
Can your lower quartile be the same as your median in a box and whisker plot? How?
Answer
463.5k+ views
Hint: To solve this question first we need to know about the box and whisker plot.
Complete step by step solution:
We know that a box plot is a graph that offers us an idea about how the values in the data should be spread. Box plot extends its lines from the boxes generally called as whiskers. Whiskers are used to indicate variability outside the upper and the lower quartile.
A box plot has a five number summary of a set of data that includes the minimum score, first quartile (lower), median, third quartile (upper) and maximum score. The lower quartile falls below 25 percent of scores and upper quartile falls below 75 percent of the scores.
Let us take an example of a dataset.
We have a sorted data as
Now, the median of the above dataset is
So we get the lower quartile of the dataset as
Now, the third quartile or upper quartile of the dataset is
Now, the five numbers summary of a set of data is
Minimum score = 1
First quartile (lower)
Median
Third quartile (upper)
Maximum score = 7
In this case we didn’t get the lower quartile the same as the median.
If we take the dataset as
Then we will get the five numbers summary of a set of data as
Minimum score = 1
First quartile (lower)
Median
Third quartile (upper)
Maximum score = 4
In this case we get the lower quartile same as the median in a box and whisker plot.
Note:
The point to be noted is that the lower quartile is the median of the lower half of the dataset. The whiskers go from each quartile to the minimum or maximum. A vertical line goes through the box at the median.
Complete step by step solution:
We know that a box plot is a graph that offers us an idea about how the values in the data should be spread. Box plot extends its lines from the boxes generally called as whiskers. Whiskers are used to indicate variability outside the upper and the lower quartile.
A box plot has a five number summary of a set of data that includes the minimum score, first quartile (lower), median, third quartile (upper) and maximum score. The lower quartile falls below 25 percent of scores and upper quartile falls below 75 percent of the scores.
Let us take an example of a dataset.
We have a sorted data as
Now, the median
So we get the lower quartile of the dataset as
Now, the third quartile or upper quartile of the dataset is
Now, the five numbers summary of a set of data is
Minimum score = 1
First quartile (lower)
Median
Third quartile (upper)
Maximum score = 7

In this case we didn’t get the lower quartile the same as the median.
If we take the dataset as
Then we will get the five numbers summary of a set of data as
Minimum score = 1
First quartile (lower)
Median
Third quartile (upper)
Maximum score = 4

In this case we get the lower quartile same as the median in a box and whisker plot.
Note:
The point to be noted is that the lower quartile is the median of the lower half of the dataset. The whiskers go from each quartile to the minimum or maximum. A vertical line goes through the box at the median.
Latest Vedantu courses for you
Grade 10 | CBSE | SCHOOL | English
Vedantu 10 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹37,300 per year
Recently Updated Pages
Master Class 10 General Knowledge: Engaging Questions & Answers for Success

Master Class 10 Computer Science: Engaging Questions & Answers for Success

Master Class 10 Science: Engaging Questions & Answers for Success

Master Class 10 Social Science: Engaging Questions & Answers for Success

Master Class 10 Maths: Engaging Questions & Answers for Success

Master Class 10 English: Engaging Questions & Answers for Success

Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Which one is a true fish A Jellyfish B Starfish C Dogfish class 10 biology CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

What is the median of the first 10 natural numbers class 10 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE
