**How to write a nursing essay on ****ST3001 – Descriptive Statistics (Solved)**

The file chosen for this discussion is Freshman 15 (This file contains the weight in kilograms and BMI of freshmen in September and in April). This Assessment requires submission of one file, a completed report including all computations, graphs, and explanations. Save your files as follows:

## Explaining Statistics to Your Boss

You are tasked with explaining some statistical concepts to your boss to help him make some company decisions. Your boss does not have any background in statistics and has a hard time with numbers in general, so you decide to choose a non-work topic to explain the concepts. You will use Statdisk to make your computations, and then present the information along with your explanations as a report. Your report should include a title page, table of contents, summary of the information, your computations and explanations, any conclusions that you make about the data, and references that you used. Keep in mind that your textbook and the course resources you use when making your computations and explanations should be cited appropriately.

To prepare for this Assessment:

Download the Statdisk program from www.Statdisk.org. You will save this to your computer for use throughout the Area of Expertise.

For this Assessment, you will need to read pages 3–4 and 7–9 of the Statdisk User Manual document.

Choose one of the following files from the Statdisk User Manual document:

Oscar Winner (This file contains the age of each actress and actor Oscar winner at the time of their win.)

Freshman 15 (This file contains the weight in kilograms and BMI of freshmen in September and in April.)

Word Count (This file contains the counts of words spoken in a day by male and female students in size different sample groups.)

Garbage Weights (This file contains the weights in pounds of household garbage.)

Passive and Active Smoke (This file contains the measured levels of serum continine in ng/ml).

Note: You will need to choose two (2) quantitative variables from the file that you chose and label them Variable 1 and Variable 2.

Part 1: Computations and Graphical Representations

Make the following computations in Statdisk, and then copy your work into your report.

Note: Be sure to copy all work into your report and to label your computations. In your report, you should:

1. Determine the type of data (quantitative or qualitative) and the level of measurement (nominal, ordinal, interval, ratio) for the data set. Explain how you determined the type of data.

2. Find the mean, median, and midrange for the data in Variable 1. Paste your results from Statdisk in your report.

3. Find the range, variance, and standard deviation for Variable 1. Paste your results from Statdisk in your report.

List any values for the first column that you think may be outliers. Why do you think that? (Hint: You may want to look at the modified boxplot, sort the data, and look at the smallest and largest values.)

4. Find the mean, median, and midrange for the data in Variable 2. Paste your results from Statdisk in your file.

5. Find the range, variance, and standard deviation for Variable 2. Paste your results from Statdisk in your file.

List any values for the second column that you think may be outliers. Why do you think that? (Hint: You may want to look at the modified boxplot, sort the data, and look at the smallest and largest values.)

6. Find the five-number summary for the data in Variables 1 and 2. You will need to label each of the columns with an appropriate measure in the top row for clarity.

7. Compare the two variables from the dataset using a boxplot of Variables 1 and 2. Paste your boxplot in your file.

8. Create a histogram for Variables 1 and 2 data. Paste it in your file.

Part 2: Interpreting Statistical Information

Using the descriptive statistics calculated earlier, what conclusions can you make when you compare the two variables? You will want to address each of the following points below. Please be sure to use specific values to support your reasoning. You must justify your conclusions with Statdisk results from the descriptive statistics, histogram, and boxplot for each portion below.

Reminder: Your boss does not have any experience with statistics, so explain your reasoning in a way that is understandable by all people. To justify your conclusions, you should:

9. Explain one conclusion about a measure of center (mean, median, midrange).

10. Explain one conclusion about the variability in the two datasets (variance, standard deviation, range).

11. Explain one conclusion about the shape of the distribution (by mentioning direction of skew and the relationship of the mean and median).

## SOLUTION TO **ST3001 – Descriptive Statistics**

**Question 1: Type of Data and Level of Measurement**

The two types of data sets commonly used in research are quantitative and qualitative data. Quantitative data represents anything that can be counted or measured. It represents numerical data that show how much or how often things occur. Qualitative data cannot be measured or counted. Qualitative data can only be observed and observations cannot be measured numerically (Mishra et al., 2018). The selected file for this discussion contains values for weight and BMI taken for freshmen in September and April. The measurements are in terms of numbers and therefore a representation of quantitative data. The information presented is factual, countable, measurable, and can be analyzed using statistical analysis.

