Answer:
B. 42, 55, 71, 87, 95
Explanation:
The five-number summary of a data set consist of the following five numbers:
- the minimum (i.e., the smallest data point),
- the lower/first quartile aka Q1 (i.e., the value under which 25% of the data fall when arranged in increasing numerical order),
- the median,
- the upper/third quartile aka Q3 (i.e., the value above which 75% of the data fall when arranged in increasing numerical order)
- and the maximum (i.e. the largest data point).
Identifying the minimum:
42 is the smallest data point, so it's the minimum.
Identifying the median:
- It's important (and perhaps necessary) to find the median before finding the lower and upper quartiles.
- Before we can find the median, we must arrange the data in increasing numerical order.
Thus, we have: 42, 45, 48, 55, 56, 63, 66, 71, 73, 77, 85, 87, 90, 94, 95.
- For a data set with an odd set of numbers, the median will have an even number.
- We see that 71 has 7 terms to the left and right of it.
Thus, 71 is the median.
Identifying the lower/first quartile (Q1):
- To find the lower/first quartile (Q1), we find the middle value of all the values smaller than the median.
- Since there 7 terms smaller than 71, this middle value will also have an even number of values to the left and right of it.
- 55 meets this requirement as it has 3 terms to the left and right of it.
Thus, the lower/first quartile (Q1) IS 55.
Identifying the upper/third quartile (Q3):
- To find the upper/third quartile (Q3), we find the middle value of all the values larger than the median.
- Since there are 7 terms smaller than 71, this middle value will also have an even number of values to the left and right of it.
- 87 meets this requirement, as it has 3 terms to the left and right of it.
Thus, the upper/third quartile (Q3) IS 87.
Identifying the maximum:
95 is the largest data point, so it's the maximum.
Since B contains the numbers 42, 55, 71, 87, and 95, which we've determined are the minimum, lower/first quartile (Q1) ,the median, the upper/third quartile (Q3), and the maximum respectively, it's the answer.