Class 10 Math Sample Paper 2019 | Q22

This 2019 CBSE class 10 Maths 3 mark question is from Statistics. Concept: Computing Mode of grouped data.

Question 22: The table shows the daily expenditure on grocery of 25 households in a locality. Find the modal daily expenditure on grocery by a suitable method.

Video Explanation

Explanatory Answer | 2019 Sample Paper Question 22

Step 1: Identify Modal class

The maximum class frequency is 12.
The class corresponding to this frequency is 200 – 250.
So, the modal class is 200 – 250.

Formula used to Compute Mode of Grouped Data

Mode = l + [ \\frac{f_1 – f_0}{2f_1 – f_0 − f_2}) ] × h
Where l is the lower limit of the modal class & h is the size of the class
f₁ is the frequency of the modal class
f₀ is the frequency of the preceding class
f₂ is the frequency of the succeeding class

Modal class = 200 – 250, lower limit (l) of modal class = 200, class size (h) = 50
frequency (f₁) of the modal class = 12
frequency (f₀) of class preceding the modal class = 5
frequency (f₂) of class succeeding the modal class = 2

Step 2: Calcuate the Modal Expenditure

Now, let us substitute these values in the formula:
Mode = l + [ \\frac{f_1 – f_0}{2f_1 – f_0 − f_2}) ] × h ⇒ 200 + \\frac{12 – 5}{2 × 12 – 5 − 2}) × 50
⇒ 200 + \\frac{7}{17}) × 50 ⇒ 220.59
Hence, the modal daily expenditure on grocery = 220.59