Question

The following distribution shows the weekly pocket allowance (in ₹) of some children of a locality. The mean pocket allowance is ₹180. Find the value of $f$ . Hence find the mode of given data.

Approach

Use the formula for mean: $\overset{x}{ˉ} = \frac{\sum f _{i} x _{i}}{\sum f _{i}}$ . Set up the equation with total frequency $= 47 + f + y = 68$ , so $f + y = 21$ . Use the mean condition $180 = \frac{\sum f _{i} x _{i}}{68}$ and solve to get $f = 13$ , $y = 8$ . Modal class is $30 - 40$ . Mode $= l + (\frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}}) h$ , compute to get mode.

Step-by-step working

1
Set up cumulative frequency table and equations: $47 + f + y = 68 \Rightarrow f + y = 21$
1.5 marks
2
Use mean $= 180$ to set up $\sum f_{i} x_{i} = 68 \times 180 = 12240$ , solve for $f$
0.5 marks
3
Solve equations to get $f = 13$
1 mark
4
Then $y = 8$ . Modal class is $30 - 40$ (highest frequency $20$ )
1 mark
5
Mode $= 30 + (\frac{20 - 9}{40 - 9 - 14}) 10 = 30 + \frac{110}{17} \approx 36.5$ (or exact value)
1 mark

Concepts used

meanmodefrequency distributiongrouped data

Approach

Step-by-step working

Concepts used

Similar question types