# Frequency distribution

1. Place the following scores in a frequency distribution table. Include columns for proportion (p) and percentage (%) in your table. The scores are: 4, 6, 2, 9, 8, 8, 5, 7, 7, 3, 6, 6, 7, 4, 5, 8, 6, 5

2. Under what circumstances should you use a grouped frequency distribution instead of a regular frequency distribution?

3. What information is available about the data in a regular frequency distribution table that is not available in a group table?

4. Describe the difference in appearance between a bar graph and a histogram, and describe the circumstances under which each type of graph should be used

5. The following are reading comprehension scores for a third-grade class of 18 students: 4, 5, 5, 6, 4, 5, 2, 6, 3

5, 6, 5, 4, 3, 6, 1, 6, 5

a. place the scores in a frequency distribution table.

b. sketch a histogram showing the distribution*

c. using your graph answer the following questions:

a. What is the shape of the distribution?

b. If a score of x=4 is considered typical for third-graders.

* (you should include the histogram. You can draw by hand or use a program such as SPSS and cut and paste into your document)

7. Complete the following frequency distribution table, and find each of the percentiles and percentile ranks requested:

X f cf c%

10 1

9 3

8 7

7 6

6 2

5 1

a. what is the percentile for x=7.5

b. what is the percentile for x=9.5

c. what is the 15th percentile?

e. what is the 80th percentile?

See attached file for full problem description.

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#### Solution Summary

Answers questions on arranging data using frequency distribution, histogram etc.

Frequency Distribution, Mean and Standard Deviation

Please see attached file for full problem description.

Use the data set collected in a) to do the following.

1. Group the data into at least 10 different classes and create a frequency distribution table for the data set, and graph the histogram of the data set; Make an educated guess about the mean, standard deviation, and make comments about whether the shape of distribution may be considered a Bell curve (Normally distributed).

2. Calculate the summary measurements, mean x and standard deviation s for the data set the "Descriptive Statistics" package in MS Excel.

3. Count the number of measurements in the intervals x ± s, x ± 2s, and x ± 3s. Express each count as a percentage of the total number of measurements. Apply Empirical Rule to discuss whether the conclusion about the shape of the data set distribution give in 1) seems correct.

4. Superimpose the Normal distribution line chart with Mean and standard deviation from 2) onto the relative Frequency bar chart of the data set. Further discuss the shaper of the data set.

The completed project report should be created in One Microsoft Excel file. The report should include

? (Sheet 1. name it Cover Sheet) A cover page with a title of your project (you select), and student names of the group.

? (Sheet 2. name it Data) A detailed discussion about objective of you analysis and the how, when, and where you collected your data. Discuss why the data you collected is representative. Provide the raw data in this sheet.

? (Sheet 3. name it Data Analysis) This sheet contains answer to question 1-4.

Give clear explanation about the class range selection, as well as the generated Table(s) and Chart(s).

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