class: Look for the highest frequency. The maximum frequency is 18. This corresponds to the class interval 4000 – 5000. So, the Modal Class is 4000–5000.

2. Identify Parameters:

• Lower limit of modal class ($l$) = 4000
• Class size ($h$) = 1000
• Frequency of modal class ($f_1$) = 18
• Frequency of preceding class ($f_0$) = 4
• Frequency of succeeding class ($f_2$) = 9

3. Apply Formula: $\text{Mode} = 4000 + \left( \frac{18 - 4}{2(18) - 4 - 9} \right) \times 1000$

4. Calculate: Numerator: $18 - 4 = 14$ Denominator: $36 - 13 = 23$ Fraction: $14/23 \approx 0.6087$ Adjustment: $0.6087 \times 1000 = 608.7$

5. Final Addition: $4000 + 608.7 = 4608.7$

Interpretation: Most top batsmen score runs in the range close to 4608.7.