NCERT Exemplar Solutions Class 10 Mathematics Solutions for Statistics and Probability - Exercise 13.3 in Chapter 13 - Statistics and Probability

Question 1 Statistics and Probability - Exercise 13.3

The weight of coffee in 70 packets are shown in the following table:

Weight (in g) Number of packets
200-201 f
201-202 26
202-203 20
203-204 9
204-205 2
205-206 1

If the modal weight is 201.7 kg then find the missing frequency.

In the given data, the highest frequency is 26, which lies in the interval 201 – 202

Here, l = 201,fm = 26,f1 = 12,f2 = 20 and (class width) h = 1

\therefore \text { Mode }=1+\left(\frac{f_{m}-f}{2 f_{m}-f-f_{2}}\right) \times h \\ \left.=201+(\frac{26-f}{2 \times 26-f-20}\right) \times 1 \\

201.7=201+\frac{26-f}{32-f}

0.7=\frac{26-f}{32-f}

0.7\left(32-f\right)=26-f

22.4-0.7f=26-f

22.4-26=-f+0.7f

-3.6=-0.3f

f=12

Therefore, the missing frequency is 12.

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