Question

The following table shows the number of coffees made for each hour that the coffee shop was open over $2$ days. Find the median class.

Number of Cappuccinos	Frequency
$0 - 3$	$2$
$4 - 7$	$3$
$8 - 11$	$8$
$12 - 15$	$3$
$16 - 19$	$2$

${\text{(A) 0 - 3}}$
${\text{(B) 12 - 15}}$
${\text{(C) 16 - 19}}$
${\text{(D) 8 - 11}}$

Answer 1

Hint: Here, in the question the given data is already arranged in ascending order; then we find the total frequency and then we will use the formula of median to calculate the median class.
Finally we get the required answer.

Formula used: \[{\text{Median class = }}\dfrac{{{\text{Total frequency + 1}}}}{{\text{2}}}\]

Complete step-by-step solution:
From the question we know the number of coffees made per hour, since we know the frequency of the coffees made each hour, we can calculate the total number of coffees made.
To find the total number of coffees made we have to all the frequencies therefore, it can be done as:
${\text{total frequency = 2 + 3 + 8 + 3 + 2}}$
It can be added the term as:
${\text{total frequency = 18}}$
The total frequency represents the total number of coffees made which is $n$therefore,
$n = 18$
Now we will find the median using the formula:
\[{\text{Median class = }}\dfrac{{{\text{Total frequency + 1}}}}{{\text{2}}}\]
On substituting the value of $n$ as $18$ we get:
${\text{Median Class = }}\dfrac{{{\text{18 + 1}}}}{{\text{2}}}$
On adding the numerator term we get:
${\text{Median Class}} = \dfrac{{19}}{2}$
Thus, ${\text{Median Class}} = 9.5$
Hence, the median class of $9.5$ lies between the class $8 - 11$ the median class is $8 - 11$

Hence the correct option is \[\left( D \right)\]

Note: Median is a measure of central tendency just like mean and mode, median helps to find the middle value of a distribution.
It is usually used when there are extreme values in the distribution or when using mean will result in an error.
Median can also be calculated by using the graph; a cumulative frequency curve also called an ogive can be used to calculate the median of a distribution.
The formula for finding median is:
\[{\text{Median = }}{\left[ {\dfrac{{{\text{n + 1}}}}{{\text{2}}}} \right]^{th}}{\text{ term if n is odd}}\]
\[{\text{or, Median = }}\left[ {\dfrac{{{{\left[ {\dfrac{{\text{n}}}{{\text{2}}}} \right]}^{th}}{\text{ term + }}{{\left[ {\dfrac{{\text{n}}}{{\text{2}}} + 1} \right]}^{th}}{\text{ term}}}}{{\text{2}}}} \right]{\text{ if n is even}}\]
Since there are no concrete values given and only the range is provided, calculating the actual median is not possible in these types of distributions.
Where $n$ represents the total number of terms in the distribution