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# When comparing two box plots what should you discuss?

2 years ago

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Buck Hammes

Leon B Verified Sherpa Tutor ✓

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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.

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Shamim H Verified Sherpa Tutor ✓

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

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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,

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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.

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Paul G Verified Sherpa Tutor ✓

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1. Compare the medians
2. Compare the inter-quartile ranges
3. Compare the shapes of the distributions (symmetry, skewness)

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Neeta Verified Sherpa Tutor ✓

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Mean range min/max values skewness inter quartile range

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Richard S Verified Sherpa Tutor ✓

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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.

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Sara R Verified Sherpa Tutor ✓

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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.

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