Question

the test scores for a group of students are shown. 60, 69, 79, 80, 86, 86, 86, 89, 90, 100. calculate the five - number summary of the data set. please type only the number in each box. if you are not sure, write \i dont know.\ minimum = first quartile (q1) = median = third quartile (q3) = maximum = iqr =

Explanation:

Step1: Identify minimum and maximum

The data set is 60, 69, 79, 80, 86, 86, 86, 89, 90, 100. The minimum value is the smallest number, which is 60. The maximum value is the largest number, which is 100.

Step2: Calculate the median

There are $n = 10$ data - points. The median position is $\frac{n + 1}{2}=\frac{10+1}{2}=5.5$. So the median is the average of the 5th and 6th ordered data - points. $\text{Median}=\frac{86 + 86}{2}=86$.

Step3: Calculate the first quartile (Q1)

The lower half of the data set is 60, 69, 79, 80, 86. There are $n_1=5$ data - points. The position of Q1 is $\frac{n_1 + 1}{2}=\frac{5+1}{2}=3$. So Q1 is the 3rd value in the lower half, which is 79.

Step4: Calculate the third quartile (Q3)

The upper half of the data set is 86, 89, 90, 100. There are $n_2 = 5$ data - points. The position of Q3 is $\frac{n_2+1}{2}=\frac{5 + 1}{2}=3$. So Q3 is the 3rd value in the upper half, which is 90.

Step5: Calculate the inter - quartile range (IQR)

$\text{IQR}=Q3 - Q1=90 - 79 = 11$.

Answer:

Minimum = 60
First Quartile (Q1) = 79
Median = 86
Third Quartile (Q3) = 90
Maximum = 100
IQR = 11