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The following table shows the ages of the patients admitted to a hospital during a month:

Age(In years)
5-15
15-25
25-35
35-45
45-55
55-65
No. of patients
6
11
21
23
14
5

Find the mode and the mean of the data given above respectively.

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Mode = 36.81, Mean = 35.37

Mode =45.84, Mean = 32.14

Mode =78.36, Mean = 33.78

Mode =14.98, Mean = 31.89

answer is A.

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Detailed Solution

We have been given data of ages of the patients admitted to a hospital during a month.

Age(In years)	5-15	15-25	25-35	35-45	45-55	55-65
No. of patients	6	11	21	23	14	5

The frequency distribution table is as follows:
. Question Image

From the table,

∑ f 1 x i

= 2830 and

∑ f i

= 80 .
Mean is calculated by,
Mean

= ∑ f 1 x i ∑ f i

⇒ M e a n = 283080 ⇒ M e a n = 35.37

Hence, the mean = 35.37.
The maximum class frequency is 23 and the class corresponding to it is 35-45.
So the modal class is 35-45,
Lower limit of the modal class is (1)=35 and the class size is h=5000.
The frequency of the modal class is

f 1 = 23

.
Frequency of class preceding the modal class is

f 0 = 21

.
Frequency of class succeeding the modal class is

f 2 = 14

.
The mode is given by,
Mode

= 1 + f 1 − f 0 2 f 1 − f 0 − f 2

⇒ Mode = 35 + 23 − 21 2 (23) − 21 − 14 (10) ⇒ Mode = 35 + 2 46 − 35 (10) ⇒ Mode = 35 + 211 (10) ⇒ Mode = 36.81

Hence, the mode is 36.81 years and the mean is 35.37 years.
Therefore, the correct answer is option (1).

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