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.
7, 7, 8, 9, 11, 12, 13, 14
min: q1: med: q3: max:
create the box plot by dragging the lines:
answer
you must answer all questions above in order to submit.

Explanation:

Step1: Find the minimum and maximum

The minimum (Min) is the smallest value in the data set.
$Min = 7$
The maximum (Max) is the largest value in the data set.
$Max=14$

Step2: Find the median

Since there are \(n = 8\) data points (even number of data points), the median (Med) is the average of the \(\frac{n}{2}\) - th and \((\frac{n}{2}+1)\) - th values.
The \(\frac{8}{2}=4\) - th value is \(9\) and the \(\frac{8}{2}+1 = 5\) - th value is \(11\).
\(Med=\frac{9 + 11}{2}=\frac{20}{2}=10\)

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

The lower half of the data is \(7,7,8,9\). Since there are \(n_1=4\) (even) data points in the lower half, \(Q1\) is the average of the \(\frac{4}{2}=2\) - th and \((\frac{4}{2}+1)=3\) - th values.
\(Q1=\frac{7 + 8}{2}=\frac{15}{2}=7.5\)
The upper half of the data is \(12,13,14,11\) (sorted as \(11,12,13,14\)). Since there are \(n_2 = 4\) (even) data points in the upper half, \(Q3\) is the average of the \(\frac{4}{2}=2\) - th and \((\frac{4}{2}+1)=3\) - th values.
\(Q3=\frac{12+13}{2}=\frac{25}{2}=12.5\)

Answer:

Min: \(7\), \(Q1:7.5\), Med: \(10\), \(Q3:12.5\), Max: \(14\)