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: 2 q1: 6 med:
q3: max:
create the box plot by dragging the lines:

Explanation:

Step1: Find Minimum (Min)

The smallest value in the data set \(2,3,6,8,9,11,12,13,15,15\) is \(2\). So, Min = \(2\).

Step2: Find Quartile 1 (Q1)

First, find the median (Med) of the lower half. The data set has \(n = 10\) values. The lower half is the first \(5\) values: \(2,3,6,8,9\). The median of this lower half is the middle value. For \(5\) values, the middle is the 3rd value. So, Q1 = \(6\) (already given, but we confirm).

Step3: Find Median (Med)

For \(n = 10\) (even), the median is the average of the 5th and 6th values. The 5th value is \(9\), the 6th is \(11\). So, Med = \(\frac{9 + 11}{2} = 10\).

Step4: Find Quartile 3 (Q3)

The upper half is the last \(5\) values: \(11,12,13,15,15\). The median of this upper half is the 3rd value (since there are \(5\) values). So, Q3 = \(13\).

Step5: Find Maximum (Max)

The largest value in the data set is \(15\). So, Max = \(15\).

Answer:

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

For the box - and - whiskers plot:

• The left whisker starts at Min (\(2\)) and ends at Q1 (\(6\)).
• The box starts at Q1 (\(6\)), has a line at Med (\(10\)) and ends at Q3 (\(13\)).
• The right whisker starts at Q3 (\(13\)) and ends at Max (\(15\)).