The measurement of variables in statistics has four different levels including nominal, ordinal, interval, or ratio. Nominal data only provides the group an observation belongs to. An example is male or female. Ordinal data depicts some order among variables and allows an individual to rank observations. An example is marks scored by students ranked from highest to lowest. Interval level classifies and orders measurements and also specifies the distance between two intervals (Mishra et al., 2018). An example is the temperature difference between two points. The last aspect of measurement is the ratio which in addition to having equal intervals, can have a meaningful value of zero as well. Ratio measurements are useful in variables like price, length, and weight of things. The level of measurement in the identified file is ratio because it deals with the weight and BMI differences of students between the months of September and April.

**Question 2. Mean, Median, and Midrange of Variable 1**

Variable 1: The first variable identified from the file is weight of students in September.

Mean: 65.0597

Median: 64

Midrange: 69.5

**Question 3. Range, Variance, and Standard Deviation of Variable 1**

Range: 55

Variance, s^2: 127.36

Standard Deviation, s: 11.285339

**Outliers: **An outlier represents data that lies an abnormal distance from other values in a random sample (Bennet et al., 2015). The values that can be considered outliers in the second column are 94, and 97. These values have great distance differences from their closest data values.

**Question 4: Mean, median, and range of Variable 2**

Variable 2: The second variable identified from the file is weight of students in April.

Mean: 66.23881

Median: 66

Midrange: 76

**Question 5: Range, variance, and Standard Deviation of Variable 2**

Range: 58

Variance, s^2: 127.336

Standard Deviation: 11.28433

**Outliers:** The outliers for weight in April are 92 and 105. These values are at an abnormal range from their closest data values. For example, the weight of 105 is far from 92 which is its closest data value.

**Question 6: Five-Number Summary**

The summary provided below highlights the minimum, 1^{st} quartile, 2^{nd} quartile, 3^{rd} quartile, and maximum weight values for the months of September and April. This summary gives a rough idea of what the data set looks like and is important in drawing the box plot graph.

Number | Variable 1
(Weight in September) |
Variable 2
(Weight in April) |

Minimum | 42 | 47 |

1^{st} Quartile |
56 | 58 |

2^{nd} Quartile (Median) |
64 | 66 |

3^{rd} Quartile |
71 | 71 |

Maximum | 97 | 105 |

** **

** **

**Question 7: Modified Box Plot of Variables**

**Key:**

Column 2: Weight in September Box plot

Column 3: Weight in April Box plot

**Question 8: Histogram**

Variable 1: Weight in September

Variable 2: Weight in April

**Question 9: Measure of Center Conclusion**

The mean weight in September was 65 compared to 66.2 in April meaning that both variables are close in range. Likewise, the median in September was 64 compared to 66 in April. However, the midrange between weights in September (69.5) and April (76) was significant. It indicates that the range between the lowest weight and the highest weight among the students increased.

**Question 10: Variability**

The range for September was 55 and is close to the range of values in April, 58. The variance for both months is identical, 127.36 and 127.33 meaning that there was no significant change in the weights of students (Bennett et al., 2015). Also, the standard deviation is 11.28 for both months indicating that there was no significant deviation of weight by the students from the mean.

**Question 11: Shape of Distribution**

The mean of September was 65 compared to 66.2 in April. The Median in September was 64 compared to 66 in April and these values give the histogram a symmetrical shape. In both months, the mean is greater than the median and this gives the histogram a right-skewed distribution (Bennett et al., 2015). This distribution indicates that the peak of the graph lies to the left with frequency observations being lower on the right side.

**References**

Bennett, J. O., Briggs, W. L., & Triola, M. F. (2015). *Statistical reasoning for everyday life*. Boston, MA: Addison-Wesley.

Mishra, P., Pandey, C. M., Singh, U., & Gupta, A. (2018). Scales of measurement and presentation of statistical data. *Annals of Cardiac Anaesthesia*, *21*(4), 419–422. https://doi.org/10.4103/aca.ACA_131_18

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