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

Which of the following are correct measures for the given data?

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Mode

= 38.8

, Mean

= 33.37

Mode

= 36.8

, Mean

= 35.37

Mode

= 35.8

, Mean

= 36.37

Mode

= 38.6

, Mean

= 37.35

answer is B.

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Detailed Solution

It is given the ages of the patients admitted in a hospital during a year.
Question Image

We convert the data in terms of the following expression.

x_{i} = \frac{lower limit + upper limit}{2}

Class Interval	$x_{i}$	$(f_{i})$	${(x}_{i}) \times (f_{i}) = (x_{i} f_{i})$
5 - 15	10	6	60
15 - 25	20	11	220
25 - 35	30	21	630
35 - 45	40	23	920
45 - 55	50	14	700
55 - 65	60	5	300
		$Σ f_{i} = 80$	$Σ f_{i} x_{i} = 2830$

From the table, we get

Σ f_{i} = 80

Σ f_{i} x_{i} = 2830

We know that,

Mean = \frac{Σ x_{i} f_{i}}{Σ f_{i}}

\Rightarrow Mean = \frac{2830}{80}

\Rightarrow Mean = 35.37

We also know that,
Mode

= l + \frac{f - f_{1}}{2 f - f_{1} - f_{2}} \times h

Where:

l \to

lower limit of the modal class

f \to

frequency of the modal class

f_{1} \to

frequency of the class preceding the modal class

f_{2} \to

frequency of the class succeeding the modal class

h \to

class width
From the given table, we get that the maximum frequency is

23

and the corresponding class is

35 - 45

. Therefore,

35 - 45

is the modal class.
According to the situation,

l = 35, h = 10, f = 23, f_{1} = 21

and

f_{2} = 14

Putting the values in the formula, we get

Mode = 35 + \frac{23 - 21}{46 - 21 - 14} \times 10

\Rightarrow Mode = 35 + \frac{2}{11} \times 10

\Rightarrow Mode = 35 + \frac{20}{11}

\Rightarrow Mode = 35 + 1.81

\Rightarrow Mode = 36.81

Therefore, the mode of the given frequency distribution is 36.81 and the mean is 35.37.
Hence, the correct option is 2.

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The following table gives the ages of the patients admitted in a hospital during a year. Which of the following are correct measures for the given data?

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

Which of the following are correct measures for the given data?