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. 3,4,4,6,6,8,9,12,15 min: q1: med: q3: max: create the box plot by dragging the lines:

Explanation:

Step1: Find Minimum (Min)

The minimum value in the data set \(3, 4, 4, 6, 6, 8, 9, 12, 15\) is the smallest number.
\( \text{Min} = 3 \)

Step2: Find Quartile 1 (Q1)

First, the data is already ordered. The median of the lower half (excluding the overall median if \(n\) is odd). The data set has \(n = 9\) values. The median (Med) is the 5th value (since \( (9 + 1)/2 = 5 \)). The lower half is \(3, 4, 4, 6\) (first 4 values). The median of this lower half is the average of the 2nd and 3rd values (since \(n = 4\) is even).
\( Q1=\frac{4 + 4}{2}=4 \)

Step3: Find Median (Med)

For \(n = 9\) (odd), the median is the middle value (5th value).
\( \text{Med} = 6 \) (the 5th value in \(3, 4, 4, 6, 6, 8, 9, 12, 15\))

Step4: Find Quartile 3 (Q3)

The upper half of the data (excluding the median) is \(8, 9, 12, 15\) (last 4 values). The median of this upper half is the average of the 2nd and 3rd values.
\( Q3=\frac{9 + 12}{2}=10.5 \)

Step5: Find Maximum (Max)

The maximum value in the data set is the largest number.
\( \text{Max} = 15 \)

Answer:

Min: \(3\), Q1: \(4\), Med: \(6\), Q3: \(10.5\), Max: \(15\)