NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.3

Question 18

Step 1: Identify the modal class.

The modal class is the class interval with the highest frequency. Looking at the table, the highest frequency is 26 in the class 201–202 g. So, modal class = 201–202 g.

Step 2: Write the formula for Mode.

Mode = \( l + \dfrac{(f_1 - f_0)}{2f_1 - f_0 - f_2} \times h \)

• \(l\) = lower boundary of the modal class
• \(h\) = class width
• \(f_1\) = frequency of the modal class
• \(f_0\) = frequency of the class just before the modal class
• \(f_2\) = frequency of the class just after the modal class

Step 3: Substitute the values.

• \(l = 201\,\text{g}\)
• \(h = 1\,\text{g}\)
• \(f_1 = 26\)
• \(f_0 = 12\)
• \(f_2 = 20\)

Step 4: Put into formula.

Mode = \(201 + \dfrac{(26 - 12)}{2(26) - 12 - 20} \times 1\) = \(201 + \dfrac{14}{52 - 32}\) = \(201 + \dfrac{14}{20}\) = \(201 + 0.7\) = 201.7 g

Final Answer: The modal weight of the coffee packets is approximately 201.7 g.