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. 1,2,2,2,2,3,4,4,4,5,6,8,11,14 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 $1,2,2,2,2,3,4,4,4,5,6,8,11,14$ is $1$.

Step2: Find the maximum value

The maximum value in the data - set is $14$.

Step3: Find the median (Med)

There are $n = 14$ data points. The median is the average of the $\frac{n}{2}=7$th and $(\frac{n}{2}+1) = 8$th ordered data - points. The $7$th value is $4$ and the $8$th value is $4$, so $Med=\frac{4 + 4}{2}=4$.

Step4: Find the lower half of the data

The lower half of the data is $1,2,2,2,2,3,4$. There are $n_1=7$ data points. The median of the lower half (Q1) is the $(\frac{7 + 1}{2})=4$th value, so $Q1 = 2$.

Step5: Find the upper half of the data

The upper half of the data is $4,5,6,8,11,14$. There are $n_2 = 7$ data points. The median of the upper half (Q3) is the $(\frac{7+1}{2}) = 4$th value in this sub - set, so $Q3=6$.

Answer:

Min: $1$, Q1: $2$, Med: $4$, Q3: $6$, Max: $14$