What is the range and the first and third quartiles of the data set?
14,16,12,15,22,18,16,10,12
A. 22, 12, 17
B. 22, 15, 17
C. 12, 12, 17
D. 12, 12, 15
Arrange the data either from smallest to largest or largest
to smallest, whichever you prefer.
The range is the largest number minus the smallest number.
The median (the 2nd quartile) of a set of data is either
1. the middle data value if there is one (when there is an
odd number of data values)
or
2. the average of the middle two data numbers (when there is
an even number of data values.
The 1st quartile is the median of just the data values below
the median of the entire data set.
The 3rd quartile is the median of just the data values above
the median of the entire data set.
The range is the largest number minus the smallest number.
Range = 22-10 = 12
I'll arrange the data from smallest to largest.
10
12
12
14
15
16
16
18
22
The median is 15, the number right in the middle since there
are an odd number of data values.
The numbers below 15 are
10
12
12
14
The median is 12, the average of the two middle numbers, which
happen to both be 12. So the 1st quartile is 12.
The numbers above 15 are
16
16
18
22
The median is 17, the average of the two middle numbers, which
are 16 and 18. .
So the answer is
range = 12, first quartile = 12, third quartile = 17.
That's choice C.
Edwin