Answer: The median speed is 12 mph
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Explanation:
Check out the attached image. The image I posted is a mark-up of what you posted.
I added on annotations marking the x and y values of each point.
Along the x axis, I've marked the following: 5, 12, 20, 30, 42
Along the y axis, I've marked the following: 11, 21, 22, 29, 40
The x axis represents speeds in mph
The y axis is the cumulative frequency
Notice the highest point is when y = 40 (shown in orange). So the cumulative frequency is 40. All of the frequencies add up to 40. Put another way: there are 40 speed values recorded (5 unique speeds)
Divide 40 by 2: 40/2 = 20
The result of 20 means that we can split the 40 speeds into two groups
Group L = Lower half
Group U = upper half
In group L, we'll have the values that are below the median. They consist of the speeds 5mph and 12mph
This is because the cumulative frequency y = 21 corresponds to x = 12. So y = 20 is fairly close. We'll leave out that one copy of 12 and put it in group U
Here's what group L looks like
{
5,5,5,5,5,5,5,5,5,5,5
12,12,12,12,12,12,12,12,12
}
There are 11 copies of '5' in that set, plus another 9 copies of '12'
So 11+9 = 20 values total
Here's what group U looks like
{
12
20
35,35,35,35,35,35,35
42,42,42,42,42,42,42,42,42,42,42
}
I've broken up the set to make it more readable. Usually all the values are on the same line. There is one copy of 12, one copy of 20, seven copies of 35 and eleven copies of 42. The total frequency of group U is 1+1+7+11 = 2+18 = 20.
The median will happen exactly at the midpoint. So it will be located between the edges of group L and group U
The edges of those two groups are 12 each
So the median is between 12 and 12, making the median itself to be 12.
To be more technical, the midpoint of a = 12 and b = 12 is
(a+b)/2 = (12+12)/2 = 24/2 = 12
So this shows why the median speed is 12 mph
