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

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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

  Is there an error in this question or solution?
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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