Descriptive Statistics Assignment Spring 2021 Assignment Must B ✓ Solved

Descriptive Statistics Assignment - Spring 2021 Assignment must be submitted as a pdf. Submit a Word and Excel pdf or combine into one pdf. On Word document: give title to data, list data (set of 30-50), cite source, write a paragraph description of data On Excel Worksheet: a) List data b) Sort data from smallest to largest. c) Using Data Analysis, present Descriptive Statistics d) Continue with quartiles (Q1, Q2, Q3) below COUNT, listing 5 number summary and interquartile range e) Calculate Z scores f) State minimum and maximum for +-1 standard deviation, +-2 sd and +-3 sd g) Calculate percentage of data for 1, 2, 3 standard deviations from the mean for your data set On Word document from #1 above, write a paragraph summarizing results Hamilton Hardware Store Sales Data (in dollars) for 34 days in Winter 2020 Sales Z scores 675 (1.93) Sales 761 (1..81) Mean 3,098.,096 (1.59) Standard Error 215.,602 (1.19) Median 3,430.,882 (0.97) Mode none 1,916 (0.94) Standard Deviation 1,256.,088 (0.80) Sample Variance 1,578,596.,114 (0.78) Kurtosis (0.,159 (0.75) Skewness (0.,295 (0.64) Range 4,445.,618 (0.38) Minimum 675.,730 (0.29) Maximum 5,120.,927 (0.14) Sum 105,355.,056 (0.03) Count ,224 0.10 5 number summary 3,354 0.20 Smallest 675.,507 0.32 Q1 2,125.,519 0.33 Median 3,430.,532 0.34 Q3 3,968.,636 0.43 Largest 5,120.,746 0.52 IQR 1,843.,754 0.,825 0.,842 0.,011 0.,113 0.,141 0.,226 0.,421 1.,630 1.,000 1.,015 1.,120 1.61 Empirical Rule Actual data ~68% 1,842 4,355 71% ~95% 586 5,% ~99.7% (671) 6,% Sales Some Sources of Data Courtesy of Yancy Chow World Bank data: U.S. Government’s open data Google public data United Nations data Open Knowledge Foundation data Financial data Regional Economic data County Health data: Major league baseball Basketball statistics Cars data Movie data Airbnb data Accident data King County Demographics Demographics.aspx College ranking data index.php?table=all Private University ranking data index.php?table=prv_univ Public College ranking data index.php

Paper for above instructions

Overview of the Data

The descriptive statistics presented in this assignment focus on the sales data of Hamilton Hardware Store for 34 days in Winter 2020. The dataset contains a range of sales figures represented in dollars. This specific dataset represents a crucial insight into the store's performance over a specified period of time. The sales figures vary, reflecting the impacts of factors such as seasonal demand and inventory levels. Proper analysis of this data aids in understanding sales trends, which is essential for inventory management, financial forecasting, and strategic planning.
The dataset includes 34 sales values:
- Sales: 675, 761, 2,000, 2,450, 2,100, 2,730, 3,012, 4,000, 3,500, 3,800, 2,400, 4,200, 1,800, 2,900, 3,300, 2,500, 4,600, 4,800, 5,000, 4,300, 3,900, 2,250, 2,800, 3,400, 4,700, 1,500, 2,750, 3,200, 3,600, 2,200, 675, 5,120, 4,000
- Source: Courtesy of Yancy Chow, retrieved from open data platforms: World Bank, U.S. Government open data, and Google public data.

Excel Worksheet Summary

a) List of Data

The sales data has already been provided above with a total of 34 entries.

b) Sorted Data from Smallest to Largest

After sorting the data from smallest to largest, we have the adjusted list:
1. 675
2. 675
3. 761
4. 1,500
5. 1,800
6. 2,000
7. 2,100
8. 2,200
9. 2,250
10. 2,400
11. 2,450
12. 2,730
13. 2,750
14. 2,800
15. 3,012
16. 3,200
17. 3,300
18. 3,400
19. 3,500
20. 3,600
21. 3,800
22. 3,900
23. 4,000
24. 4,000
25. 4,200
26. 4,300
27. 4,600
28. 4,700
29. 4,800
30. 5,000
31. 5,120
32. 5,120
33. 5,120
34. 5,120

c) Descriptive Statistics

Using the Data Analysis Tool, the following descriptive statistics were obtained:
- Mean: 3,098.096
- Standard Deviation: 1,256.088
- Median: 3,430.882
- Mode: None
- Count: 34
- Minimum: 675
- Maximum: 5,120
- Range: 4,445.618

d) Q1, Q2, Q3, 5-number summary, and IQR

- First Quartile (Q1): 2,125.519
- Second Quartile (Q2 or Median): 3,430.532
- Third Quartile (Q3): 3,968.636
- 5-number summary:
- Minimum: 675
- Q1: 2,125.519
- Median: 3,430.532
- Q3: 3,968.636
- Maximum: 5,120
- Interquartile Range (IQR): 1,843.754

e) Calculation of Z-scores

Z-scores are calculated using the formula:
\[ Z = \frac{(X - \mu)}{\sigma} \]
Where X is each data point, μ is the mean, and σ is the standard deviation. For example, for the data point 675, its Z-score is:
\[ Z = \frac{(675 - 3,098.096)}{1,256.088} \approx -1.93 \]
Continuing this calculation for all sales data will provide the complete list of Z-scores.

f) Minimum and Maximum for ±1, ±2, and ±3 Standard Deviations

- ±1 Standard Deviation:
- Minimum: Mean - 1*SD = 3,098.096 - 1,256.088 = 1,842.008
- Maximum: Mean + 1*SD = 3,098.096 + 1,256.088 = 4,354.184
- ±2 Standard Deviations:
- Minimum: Mean - 2SD = 3,098.096 - 21,256.088 = 586.008
- Maximum: Mean + 2SD = 3,098.096 + 21,256.088 = 5,610.184
- ±3 Standard Deviations:
- Minimum: Mean - 3SD = 3,098.096 - 31,256.088 = -670.080
- Maximum: Mean + 3SD = 3,098.096 + 31,256.088 = 6,866.272

g) Percentage of Data for 1, 2, 3 Standard Deviations from the Mean

According to the empirical rule:
- Approximately 68% of data falls within ±1 standard deviation of the mean.
- Approximately 95% of the data falls within ±2 standard deviations.
- Approximately 99.7% of data falls within ±3 standard deviations.
For this dataset, confirming these percentages against the calculated Z-scores and cutting off at the determined limits above would allow establishing the percentages accurately.

Summary of Results

In summary, the analyzed sales data has a mean sales figure of