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Lesson 6: Interquartile range (IQR)

# Median & range puzzlers

Sal solves an interesting median and range challenge problem.

## Want to join the conversation?

• That was the most confusing video on here! • 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.
• Range:
Range is the difference between the largest amount with the smallest amount.
Ex.

Here is the cups of lemonade Shelly sold each day
2, 5, 7, 1, 3, 4

The biggest value is 7 if you lay out the list in order, the least value is 1, so the range of this list is 6, because 7 - 1 = 6

Median:
Median is the middle number when you lay out the numbers in order.
Ex.

Here is Anna's number of lemonade cups sold on each day.
4, 9, 2, 6, 3

Here is the list if you lay out the numbers in order.
2, 3, 4, 6, 9

The middle number in the list is 4.

Mode:
Mode is the number that repeats the most in a list.
Ex.

This is Jhon's pay every day. He earns 69 dollars at max every hour. This is the amount of money he earned every hour today.
54, 23, 76, 69, 69, 69, 23, 56, 43

The number that is repeated the most is 69(intentional number).

If there was 2 or more numbers that were repeated the most the same amount, like 23, 23, 42, 42, 69, 69, the mode is 23, 42, and 69.

Mean(The worst one):
Mean is when you add every number in the list and divide it by the amount of numbers in the list.
Ex.

The list is shown below
(Sorry! There is no available story problem).
1,2,3,4,5
(This number list was chosen because it is easier to calculate mean)

Step 1: Add all the numbers, it is 15
Step 2: Divide 15 by the amount of numbers in the list, which is 5
Step 3: Divide 15 by 3, it is 5

Peace out.

All material is written by aarnav.school. Pls don't copy and comment again. This can be used in a presentation, when used, include this text.
Year written: 2023
Month written: May
Written by: aarnav.school • 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 • Can someone pls vote pls • Sal's drawing skills on point 🚘😎 • 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? • hello i have a question I need more videos I do not get this subject • 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....  