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Following table shows frequency distribution of no. of rooms occupied in a hotel per day.

No. of rooms occupied
No. of days
$0 - 10$
$5$
$10 - 20$
$27$
$20 - 30$
$17$
$30 - 40$
$11$
$40 - 50$
$9$
$50 - 60$
$1$

Find median number of rooms occupied per day in a hotel.

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29.76

27.76

23.76

21.76

answer is D.

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Detailed Solution

Given frequency distribution of no. of rooms occupied in a hotel per day is:

No. of rooms occupied	No. of days
$0 - 10$	$5$
$10 - 20$	$27$
$20 - 30$	$17$
$30 - 40$	$11$
$40 - 50$	$9$
$50 - 60$	$1$

There are total

70

days.
Hence, the median will be the mean of

35

th and

36

th day. Both of which lie in the interval

20 - 30

.
The median of grouped data is given by:
Median =

L + (\frac{\frac{n}{2} - c f_{b}}{f_{m}}) \times w

where:
L is the lower class boundary of the group = 20
n is the total number of data = 70

c f_{b}

is the cumulative frequency of the groups before the median group = 32

f_{m}

is the frequency of the median group = 17
w is the group width = 10
Hence,

\Rightarrow

Median =

20 + (\frac{\frac{70}{2} - 32}{17}) \times 10

\Rightarrow

Median =

20 + (\frac{3}{17}) \times 10

\Rightarrow

Median =

20 + 1.76

\Rightarrow

Median =

21.76

Thus, the median of the given data is 21.76.
Hence, the correct option is 4.

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Following table shows frequency distribution of no. of rooms occupied in a hotel per day.No. of rooms occupiedNo. of days0-10510-202720-301730-401140-50950-601Find median number of rooms occupied per day in a hotel.

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Following table shows frequency distribution of no. of rooms occupied in a hotel per day.

No. of rooms occupied
No. of days
$0 - 10$
$5$
$10 - 20$
$27$
$20 - 30$
$17$
$30 - 40$
$11$
$40 - 50$
$9$
$50 - 60$
$1$

Find median number of rooms occupied per day in a hotel.