You Will Submit The Excel Sheet With The Following Informati ✓ Solved

You will submit the Excel sheet with the following information:

You will submit the Excel sheet with the following information: Make a Frequency Distribution with 5 classes, also list the midpoints, relative frequency, and cumulative relative frequency. Make a relative frequency ogive. Don’t forget descriptive title and labels on x and y axis (ogive is not descriptive, what does the graph represent?). Make a frequency polygon. Don’t forget a descriptive title and labels on x and y axis (polygon is not descriptive, what does the graph represent?). Calculate the mean, calculate the median, calculate the sample standard deviation (our data is sample from our class, not a population!), calculate the Q1 and Q3 values.

Paper For Above Instructions

To meet the requirements of the assignment, we will need to create a comprehensive Excel sheet that includes various components of statistical analysis based on a dataset. Here’s how we approach the problem step by step:

1. Frequency Distribution

A frequency distribution is created by sorting the dataset into classes. For our analysis, we can assume that we have a dataset of 50 observations. We will divide these observations into 5 distinct classes and calculate the frequencies.

For example, if our data points represent students’ test scores, we can create classes such as:

• Class 1: 0-20
• Class 2: 21-40
• Class 3: 41-60
• Class 4: 61-80
• Class 5: 81-100

2. Midpoints of Classes

The midpoint of each class can be calculated as:

• Midpoint of the first class (0-20) = (0 + 20) / 2 = 10
• Midpoint of the second class (21-40) = (21 + 40) / 2 = 30.5
• Midpoint of the third class (41-60) = (41 + 60) / 2 = 50.5
• Midpoint of the fourth class (61-80) = (61 + 80) / 2 = 70.5
• Midpoint of the fifth class (81-100) = (81 + 100) / 2 = 90.5

3. Relative Frequency and Cumulative Relative Frequency

Relative frequency is calculated by dividing the frequency of each class by the total number of observations. Cumulative relative frequency is obtained by summing the relative frequencies up to a certain point. For example, if the frequencies are 5, 10, 15, 10, and 10, the relative frequencies would be:

• Relative frequency of Class 1 = 5/50 = 0.1
• Relative frequency of Class 2 = 10/50 = 0.2
• Relative frequency of Class 3 = 15/50 = 0.3
• Relative frequency of Class 4 = 10/50 = 0.2
• Relative frequency of Class 5 = 10/50 = 0.2

To find the cumulative relative frequencies, we add these values as we proceed through the classes.

4. Creating an Ogive

An ogive represents cumulative frequency, and it can be plotted based on cumulative relative frequency. Each point is plotted at the upper boundary of each class, with the y-axis showing the cumulative relative frequency. The title could be "Cumulative Relative Frequency of Student Test Scores".

5. Frequency Polygon

A frequency polygon utilizes midpoints, connecting points representing the frequency of each class. For the title, we can use "Frequency Distribution of Student Test Scores". The x-axis would represent the midpoints whereas the y-axis shows frequencies.

6. Measures of Central Tendency

We will calculate:

• Mean: Mean is calculated using the formula: Σ(midpoint * frequency) / total frequency.
• Median: This is the middle value of the ordered dataset.

Given the assumed dataset, we will have to find the exact values by sorting and finding the middle entries.

7. Sample Standard Deviation

The sample standard deviation is calculated using the formula:

• s = √[Σ(xi - x̄)² / (n - 1)]

Where xi are the data points, x̄ is the mean, and n is the number of observations.

8. Quartiles Calculation (Q1 and Q3)

Quartiles can be calculated by ordering the data points. Q1 (the first quartile) is the median of the first half of the dataset, while Q3 (the third quartile) is the median of the second half.

• Q1 = value at position (1/4)(n+1)
• Q3 = value at position (3/4)(n+1)

Conclusion

This structured approach will enable the creation of the Excel sheet that will include all required elements: frequency distribution, midpoints, relative frequencies, ogive, frequency polygon, and calculations for mean, median, sample standard deviation, Q1, and Q3. Each section of data will be clear, labeled appropriately, making the analysis understandable and visually engaging.

References

• Weiss, N.A. (2015). Introductory Statistics. Pearson.
• Bluman, A.G. (2018). Elementary Statistics: A Step by Step Approach. McGraw Hill.
• Scheaffer, R.L., Mendenhall, W., & Beaver, R.J. (2015). Statistics. Cengage Learning.
• Triola, M.F. (2018). Essentials of Statistics. Pearson.
• McClave, J.T., & Sincich, T. (2017). Statistics. Pearson.
• De Veaux, R.D., Velleman, P.F., & Bock, D.E. (2016). Intro Stats. Pearson.
• Moore, D.S., McCabe, G.P., & Craig, B. (2016). Introduction to the Practice of Statistics. W.H. Freeman.
• Newman, D.J. (2017). Statistics: A Very Short Introduction. Oxford University Press.
• Gravetter, F.J., & Wallnau, L.B. (2017). Statistics for The Behavioral Sciences. Cengage Learning.
• Lewis-Beck, M.S. (2015). Applied Regression: An Introduction. SAGE Publications.