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, 4, 5, 5, 6, 6, 8, 10, 11, 11, 12, 14
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. The data set is \(4,4,5,5,6,6,8,10,11,11,12,14\). So, \(Min = 4\).
The maximum (Max) is the largest value in the data set. So, \(Max=14\).

Step2: Find the median (Med)

Since there are \(n = 12\) data points. The median is the average of the \(\frac{n}{2}\) - th and \((\frac{n}{2}+1)\) - th values. \(\frac{n}{2}=6\), \(\frac{n}{2}+1 = 7\). The 6 - th value is \(6\) and the 7 - th value is \(8\). Then \(Med=\frac{6 + 8}{2}=7\).

Step3: Find Q1 and Q3

For the lower half of the data (the first 6 values: \(4,4,5,5,6,6\)), since \(n_1=6\), the median of the lower half (Q1) is the average of the 3 - rd and 4 - th values. The 3 - rd value is \(5\) and the 4 - th value is \(5\). So, \(Q1=\frac{5 + 5}{2}=5\).
For the upper half of the data (the last 6 values: \(10,11,11,12,14\)), since \(n_2 = 6\), the median of the upper half (Q3) is the average of the 3 - rd and 4 - th values. The 3 - rd value is \(11\) and the 4 - th value is \(12\). So, \(Q3=\frac{11+12}{2}=11.5\).

Answer:

Min: \(4\), Q1: \(5\), Med: \(7\), Q3: \(11.5\), Max: \(14\)