Question

5 from unit 1, lesson 9
a. what is the five - number summary for the data?
2 2 4 4 5 5 6 7 9 15

Explanation:

Step1: Sort the data (already sorted)

The data set is $2,2,4,4,5,5,6,7,9,15$.

Step2: Find the minimum

The minimum value is the first value in the sorted - set, so the minimum is $2$.

Step3: Find the first quartile ($Q_1$)

The position of $Q_1$ for a data set of size $n = 10$ is $0.25(n + 1)=0.25\times(10 + 1)=2.75$. Interpolating between the 2nd and 3rd ordered values. The 2nd value is $2$ and the 3rd value is $4$. So $Q_1=2+(4 - 2)\times0.75=2 + 1.5 = 3.5$.

Step4: Find the median ($Q_2$)

The position of the median for $n = 10$ is $0.5(n + 1)=0.5\times(10+1)=5.5$. Interpolating between the 5th and 6th ordered values. The 5th value is $5$ and the 6th value is $5$, so $Q_2=\frac{5 + 5}{2}=5$.

Step5: Find the third quartile ($Q_3$)

The position of $Q_3$ is $0.75(n + 1)=0.75\times(10 + 1)=8.25$. Interpolating between the 8th and 9th ordered values. The 8th value is $7$ and the 9th value is $9$. So $Q_3=7+(9 - 7)\times0.25=7 + 0.5 = 7.5$.

Step6: Find the maximum

The maximum value is the last value in the sorted - set, so the maximum is $15$.

Answer:

Minimum: $2$, $Q_1:3.5$, Median: $5$, $Q_3:7.5$, Maximum: $15$