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. 5, 6, 7, 7, 7, 7, 9, 10, 10, 11, 11, 15, 17, 17 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 $5,6,7,7,7,7,9,10,10,11,11,15,17,17$ is $5$.

Step2: Find the maximum value

The maximum value in the data - set is $17$.

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 7 - th value is $9$ and the 8 - th value is $10$. So, $Med=\frac{9 + 10}{2}=9.5$.

Step4: Find the lower half of the data

The lower half of the data consists of the first 7 values: $5,6,7,7,7,7,9$.

Step5: Find the first quartile (Q1)

Since there are $n_1=7$ values in the lower half, the median of the lower half (Q1) is the 4 - th value. So, $Q1 = 7$.

Step6: Find the upper half of the data

The upper half of the data consists of the last 7 values: $10,11,11,15,17,17$.

Step7: Find the third quartile (Q3)

Since there are $n_2 = 7$ values in the upper half, the median of the upper half (Q3) is the 4 - th value. So, $Q3=11$.

Answer:

Min: $5$, Q1: $7$, Med: $9.5$, Q3: $11$, Max: $17$