1,1,1,3,4,5,5,8,10,12,12,15\n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15\nmin =\nq1 =\nmedian =\nq3 =\nmax =

Answer

Explanation:

Step1: Find the minimum value

The minimum value in the data - set (1,1,1,3,4,5,5,8,10,12,12,15) is the smallest number. Min = 1

Step2: Calculate the first - quartile (Q1)

First, find the position of Q1. The formula for the position of Q1 for a data - set of size (n) is (i=\frac{n + 1}{4}). Here (n = 12), so (i=\frac{12+1}{4}=3.25). The first - quartile is the value between the 3rd and 4th ordered data points. The 3rd value is 1 and the 4th value is 3. Using linear interpolation, (Q1=1+(3 - 1)\times0.25=1.5)

Step3: Calculate the median

The formula for the position of the median for a data - set of size (n) (where (n = 12), an even number) is (i=\frac{n}{2}=6) and (i + 1=7). The median is the average of the 6th and 7th ordered data points. The 6th value is 5 and the 7th value is 5. So, Median=(\frac{5 + 5}{2}=5)

Step4: Calculate the third - quartile (Q3)

The formula for the position of Q3 is (i=\frac{3(n + 1)}{4}). For (n = 12), (i=\frac{3\times(12 + 1)}{4}=9.75). The third - quartile is the value between the 9th and 10th ordered data points. The 9th value is 10 and the 10th value is 12. Using linear interpolation, (Q3=10+(12 - 10)\times0.75=11.5)

Step5: Find the maximum value

The maximum value in the data - set (1,1,1,3,4,5,5,8,10,12,12,15) is the largest number. Max = 15

Answer:

Min = 1 Q1 = 1.5 Median = 5 Q3 = 11.5 Max = 15