Question 1202735: Consider the following test scores in a class of 34 students:
56, 60, 60, 61, 62, 63, 65, 66, 70, 70, 72, 73, 74, 74, 75, 75, 78, 78, 79, 80, 81, 85, 86, 87, 88, 88, 89, 89, 90, 94, 99, 99, 100, 100.
What is the five-number summary?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Answer:
min = 56
Q1 = 70
median = 78
Q3 = 88
max = 100
Explanation:
The first step is to sort the data.
Luckily that has been done for us already.
There are n = 34 values in the set.
n/2 = 34/2 = 17
The middle most value is a tie between the values in slots 17 and 18. Those values are 78 and 78.
There's no need to use the midpoint formula, but you could if you wanted to.
Median = 78
We'll split the data into two subsets
L = lower set = stuff smaller than the median
U = upper set = stuff larger than the median
L = {56, 60, 60, 61, 62, 63, 65, 66, 70, 70, 72, 73, 74, 74, 75, 75, 78}
U = {78, 79, 80, 81, 85, 86, 87, 88, 88, 89, 89, 90, 94, 99, 99, 100, 100}
Set L has 17 items
17/2 = 8.5 which rounds to 9
The value in slot 9 of set L is 70
Therefore, the median of set L is 70, and it is the first quartile (Q1)
Q1 = 70
Through similar steps, the value of Q3 = 88 because it is the median of set U.
The min and max are the smallest and largest elements of the original set.
min = 56
max = 100
To wrap things up:
min = 56
Q1 = 70
median = 78
Q3 = 88
max = 100
|
|
|
