The following table shows the ages of the patients admitted in a hospital during a year.
Age (in years)
No. of patients
5-15
6
15-25
11
25-35
21
35-45
23
45-55
14
55-65
5
Find the mode and the mean of the data given above. Compare and interpret the measures of central tendency.

Question

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

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

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

Filo · Accepted Answer

Since the maximum frequency is 23 and it corresponds to the class 35−45.∴ modal class =35−45Here, xk​=35,h=10,fk​=23,fk−1​=21,fk+1​=14We know that mode M0​ is given byM0​=xk​+h2fk​−fk−1​−fk+1​fk​−fk−1​​=35+10(2(23)−21−1423−21​)=35+1110(2)​=35+1120​=35+1.8=36.8 years nearlyAgain, we have Age (in years)Number of patients (fi​)Mid-value (xi​)fi​xi​5−156106015−25112022025−35213063035−45234092045−55145070055−65560300∑fi​=80∑fi​xi​=2830Mean x=∑fi​∑fi​xi​​=802830​=8283​=35.37yearsThis shows that maximum number of patients admitted in the hospital are of the age 36.8 years while on an average the age of a patient admitted to the hospital is 35.37 years.

Age (in years)	Number of patients $(f_{i})$	Mid-value $(x_{i})$	$f_{i} x_{i}$
$5 - 15$	$6$	$10$	$60$
$15 - 25$	$11$	$20$	$220$
$25 - 35$	$21$	$30$	$630$
$35 - 45$	$23$	$40$	$920$
$45 - 55$	$14$	$50$	$700$
$55 - 65$	$5$	$60$	$300$
	$\sum f_{i} = 80$		$\sum f_{i} x_{i} = 2830$

Question Text	The following table shows the ages of the patients admitted in a hospital during a year. Find the mode and the mean of the data given above. Compare and interpret the measures of central tendency.
Answer Type	Text solution:1
Upvotes	150

The following table shows the ages of the patients admitted in a hospital during a year.
Age (in years)
No. of patients
5-15
6
15-25
11
25-35
21
35-45
23
45-55
14
55-65
5
Find the mode and the mean of the data given above. Compare and interpret the measures of central tendency.

Text solutionVerified

Practice questions from similar books

The following table shows the ages of the patients admitted in a hospital during a year.Age (in years)No. of patients5-15615-251125-352135-452345-551455-655Find the mode and the mean of the data given above. Compare and interpret the measures of central tendency.

Text solutionVerified

Practice questions from similar books

The following table shows the ages of the patients admitted in a hospital during a year.
Age (in years)
No. of patients
5-15
6
15-25
11
25-35
21
35-45
23
45-55
14
55-65
5
Find the mode and the mean of the data given above. Compare and interpret the measures of central tendency.