The Following Distribution Shows The Daily Pocket Allowance Of Children Of A Locality. The Mean Pocket Allowance Is Rs 1 8. Find The Missing Frequency F.
The Following Distribution Shows The Daily Pocket Allowance Of Children Of A Locality. The Mean Pocket Allowance Is Rs 18. Find The Missing Frequency F.
Answer:
To find the missing frequency, we need to use the concept of mean (average) and formula for calculating the mean. The mean is calculated by dividing the sum of all values by the total number of values.
Given:
Class interval = Rs 16 - Rs 20
Mean (average) pocket allowance = Rs 18
Let’s assume:
Missing frequency = F
Frequency of the given class interval = 5
The formula to find the mean of grouped data is:
Mean (µ) = ∑(f * x) / N,
where
µ = mean,
f = frequency,
x = midpoint of the class interval,
N = total frequency
First, we need to calculate the midpoint of the given class interval:
Midpoint = (Lower limit + Upper limit) / 2
Midpoint = (16 + 20) / 2
Midpoint = 36 / 2
Midpoint = 18
Now, we can calculate the sum of (f * x) for the given frequencies:
5 * 18 = 90
Given that the mean is 18, and we have one missing frequency (F), we can set up the equation as:
(90 + 18F) / (5 + F) = 18
Solving this equation will give us the missing frequency:
(90 + 18F) = 18 * (5 + F)
90 + 18F = 90 + 18F
18F = 90 + 18
18F = 108
F = 6
Therefore, the missing frequency F is 6.