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

Age (in years)5-1515-2525-3535-4545-5555-65
Number of patients6112123145

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

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detailed solution

Correct option is A

For the modal class, let us the consider the class interval with highest frequency

Here, the greatest frequency = 23, so the modal class = 35 – 45,

l = 35,

class width (h) = 10,

fm = 23,

f1 = 21 and f2 = 14

The formula to find the mode is

Mode = l+ [(fm-f1)2fm-f1-f2]×h

Substitute the values in the formula, we get

Mode = 35+[(23-21)46-21-14]×10

Mode = 35+(2011) = 35+1.8

Mode = 36.8 year

So the mode of the given data = 36.8 year

Calculation of Mean:

First find the midpoint using the formula, xi upper limit+lower limit2

Class IntervalFrequency (fi)Mid-point (xi)fixi
5-1561060
15-251120220
25-352130630
35-452340920
45-551450700
55-65560300
 Sum fi = 80 Sum fixi = 2830

The mean formula is

Mean = x̄ =  fixi fi

283080

= 35.37 years

Therefore, the mean of the given data = 35.37 years

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detailed solution

Correct answer is 1

For the modal class, let us the consider the class interval with highest frequency

Here, the greatest frequency = 23, so the modal class = 35 – 45,

l = 35,

class width (h) = 10,

fm = 23,

f1 = 21 and f2 = 14

The formula to find the mode is

Mode = l+ [(fm-f1)2fm-f1-f2]×h

Substitute the values in the formula, we get

Mode = 35+[(23-21)46-21-14]×10

Mode = 35+(2011) = 35+1.8

Mode = 36.8 year

So the mode of the given data = 36.8 year

Calculation of Mean:

First find the midpoint using the formula, xi upper limit+lower limit2

Class IntervalFrequency (fi)Mid-point (xi)fixi
5-1561060
15-251120220
25-352130630
35-452340920
45-551450700
55-65560300
 Sum fi = 80 Sum fixi = 2830

The mean formula is

Mean = x̄ =  fixi fi

283080

= 35.37 years

Therefore, the mean of the given data = 35.37 years

Talk to our academic expert!

+91

Are you a Sri Chaitanya student?

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