# Describing and Graphing Data Sets

TREPHENA HARDING SCOTT

The letters in the above name represents the data set. From the given data set please answer the questions below.

What is the type of your data?

1. What is the size of your data set?

2. Write your data in order from A to Z. For example, the student whose complete name is First Middle Last would have

A, D, D, E, F, I, I, L, L, M, R, S, S, T, T

3. What is (are) the mode(s) of your data set, if any? Is your data set modeless, unimodal, bimodal, trimodal?

4. Following the example provided in the conference named "Frequency Distribution Table," create a complete (seven-column) frequency distribution table. You should use the following headings for your table:

Letter, Frequency (F), Relative Frequency (RF), Percent Relative Frequency (PRF), Cumulative Frequency (CF), Cumulative Relative Frequency (CRF), and Cumulative Percent Relative Frequency (CPRF).

5. By examining appropriate rows and columns of the frequency table in Step 6 above, determine the fraction (both in decimals and percentage) of your data set that the vowels A, E, I, O, and U comprise individually and collectively.

6. Using graph paper (preferably) and the frequency table created in Step 6 above,

(a) Construct a bar chart for the frequency (F) distribution.

(b) Construct a bar chart for the percent relative frequency (PRF) distribution.

(c) Construct a bar chart for the PRF distribution, but this time, display the categories from highest PRF to lowest PRF (from left to right); the resulting bar chart is (a portion of) "Pareto Diagram."

Please note that each bar chart must have a descriptive title, and the x and y axes must have descriptive labels.

7. Plot the points corresponding to the cumulative percent relative frequency (CPRF) distribution and connect them; the graph constructed by the line segments is called "ogive." Please note that your ogive would be an "increasing curve." The plot should have a title and the axes should be appropriately tick marked and labeled. (This plot can be "superimposed" on the bar chart for Step 8(c) above to complete the Pareto Diagram. This superposition would require an additional y-axis, e.g., a y-axis on the right of the bar chart, to represent the CPRF values.)

8. Construct a pie chart to graphically display the relative frequencies in percentages. Show your calculations leading to the angle for each sector.

9. From the constructed table in Step 6 above, which category(ies) (letter[s]) has the minimum frequency, and which one(s) has the maximum frequency? State the minimum and the maximum frequencies in terms of F, RF, and PRF.

#### Solution Preview

TREPHENA HARDING SCOTT

Please see attachment for graphs.

What is the type of your data?

This is an ordinal data.

1. What is the size of your data set?

The size of the data set is 20.

2. Write your data in order from A to Z. For example, the student whose complete name is First Middle Last would have

A, D, D, E, F, I, I, L, L, M, R, S, S, T, T

The data in order are: A, A, C, D, E, E,G, H,H, I, N,N,O,P,R,R,S,T,T,T,

3. What is (are) the mode(s) of your data set, if any? Is your data set modeless, unimodal, bimodal, trimodal,?

The mode is T and the data set is unimodal.

4. Following the example provided in the conference named "Frequency Distribution Table," create a complete (seven-column) frequency distribution table. You should use the following headings for your table:

Letter, Frequency (F), Relative Frequency (RF), Percent Relative Frequency (PRF), Cumulative Frequency (CF), Cumulative Relative ...

#### Solution Summary

The expert describes and graphs data sets. The types of data that is presented is determined.