# Class 10 Math Sample Paper 2019 | Q22

#### Mode of Grouped data

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.

Daily Expenditure 100-150 150-200 200-250 250-300 300-350
Frequency 4 5 12 2 2

## NCERT Solution to Class 10 Maths

### 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

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