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Lesson 6: Interquartile range (IQR)

# Median & range puzzlers

In a car dealership with 11 salespeople, the median number of cars sold is six, and the range of cars sold is four. This means the difference between the highest and lowest number of cars sold is four. Therefore, it's impossible for any salesperson to have sold more than 10 cars.

## Want to join the conversation?

• That was the most confusing video on here!
• What were you confused about? Maybe I can help :)
• I think that when you have an odd number of people is easy, but what about even numbers? Like in this video, it said 11 salespeople, but what about 10 salespeople? Maybe you can do a video about an even amount of people or things?
• It certainly does make the question a lot harder.
Just for fun, lets try to solve it anyway.
Instead of 11 salespersons, lets have 10!

min, _, _, _, A ,B, _, _, _ ,max

We know that (A + B)/2 = 6, so A + B = 12
We also know that the range in 4, so max - min = 4

To test the claim that at least one salesperson sold more than 10 cars, lets make the max = 11.
As, max - min = 4, min = 7

7, _, _, _, A ,B, _, _, _ ,11

The lowest possible value of A is 7 (7, 7, 7, 7, A ,B, _, _, _ ,11).
If A = 7, then B = 5 because we knew A + B =12

But B cannot be less than A, therefore the statement that at least one salesperson sold more than 10 cars is false.

The key lies in the fact that if there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.

I hope this helps.
• Sal's drawing skills on point 🚘😎
• We can have 10 as maximum, and actually we can even have 5 10 in total.
e.g. 6 6 6 6 6 6 10 10 10 10 10
Median is 6
Range is 4
• I think you could be right
(1 vote)
• I’m still confused :D
• Can't we use this method? We know the median equals (min+max)/2 so (min+max)/2 = 6 => min + max = 12
and we know the range = max - min. and the range is 4. so max = 4 + min. so we have two equations. min + max =12 and max = 4 + min. If we substitute in place of max we will have. min + 4 + min =12 =>2min=8 => min = 4 and max = 8. now we have the exact number. isn't this a more efficient way?
• I wonder if ur still active on khan bc this was a while ago
• Why does the video have to be like 7 minutes long when on the lesson only has 4 questions.
• hello i have a question I need more videos I do not get this subject
• sal is an npc
• if minimum data is 6, max will be 10(bcz range is 4)
if min is 5 ,max will be 9
if min 4 , max will be 10

the max will be more than 10 only, if that minimun value is more than 6.
but that's impossible bcz we have median value 6(so that is impossible minimum value >=6 hence we never get number more than 10)

finally remember the statement they asked more than 10....