question answer the statistical measures and create a box and whiskers plot for the following set of data…

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. 3,5,5,8,9,10,10,12,12,12,13,14,14,16 min: q1: med: q3: max: create the box plot by dragging the lines:

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. 3,5,5,8,9,10,10,12,12,12,13,14,14,16 min: q1: med: q3: max: create the box plot by dragging the lines:

Answer

Explanation:

Step1: Find the minimum value

The minimum value in the data - set $3,5,5,8,9,10,10,12,12,12,13,14,14,16$ is $3$.

Step2: Find the first quartile (Q1)

First, find the median of the lower half of the data. The data set has $n = 14$ values. The lower half of the data is $3,5,5,8,9,10,10$. The median of this set (Q1) is $\frac{5 + 8}{2}=6.5$.

Step3: Find the median (Med)

Since $n = 14$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. The $\frac{14}{2}=7$th and $8$th values are $10$ and $12$, so the median is $\frac{10 + 12}{2}=11$.

Step4: Find the third quartile (Q3)

The upper half of the data is $12,12,13,14,14,16$. The median of this set (Q3) is $\frac{13+14}{2}=13.5$.

Step5: Find the maximum value

The maximum value in the data - set is $16$.

Answer:

Min: $3$, Q1: $6.5$, Med: $11$, Q3: $13.5$, Max: $16$