Question

From the given table, find the median number of rooms occupied per day in hotel.
Number of rooms occupied : 0-10
10-20
20-30
30-40
40-50
Nuber of days (f)
5
15
25
10
5

Answer 1

Answer:

Median No of rooms occupied per day = 24

Step-by-step explanation:

Given: Data in continuous frequency distribution table.

To find: Median No of rooms occupied per day

Now we use formula of median of continuous series

$Median\,=\,l+\frac{\frac{N}{2}-cf}{f}\times h$

where, l =  lower limit of median class

           cf = cumulative frequency of class preceding the median class

           f = frequency of median class

          h = height of median class

Median class is class interval whose cf is just greater than $\frac{N}{2}$.

Here in given data,

Median class :  20 - 30

l = 20 , cf = 20 , f = 25 , h = 10 , N = 60

Putting these value in formula we get

$Median\,=\,20+\frac{\frac{60}{2}-20}{25}\times10$

$Median\,=\,20+\frac{30-20}{25}\times10$

$Median\,=\,20+\frac{10}{5}\times2$

$Median\,=\,20+\frac{20}{5}$

$Median\,=\,\frac{100+20}{5}$

$Median\,=\,\frac{120}{5}$

Median = 24

Therefore, Median No of rooms occupied per day = 24