Question

question answer the statistical measures and create a box and whiskers plot for the following set of data. enter all values as whole numbers or decimals. 4,6,9,10,11,12,13,13,14,15,17,17,19 min: q1: med: q3: max: create the box plot by dragging the lines:

Explanation:

Step1: Find the minimum value

The minimum value of the data - set $4,6,9,10,11,12,13,13,14,15,17,17,19$ is $4$.

Step2: Find the first - quartile (Q1)

The data - set has $n = 13$ values. The position of Q1 is $\frac{n + 1}{4}=\frac{13+1}{4}=3.5$. So, Q1 is the average of the 3rd and 4th ordered values. The 3rd value is $9$ and the 4th value is $10$. Then $Q1=\frac{9 + 10}{2}=9.5$.

Step3: Find the median (Med)

The position of the median for $n = 13$ values is $\frac{n + 1}{2}=\frac{13+1}{2}=7$. So, the median is the 7th value, which is $13$.

Step4: Find the third - quartile (Q3)

The position of Q3 is $\frac{3(n + 1)}{4}=\frac{3\times(13 + 1)}{4}=10.5$. So, Q3 is the average of the 10th and 11th ordered values. The 10th value is $15$ and the 11th value is $17$. Then $Q3=\frac{15+17}{2}=16$.

Step5: Find the maximum value

The maximum value of the data - set is $19$.

Answer:

Min: $4$, Q1: $9.5$, Med: $13$, Q3: $16$, Max: $19$