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I have two categories of DVDs: 'Feature Films' and 'Children's Film and TV'. The IQRs of their prices are £6.50 and £3.50 respectively.

What would the interquartile range show overall?

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    $\begingroup$ Ask yourself, what is IQR? How do you define and calculate it? That might lead you to a good answer. $\endgroup$ Commented Mar 10, 2016 at 14:45
  • $\begingroup$ It's a measure of dispersion! One of many, actually. $\endgroup$
    – JohnK
    Commented Mar 10, 2016 at 16:12

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As Greenparker pointed out, understanding what the IQR is generally is 90% of your answer here.

What it describes is the range between the 1st and the 3rd quartile (i.e. the point at which 25% of values are lower and the point where 75% of values are lower)

In the movie case, the range alone tells you exactly that: 50% of movies lie within price differences of 6.50 and 3.50 respectively.

Together with concrete values for your quartiles (and additionally the median) it describes roughly how your DVD prices are distributed.

Let's say the median price of a DVD is 10, the 1st quartile is 8 and the 3rd quartile is 14.50 (IQR = 6.50). Then that means that 25% of your DVDs cost less than 8, 25% cost between 8 and 10, 25% between 10 and 14.50 and 25% are more expensive than that.

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Just a single IQR value is not that much interpretable. Though when you're comparing two IQR values obtained from two data which have the same units, as in your case is £ or price basically, then here's the conclusion you can make.

  • "Feature Films" which has higher IQR than that of "Children's Film and TV", so you can say that, it's more likely that the price for "Feature Films" will vary much as compared to "Children's Film and TV".

  • Certainly, one reason might be because "Feature Films" is likely to have more variety of films "Children's Film and TV". (Not necessarily thought)

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