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:
answer attempt 1 out of 2
you must answer all questions above in order to submit.

Explanation:

Step1: Find Min and Max

The minimum (Min) is the smallest value in the data set.
The maximum (Max) is the largest value in the data set.
For the data set \(5,9,9,10,12,13,15,16,17,17\), \(Min = 5\) and \(Max=17\).

Step2: Find the median (Med)

Since \(n = 10\) (even number of data points), the median is the average of the \(\frac{n}{2}\) - th and \((\frac{n}{2}+1)\) - th values.
\(\frac{n}{2}=\frac{10}{2} = 5\), \(\frac{n}{2}+1=6\)
The 5 - th value is \(12\) and the 6 - th value is \(13\).
\(Med=\frac{12 + 13}{2}=\frac{25}{2}=12.5\)

Step3: Find \(Q1\) and \(Q3\)

The lower half of the data is \(5,9,9,10,12\). Since \(n_1 = 5\) (odd number of data points in the lower half), \(Q1\) is the \(\frac{n_1 + 1}{2}\) - th value. \(\frac{5+1}{2}=3\) - rd value. So \(Q1 = 9\)
The upper half of the data is \(13,15,16,17,17\). Since \(n_2=5\) (odd number of data points in 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: \(17\)