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.

33, 23, 24, 27, 27, 33, 34, 33

1. write 3 comments that interpret the data. pause here for instructions on visiting the other displays.

Explanation:

Step1: Create dot - plot

1. First, list out the unique values in the data set: 23, 24, 27, 33, 34.
2. Then, for each value, count the number of times it appears in the data set {33, 23, 24, 27, 27, 33, 34, 33, 23}. The counts are: 23 appears 2 times, 24 appears 1 time, 27 appears 2 times, 33 appears 3 times, 34 appears 1 time.
3. On a number - line, place a dot above the number for each occurrence. For example, above 23, place 2 dots; above 24, place 1 dot; above 27, place 2 dots; above 33, place 3 dots; above 34, place 1 dot.

Step2: Create box - plot

1. First, order the data set: 23, 23, 24, 27, 27, 33, 33, 33, 34.
2. Find the median (Q2). Since there are 9 data points, the median is the 5th value, so Q2 = 27.
3. Find the lower half of the data: 23, 23, 24, 27. The median of the lower half (Q1) is the average of the 2nd and 3rd values, so Q1=$\frac{23 + 24}{2}=23.5$.
4. Find the upper half of the data: 33, 33, 33, 34. The median of the upper half (Q3) is the average of the 2nd and 3rd values, so Q3 = 33.
5. The minimum value is 23 and the maximum value is 34. Draw a box from Q1 to Q3 with a line at Q2 inside the box. Draw whiskers from the box to the minimum and maximum values.

Step3: Write 3 comments

1. The data is somewhat skewed to the right as the upper half of the data (from Q2 to Q3 and to the maximum) has larger values and a larger spread compared to the lower half.
2. The most frequent value is 33 as indicated by the dot - plot, which has 3 dots above it.
3. The inter - quartile range (IQR = Q3 - Q1=33 - 23.5 = 9.5) shows that the middle 50% of the data has a spread of 9.5.

Answer:

Dot - plot and box - plot are created as described above, and the three comments are: "The data is somewhat skewed to the right", "The most frequent value is 33", "The inter - quartile range is 9.5".