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The weight of coffee in 70 packets are shown in the following table
Weight (in g) Number of packets
200 - 201 12
201 - 202 26
202 - 203 20
203 - 204 9
204 - 205 2
205 - 206 1
Determine the modal weight

Solution:

Given, the weight of coffee in 70 packets.

We have to find the modal weight.

Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)]h

Where, l is the lower limit of the modal class

f₁ is the frequency of the modal class

f₀ is the frequency preceding the modal class

f₂ is the frequency succeeding the modal class

h is the class size

From the table,

Maximum frequency = 26

This frequency lies in the class 201 - 202

l = 201

h = 1

f₁ = 26

f₀ = 12

f₂ = 20

Now, f₁ - f₀ = 26 - 12 = 14

2f₁ - f₀ - f₂ = 2(26) - 12 - 20

= 52 - 32

= 20

[(f₁ - f₀)/(2f₁ - f₀ - f₂)] = 14/20

= 7/10

= 0.7

Now, mode = 201 + 0.7(1)

= 201 + 0.7

= 201.7

Therefore, the mode is 201.7 g

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

Determine the modal weight.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14

NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 18

The weight of coffee in 70 packets are shown in the following table: Weight (in g) Number of packets 200 - 201 12 201 - 202 26 202 - 203 20 203 - 204 9 204 - 205 2 205 - 206 1. Determine the modal weight

Summary:

The modal weight of coffee in 70 packets is 201.7 g

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