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# The following table shows the ages of the patients admitted in a hospital during a year - CBSE Class 10 - Mathematics

#### Question

The following table shows the ages of the patients admitted in a hospital during a year:

 age (in years) 5 − 15 15 − 25 25 − 35 35 − 45 45 − 55 55 − 65 Number of patients 6 11 21 23 14 5

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

#### Solution

To find the class marks (xi), the following relation is used.

x_i  = ("Upper class limit + Lower class limit")/2

Taking 30 as assumed mean (a), di and fidiare calculated as follows.

 Age (in years) Number of patients fi Class mark xi di = xi − 30 fidi 5 − 15 6 10 − 20 − 120 15 − 25 11 20 − 10 − 110 25 − 35 21 30 0 0 35 − 45 23 40 10 230 45 − 55 14 50 20 280 55 − 65 5 60 30 150 Total 80 430

From the table, we obtain

sumf_i = 80

sumf_iu_i = 430

"Mean " barx = a+ ((sumf_iu_i)/(sumf_i))xh

= 30+(430/80)

= 30+5.375

= 35.375

= 35.38

Mean of this data is 35.38. It represents that on an average, the age of a patient admitted to hospital was 35.38 years.

It can be observed that the maximum class frequency is 23 belonging to class interval 35 − 45.

Modal class = 35 − 45

Lower limit (l) of modal class = 35

Frequency (f1) of modal class = 23

Class size (h) = 10

Frequency (f0) of class preceding the modal class = 21

Frequency (f2) of class succeeding the modal class = 14

Mode = l + ((f_1-f_0)/(2f_1-f_0-f_2)xh)

= 35+((23-21)/(2(23)-21-14))xx10

=35+[2/(46-35)]xx10

= 35+20/11

= 36.8

Mode is 36.8. It represents that the age of maximum number of patients admitted in hospital was 36.8 years

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#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 14: Statistics
Ex.14.20 | Q: 1 | Page no. 275
NCERT Solution for Mathematics Textbook for Class 10 (2018 to Current)
Chapter 14: Statistics
Ex.14.20 | Q: 1 | Page no. 275
Solution The following table shows the ages of the patients admitted in a hospital during a year Concept: Mode of Grouped Data.
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