What are the minimum, first quartile, median, third quartile, and maximum of the data set. 45, 76, 12, 39, 87, 65, 23, 32
To find the minimum and maximum, simply locate the smallest and largest values in the set:
Minimum: 12
Maximum: 87
To find the quartiles and median, we need to order the data and calculate the median (middle value), and then the median of the lower and upper halves (quartiles). So first we order the data:
12, 23, 32, 39, 45, 65, 76, 87
There are 8 values, so the median is the average of the fourth and fifth values:
Median: (45 + 65) / 2 = 55
Now we split the data into lower and upper halves, excluding the median:
Lower half: 12, 23, 32, 39
Upper half: 76, 87, 65
There are 4 values in the lower half, so the first quartile (Q1) is the median of the lower half:
Q1: (23 + 32) / 2 = 27.5
There are 3 values in the upper half, so the third quartile (Q3) is the median of the upper half:
Q3: (65 + 76) / 2 = 70.5
Therefore, the minimum, Q1, median, Q3, and maximum of the data set are:
Minimum: 12
Q1: 27.5
Median: 55
Q3: 70.5
Maximum: 87