Box Plot
Ms. Delgado has 25 students in her class. They all recently took their math test and the
following were the results for each student.
45, 60, 70, 70, 72, 74, 76, 78, 80, 82, 82, 84, 86, 86, 86, 88, 94, 94, 94, 94 96, 98, 98, 98,
100
Median
Since we have an odd amount of data, we need to make sure that there is an even amount
on both sides of the data. The number that separates the data evenly is then referred to as
the median.
45, 60, 70, 70, 72, 74, 76, 78, 80, 82, 82, 84, 86, 86, 86, 88, 94, 94, 94, 94 96, 98, 98, 98,
100
Q1
The Q1 of this data is found in the left side of the median. In this case we have two
numbers that are the middle numbers; therefore, we must add these two numbers. The
addition is then divided by 2, which will give us the result of 75 making it the Q1.
[45, 60, 70, 70, 72, 74, 76, 78, 80, 82, 82, 84,] 86, 86, 86, 88, 94, 94, 94, 94 96, 98, 98,
98, 100
Q3
The Q3 of this data is found on the right side of the median. Just like we had found Q1,
we will find Q3. We see that the two middle numbers from the right side are 94 and 94. If
we add them we get 188. We then divide 188 by 2. The result is 94, making it Q3.
45, 60, 70, 70, 72, 74, 76, 78, 80, 82, 82, 84, 86, [86, 86, 88, 94, 94, 94, 94 96, 98, 98, 98,
100]
IQR
In order to find the lower and upper extremes, we must first find the IQR. To do this, we
subtract the Q1 from the Q3.
IQR= Q3-Q1
94-75=19
Lower Extreme
Before find the lower extreme, we must multiply the IQR with 1.5.
19x1.5=28.5
Once we do this, we subtract the product from the Q1.
75-28.5=46.5
The result does not belong to the data; therefore, the lower extreme will be the lowest
number in the data, which will be 45.
Upper Extreme
To find the upper extreme we add the product of 19x1.5 to the Q3.
94+28.5=122.5
The result does not belong to the data; therefore, the upper extreme will be the highest
number in the data, which will be 100.
Outlier
An outlier is a piece of data or value that is widely separated from the rest of the data. If
we carefully look at the data, one can pinpoint a number that is widely separated, 45.
However, we can prove this by doing the following:
IQRx1.5
19x1.5=28.5
94+28.5=122.5 anything above this number is an outlier
75-28.5=46.5 anything below this number is an outlier
Therefore, the only outlier we have will be 45.