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. 5,9,9,10,12,13,15,16,17,17 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 \(5,9,9,10,12,13,15,16,17,17\) is \(5\).

Step2: Find the maximum value

The maximum value in the data - set is \(17\).

Step3: Find the median (Med)

There are \(n = 10\) data points. The median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered values. \(\frac{n}{2}=5\) and \(\frac{n}{2}+1 = 6\). The \(5\)th value is \(12\) and the \(6\)th value is \(13\). So, \(Med=\frac{12 + 13}{2}=12.5\).

Step4: Find the lower half of the data

The lower half of the data is \(5,9,9,10,12\).

Step5: Find Q1

Since there are \(n_1=5\) values in the lower - half, the median of the lower - half (Q1) is the \(\frac{n_1 + 1}{2}\)th value. \(\frac{5+1}{2}=3\)rd value. So, \(Q1 = 9\).

Step6: Find the upper half of the data

The upper half of the data is \(13,15,16,17,17\).

Step7: Find Q3

Since there are \(n_2 = 5\) values in the upper - half, the median of the upper - half (Q3) is the \(\frac{n_2+1}{2}\)th value. \(\frac{5 + 1}{2}=3\)rd value. So, \(Q3=16\).

Answer:

Min: \(5\)
Q1: \(9\)
Med: \(12.5\)
Q3: \(16\)
Max: \(17\)