Question

keystone math as_create box plots 2

1. fill in the values below and use them to create a box and whiskers plot for the following set of data.

3,6,7,8,9,9,10,10,14,16
min: _ q1: _ med: _ q3: _ max: ___

Explanation:

Step1: Find Min and Max

The minimum value (Min) is the smallest number in the data set.
$Min = 3$
The maximum value (Max) is the largest number in the data set.
$Max=16$

Step2: Find the median (Med)

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

Step3: Find Q1

The first quartile (Q1) is the median of the lower half of the data. The lower half of the data is \(3,6,7,8,9\). Since \(n = 5\) (odd - numbered), the median of the lower half is the \(\frac{5 + 1}{2}=3\)rd value.
\(Q1 = 7\)

Step4: Find Q3

The third quartile (Q3) is the median of the upper half of the data. The upper half of the data is \(10,10,14,16,9\) (sorted upper - half: \(9,10,10,14,16\)). Since \(n = 5\) (odd - numbered), the median of the upper half is the \(\frac{5+1}{2}=3\)rd value.
\(Q3 = 10\)

Answer:

Min: \(3\), Q1: \(7\), Med: \(9\), Q3: \(10\), Max: \(16\)