Maths

>

A-Level

>

Statistical Sampling

>

When compa...

Question
# When comparing two box plots what should you discuss?

2 years ago

·

7 Replies

·

1989 views

B

Buck Hammes

7 Answers

Leon B
Verified Sherpa Tutor ✓

Here to support the next generation of Mathematicians

The main things you will need to discuss are the Median, Interquartile range(IQR) and the quartiles. You must attach numerical values to these points of interest and provide context with your answers if you are provided with a scenario.

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
Shamim H
Verified Sherpa Tutor ✓

Experienced Maths Teacher (16 yrs) & Examiner for 2 Major Exam Boards

29 reviews

Look for average (median) compare the 2 box plots and comment on the expected result for the 2 box plots. you may also comment on LQ and UQ. Comment on consistency by mentioning the range and IQR to states which Box plot holds consistent data,

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
Callum J
Verified Sherpa Tutor ✓

Professional Maths & Physics tutor with a decade of experience (MEng)

Boxplots can be very handy for making comparisons between data sets, so knowing what to look for is really useful!

Let's start in the middle and work our way out:

The line in the middle of the box shows the 'median', which is the middle value of the data (once it has been arranged into it's correct order). Comparing the two median values from two different box plots tells us which data has the highest/lowest middle point.

Then we have the edges of the box. The first (left hand) edge is known as the 'lower quartile' or Q1 and the next (right hand) edge is known as the 'upper quartile' or Q3. Comparing the positions of the upper and lower quartiles from each data set can be useful, but what is often even more useful is comparing the 'inter-quartile range'.

You can calculate the inter-quartile range by subtracting the value Q1 from Q3. The interquartile range tells us the spread of the middle part of the data, which can be a bit more reliable than the spread, since it does not include any potential outliers.

Finally we have the end points (sometimes called whiskers!). These tell you the first and last data points, which you can use to work out the spread of the data by subtracting the value of the first whisker from the value of the last whisker. The range of the data sets is another thing to discuss when comparing two data sets.

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
Paul G
Verified Sherpa Tutor ✓

Very experienced A-level Maths & Further Maths teacher

9 reviews

- Compare the medians
- Compare the inter-quartile ranges
- Compare the shapes of the distributions (symmetry, skewness)

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
Neeta
Verified Sherpa Tutor ✓

Qualified GCSE & A Level Maths teacher and examiner - Great to meet you!

Mean range min/max values skewness inter quartile range

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
Richard S
Verified Sherpa Tutor ✓

Highly experienced teacher who inspires a love for Mathematics

1 reviews

Basically these questions are usually for 2 marks.

1 mark is for comparing the medians- write your statement in the context of the problem eg, set A has a higher median therefore they are better at Maths as on average they scored higher.

1 mark is for comparing the Inter quartile Range - a lower IQR would mean the data is less spread and therefore more consistent.

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
Sara R
Verified Sherpa Tutor ✓

Experienced Maths iGCSE & A-level teacher & tutor

3 reviews

Hi Buck,

As a general rule, I would always compare the medians and the Inter Quartile Ranges. State which is larger/smaller for each measure. This is usually sufficient for 2 marks.

If there are not two obviously distinct differences with the medians and IQRs, look to see if there is any difference in the overall ranges, or shapes of the distributions.

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.Think you can help?

More Maths A-Level Questions
##
Need
an A-Level
Maths
tutor?

Get started with a free online introductions with an experienced and qualified online tutor on Sherpa.

Find an A-Level Maths Tutor