Question

3.2 data displays
your teacher will assign your group a statistical question. as a group:

1. create a dot plot and a box plot to display the distribution of the data.
2. write 3 comments that interpret the data. pause here for instructions on visiting the other displays.

Explanation:

Step1: Organize data

The data set is \(33, 23, 24, 27, 27, 33, 34, 33\). First, sort it: \(23, 24, 27, 27, 33, 33, 33, 34\).

Step2: Create dot - plot

For each value in the data set, place a dot above that value on a number line. For example, for \(23\) there is 1 dot, for \(24\) there is 1 dot, for \(27\) there are 2 dots, for \(33\) there are 3 dots and for \(34\) there is 1 dot.

Step3: Calculate quartiles for box - plot

The median (\(Q2\)) of the data set with \(n = 8\) values is the average of the 4th and 5th ordered values. So \(Q2=\frac{27 + 33}{2}=30\). The lower half of the data is \(23, 24, 27, 27\), and its median (\(Q1\)) is \(\frac{24+27}{2}=25.5\). The upper half of the data is \(33, 33, 33, 34\), and its median (\(Q3\)) is \(\frac{33 + 33}{2}=33\). The minimum value is \(23\) and the maximum value is \(34\). Draw a box from \(Q1 = 25.5\) to \(Q3=33\) with a line at \(Q2 = 30\), and whiskers from the box to the minimum (\(23\)) and maximum (\(34\)) values.

Step4: Write data interpretations

Comment 1: The most frequent value (mode) is \(33\), which occurs 3 times.
Comment 2: The data is somewhat skewed to the right since the right - hand whisker (from \(33\) to \(34\)) is shorter compared to the left - hand whisker (from \(25.5\) to \(23\)) and the median is closer to the lower quartile.
Comment 3: The inter - quartile range \(IQR=Q3 - Q1=33 - 25.5 = 7.5\), which shows the spread of the middle 50% of the data.

Answer:

Dot - plot and box - plot are created as described above, and the three comments for data interpretation are: "The most frequent value (mode) is 33, which occurs 3 times.", "The data is somewhat skewed to the right since the right - hand whisker is shorter compared to the left - hand whisker and the median is closer to the lower quartile.", "The inter - quartile range \(IQR = 7.5\), which shows the spread of the middle 50% of the data."