Question

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.
4,7,7,9,9,10,13,13,15,16
min: q1: med: q3: max:
create the box plot by dragging the lines:
answer attempt 1 out of 2
you must answer all questions above in order to submit.

Explanation:

Step1: Find Min and Max

The minimum (Min) is the smallest value in the data set.
$Min = 4$
The maximum (Max) is the largest value in the data set.
$Max=16$

Step2: Find the median (Med)

The data set has \(n = 10\) values. The median for an even - numbered data set \(n\) is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values.
For \(n = 10\), \(\frac{n}{2}=5\) and \(\frac{n}{2}+1 = 6\).
The 5th value is \(9\) and the 6th value is \(10\).
\(Med=\frac{9 + 10}{2}=9.5\)

Step3: Find Q1

The first half of the data set is \(4,7,7,9,9\).
Since \(n_1=5\) (odd - numbered), the first quartile \(Q1\) is the \(\frac{n_1 + 1}{2}\)th value.
\(\frac{5+1}{2}=3\)rd value.
\(Q1 = 7\)

Step4: Find Q3

The second half of the data set is \(10,13,13,15,16\).
Since \(n_2 = 5\) (odd - numbered), the third quartile \(Q3\) is the \(\frac{n_2+1}{2}\)th value.
\(\frac{5 + 1}{2}=3\)rd value.
\(Q3=13\)

Answer:

Min: \(4\), Q1: \(7\), Med: \(9.5\), Q3: \(13\), Max: \(16\)