Question

statistical measures and create a box and whiskers plot for the
hole numbers or decimals.
5,5,5,7,9,10,11,13,13,14,15,15,16,17
min: 5 q1: 7 med: 12 q3: 15 max: 17
create the box plot by dragging the lines:

Explanation:

Step1: Identify the minimum value

The minimum value (Min) is the smallest number in the data set.
The data set is \(5,5,5,7,9,10,11,13,13,14,15,15,16,17\).
So, \(Min = 5\).

Step2: Calculate the first quartile (Q1)

The first quartile is the median of the lower half of the data.
The lower half of the data is \(5,5,5,7,9,10\).
The median of this lower half is \(\frac{5 + 7}{2}=6\). But wait, let's re - check. The formula for the position of Q1: \(n = 14\) (number of data points). The position of Q1 is \(\frac{n + 1}{4}=\frac{14+1}{4}=3.75\).
Using linear interpolation: The 3rd value is \(5\) and the 4th value is \(7\). \(Q1=5+(7 - 5)\times0.75=6.5\). But if we consider the common method for even - numbered data sets (split into two halves of \(n/2 = 7\) each). The lower half is \(5,5,5,7,9,10,11\) (wait no, original data set \(n = 14\), split as first 7 and last 7). The lower half is \(5,5,5,7,9,10,11\). The median of the lower half (Q1) is the 4th value. So \(Q1 = 7\).

Step3: Calculate the median (Med)

The median is the middle value. For \(n = 14\) data points, the median is the average of the 7th and 8th values.
The 7th value is \(11\) and the 8th value is \(13\). \(Med=\frac{11 + 13}{2}=12\).

Step4: Calculate the third quartile (Q3)

The third quartile is the median of the upper half of the data.
The upper half of the data is \(13,14,15,15,16,17\) (using the split of \(n/2=7\) each). The median of the upper half (Q3) is the 11th value (if we consider the original ordered data). The upper half (when split as \(n = 14\) into two halves of 7) is \(13,14,15,15,16,17\). Using the formula for the position of Q3: \(\frac{3(n + 1)}{4}=\frac{3\times(14 + 1)}{4}=11.25\).
Using linear interpolation (or taking the 11th value in the ordered data set). The 11th value is \(15\). So \(Q3 = 15\).

Step5: Identify the maximum value

The maximum value (Max) is the largest number in the data set.
So, \(Max = 17\).

To create the box - and - whiskers plot:

• The left - most whisker is at \(Min = 5\).
• The left - hand side of the box is at \(Q1 = 7\).
• The line inside the box is at \(Med = 12\).
• The right - hand side of the box is at \(Q3 = 15\).
• The right - most whisker is at \(Max = 17\).

Answer:

Min: \(5\), Q1: \(7\), Med: \(12\), Q3: \(15\), Max: \(17\)