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. 4,5,6,8,9,9,10,12,12,12,17,17,18,18 min: q1: med: q3: max: create the box plot by dragging the lines:

Explanation:

Step1: Find the minimum value

The minimum value in the data - set $4,5,6,8,9,9,10,12,12,12,17,17,18,18$ is $4$.

Step2: Find the maximum value

The maximum value in the data - set is $18$.

Step3: Find the median (Med)

There are $n = 14$ data points. The median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{n}{2}=7$ and $\frac{n}{2}+1 = 8$. The 7th value is $10$ and the 8th value is $12$. So, $Med=\frac{10 + 12}{2}=11$.

Step4: Find the lower half of the data

The lower half of the data is $4,5,6,8,9,9,10$.

Step5: Find the first quartile (Q1)

There are $n_1=7$ data points in the lower half. The median of the lower half (Q1) is the 4th value. So, $Q1 = 8$.

Step6: Find the upper half of the data

The upper half of the data is $12,12,12,17,17,18,18$.

Step7: Find the third quartile (Q3)

There are $n_2 = 7$ data points in the upper half. The median of the upper half (Q3) is the 4th value. So, $Q3=17$.

Answer:

Min: $4$, Q1: $8$, Med: $11$, Q3: $17$, Max: $18$