Question

1,1,1,3,4,5,5,8,10,12,12,15
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
min =
q1 =
median =
q3 =
max =

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