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.
2,4,4,7,10,11,12,13,16,17,18
min: q1: med: q3: max:
create the box plot by dragging the lines:

Explanation:

Step1: Find Minimum (Min)

The minimum value is the smallest number in the data set.
Looking at the data \(2, 4, 4, 7, 10, 11, 12, 13, 16, 17, 18\), the smallest number is \(2\).

Step2: Find Maximum (Max)

The maximum value is the largest number in the data set.
In the given data, the largest number is \(18\).

Step3: Find Median (Med)

The median is the middle value when the data is ordered. Since there are \(n = 11\) (odd number of observations), the median is the \(\frac{n + 1}{2}=\frac{11+ 1}{2}=6^{\text{th}}\) value.
Ordering the data: \(2, 4, 4, 7, 10, 11, 12, 13, 16, 17, 18\). The \(6^{\text{th}}\) value is \(11\).

Step4: Find Q1 (First Quartile)

Q1 is the median of the lower half of the data. The lower half is the data before the median. The lower half has \(n_1=\frac{11 - 1}{2}=5\) values (since the median is the \(6^{\text{th}}\) value, the lower half is the first \(5\) values: \(2, 4, 4, 7, 10\)).
The median of the lower half (for \(n_1 = 5\) (odd)) is the \(\frac{5+ 1}{2}=3^{\text{rd}}\) value. The \(3^{\text{rd}}\) value in \(2, 4, 4, 7, 10\) is \(4\).

Step5: Find Q3 (Third Quartile)

Q3 is the median of the upper half of the data. The upper half is the data after the median. The upper half has \(n_2=\frac{11 - 1}{2}=5\) values: \(12, 13, 16, 17, 18\).
The median of the upper half (for \(n_2=5\) (odd)) is the \(\frac{5 + 1}{2}=3^{\text{rd}}\) value. The \(3^{\text{rd}}\) value in \(12, 13, 16, 17, 18\) is \(16\).

Answer:

Min: \(2\)
Q1: \(4\)
Med: \(11\)
Q3: \(16\)
Max: \(18\)

For the box - and - whiskers plot:

• The left whisker extends from the minimum value (\(2\)) to Q1 (\(4\)).
• The box extends from Q1 (\(4\)) to Q3 (\(16\)), with a line inside the box at the median (\(11\)).
• The right whisker extends from Q3 (\(16\)) to the maximum value (\(18\)).