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The following data gives the age distribution of cases of a certain disease admitted during a year in a particular hospital. Calculate the mode and mean of the data given.

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mean =

35.375

, mode=36.8

mean =35.5, mode=38.71

mean =34.5, mode=39.71

mean =34, mode=38.71

answer is A.

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Detailed Solution

Given table is,
Question Image

We know,
The formula to find mode for grouped data with cumulative frequency is:

Mode = l + f 1 − f 0 2 f 1 − f 0 − f 2 × h

Where,
l is the lower limit of the modal class.

f 1

is the frequency of the modal class.

f 2

is the frequency of the class succeeding the modal class.

f 0

is the frequency of the class preceding the modal class.
h is the width of the class intervals.
And, mean is given by,

x ¯ = ∑ f i x i ∑ f i

Mode = l + f 1 − f 0 2 f 1 − f 0 − f 2 × h

Consider the table,
Question Image

The modal class of the grouped distribution is 35-44 having the highest frequency of 35.

l = 35 f 1 = 23 f 2 = 14 f 0 = 21 h = 45 − 35 ⇒ h = 10

Using the formula, substitute the values,
Question Image

Again,
Consider the table,
Question Image

The sum of frequency from the table is,

∑ f i = 6 + 11 + 21 + 23 + 14 + 5 ⇒ ∑ f i = 80

The sum of

f i x i

is:

∑ f i x i = 60 + 220 + 630 + 920 + 700 + 300 ⇒ ∑ f i x i = 2830

Therefore, mean is given by,

x ¯ = ∑ f i x i ∑ f i ⇒ x ¯ = 283080 ⇒ x ¯ = 35.375

Therefore, the mean and mode are 35.375 and 36.8 respectively.
Hence, option 1 is correct.

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