3) 67, 100, 94, 77, 80, 62, 79, 68, 95, 86, 73, 84\nminimum : ____________ maximum : ____________\nq1…

Explanation:

Step1: Arrange data in ascending order

62, 67, 68, 73, 77, 79, 80, 84, 86, 94, 95, 100

Step2: Find the minimum value

The minimum value is the smallest number in the data - set. So, the minimum is 62.

Step3: Find the maximum value

The maximum value is the largest number in the data - set. So, the maximum is 100.

Step4: Find the median (Q2)

There are (n = 12) data points. The median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+1))th ordered values. (\frac{n}{2}=6) and (\frac{n}{2}+1 = 7). The 6th value is 79 and the 7th value is 80. So, (Q2=\frac{79 + 80}{2}=79.5).

Step5: Find Q1

The lower half of the data is 62, 67, 68, 73, 77, 79. There are (n_1=6) data points. The median of the lower half (Q1) is the average of the (\frac{n_1}{2})th and ((\frac{n_1}{2}+1))th ordered values. (\frac{n_1}{2}=3) and (\frac{n_1}{2}+1 = 4). The 3rd value is 68 and the 4th value is 73. So, (Q1=\frac{68+73}{2}=70.5).

Step6: Find Q3

The upper half of the data is 84, 86, 94, 95, 100. There are (n_2 = 6) data points. The median of the upper half (Q3) is the average of the (\frac{n_2}{2})th and ((\frac{n_2}{2}+1))th ordered values. (\frac{n_2}{2}=3) and (\frac{n_2}{2}+1 = 4). The 3rd value is 94 and the 4th value is 95. So, (Q3=\frac{94 + 95}{2}=94.5).

Answer:

Minimum: 62 Maximum: 100 Q1: 70.5 Q2: 79.5 Q3: 94.5