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.
2, 3, 6, 8, 9, 11, 12, 13, 15, 15
min: q1: med: q3: max:
create the box plot by dragging the lines:
answer attempt 1 out of 2

Explanation:

Step1: Find Min and Max

The minimum (Min) is the smallest value in the data set, and the maximum (Max) is the largest value.
For the data set \(2,3,6,8,9,11,12,13,15,15\), \(Min = 2\) and \(Max=15\).

Step2: Find the Median (Med)

Since there are \(n = 10\) data points (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values.
\(\frac{n}{2}=5\) and \(\frac{n}{2}+1 = 6\). The 5th value is \(9\) and the 6th value is \(11\).
\(Med=\frac{9 + 11}{2}=\frac{20}{2}=10\).

Step3: Find Q1 and Q3

The lower half of the data is \(2,3,6,8,9\) (first 5 values). Since \(n_1=5\) (odd), \(Q1\) is the \(\frac{n_1 + 1}{2}\)th value. \(\frac{5+1}{2}=3\)rd value. So \(Q1 = 6\).
The upper half of the data is \(11,12,13,15,15\) (last 5 values). Since \(n_2=5\) (odd), \(Q3\) is the \(\frac{n_2+1}{2}\)th value. \(\frac{5 + 1}{2}=3\)rd value. So \(Q3=13\).

Answer:

Min: \(2\), Q1: \(6\), Med: \(10\), Q3: \(13\), Max: \(15\)