Question

In a basket there are 10 tomatoes. The weight of each of these tomatoes in grams is as follows: 60, 70, 90, 95, 50, 65, 70, 80, 85, 95. Find the median of the weights of tomatoes. Prepare a frequency distribution table of the data.

Answer 1

Hint: First, we will prepare a frequency distribution table i.e. table displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of occurrences of values within a particular group. Then we will use the formula of median for even numbers i.e. $ median=\left[ \dfrac{{{\left( \dfrac{n}{2} \right)}^{th}}term+{{\left( \dfrac{n}{2}+1 \right)}^{th}}term}{2} \right] $ where n is 10 as we have 10 tomatoes. Using this, we will get our answer.

Complete step-by-step answer:
Here, we will first prepare the frequency distribution with weight in column 1 and how many times it has occurred in the list i.e. 60, 70, 90, 50, 65, 70, 80, 85, 95.

Weight of tomatoes	Frequency
50	1
60	1
65	1
70	2
80	1
85	1
90	1
95	2

Thus, the above table is a frequency distribution table.
Now, we have to find the median of the weights. So, first we have to arrange the list in ascending order. It is given as
50, 60, 65, 70, 70, 80, 85, 90, 95, 95
Now, there are two formulas to find the median. First is for odd numbers and second is for even numbers. Here, we have a total 10 tomatoes i.e. 10 i.e. even number. So, formula will be
 $ median=\left[ \dfrac{{{\left( \dfrac{n}{2} \right)}^{th}}term+{{\left( \dfrac{n}{2}+1 \right)}^{th}}term}{2} \right] $
So, using this we will place n as 10 in the equation. We get as
 $ median=\left[ \dfrac{{{\left( \dfrac{10}{2} \right)}^{th}}term+{{\left( \dfrac{10}{2}+1 \right)}^{th}}term}{2} \right] $
On solving we get as,
 $ median=\left[ \dfrac{{{5}^{th}}term+{{6}^{th}}term}{2} \right] $
Now, we will take $ {{5}^{th}} $ and $ {{6}^{th}} $ term from the list i.e.
 $ median=\left[ \dfrac{70+80}{2} \right]=75 $
Thus, the median weight of tomatoes is 75.

Note: Sometimes students get confused regarding both the median formula of odd and even numbers and mistakes happens. For odd numbers, formula is $ median=\left[ \dfrac{{{\left( \dfrac{n}{2}+1 \right)}^{th}}term}{2} \right] $ . So, students generally apply this formula in even numbers and calculate answer to be only $ median=\left[ \dfrac{{{6}^{th}}term}{2} \right]=\dfrac{80}{2}=40 $ . Thus, the answer will be wrong. So, do not make this mistake.