Descriptive Statistics Variables in the Dataset Order Instructions: Module 2 – SLP
DESCRIPTIVE STATISTICS
Using the provided dataset in Excel, calculate the appropriate descriptive statistics for each of the variables in the dataset.
Include a 2-3 page description of the descriptive statistics including tables of the summarized data, similar to a “Results” section in a published manuscript or journal article.
SLP Assignment Expectations
Length: SLP assignments should be at least 2 pages (500 words) in length.
References: At least two references must be included from academic sources (e.g. peer-reviewed journal articles). Required readings are included. Quoted material should not exceed 10% of the total paper (since the focus of these assignments is critical thinking). Use your own words and build on the ideas of others. When material is copied verbatim from external sources, it MUST be enclosed in quotes.
Descriptive Statistics Variables in the Dataset Essay Paper Format
The references should be cited within the text and also listed at the end of the assignment in the References section (APA format recommended).
Organization: Subheadings should be used to organize your paper according to question
Format: APA format is recommended for this assignment. See Syllabus page for more information on APA format.
Grammar and Spelling: While no points are deducted for minor errors, assignments are expected to adhere to standards guidelines of grammar, spelling, punctuation, and sentence syntax. Points may be deducted if grammar and spelling impact clarity.
The following items will be assessed in particular:
• Achievement of learning outcomes for SLP assignment.
• Relevance—all content is connected to the question.
• Precision—specific question is addressed; statements, facts, and statistics are specific and accurate.
• Depth of discussion—points that lead to deeper issues are presented and integrated.
• Breadth—multiple perspectives and references, multiple issues/factors considered/
• Evidence—points are well-supported with facts, statistics, and references.
• Logic—presented discussion makes sense; conclusions are logically supported by premises, statements, or factual information.
• Clarity—writing is concise, understandable, and contains sufficient detail or examples.
• Objectivity—use of first person and subjective bias are avoided.
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Module 2 – Background
DESCRIPTIVE STATISTICS
Descriptive Statistics Variables in the Dataset Required Reading
Module Overview
• SLP
o Demonstrate proficiency in calculating descriptive statistics including proportions and mean.
Data are most often presented using descriptive statistics. Categorical variables are introduced using proportions (%) and sample sizes (n). Continuous variables are most often described with mean and standard deviation (although a range can also be used in lieu of a SD). An example of a results table is shown below:
Descriptive Statistics for Entire Study Population:
StatTrek: One-Way Tables in Statistics. Retrieved from http://stattrek.com/statistics/one-way-table.aspx?Tutorial=Stat
Descriptive Statistics for Subpopulations (e.g. Study Population Divided by Gender or Disease Status)
StatTrek: Two-Way Tables in Statistics. Retrieved from http://stattrek.com/statistics/two-way-table.aspx?Tutorial=Stat
Mean, Median, Modes, and Standard Deviation
Australian Bureau of Statistics. Statistical Language – Measures of Central Tendency. Retrieved from http://www.abs.gov.au/websitedbs/a3121120.nsf/home/statistical+language+-+measures+of+central+tendency
Lake Tahoe Community College. Mean, Mode, Median, and Standard Deviation. Retrieved from http://www.ltcconline.net/greenl/courses/201/descstat/mean.htm
The Michigan Chemical Process Dynamics and Controls Open Text Book. Basic statistics: mean, median, average, standard deviation, z-score, and p-value. Retrieved from https://controls.engin.umich.edu/wiki/index.php/
Basic_statistics:_mean,_median,_average,_standard_deviation,_z-scores,_and_p-value
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Descriptive Statistics Variables in the Dataset Sample Answer
The frequency distribution of the race is as summarized in Table 1.
| Table 1:
Race |
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| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | White | 164 | 54.7 | 54.7 | 54.7 |
| Hispanic | 55 | 18.3 | 18.3 | 73.0 | |
| African-American | 35 | 11.7 | 11.7 | 84.7 | |
| Native-American | 9 | 3.0 | 3.0 | 87.7 | |
| Asian-American | 21 | 7.0 | 7.0 | 94.7 | |
| Other | 16 | 5.3 | 5.3 | 100.0 | |
| Total | 300 | 100.0 | 100.0 | ||
The results indicate that the sample population consists of 54.7% of White peoples, 18.3% of Hispanic, 11.7% of African-American, 7.0% Asian-American, 3.0% Native-American, and 5.3% Others. This is a clear indication that this variable was asymmetric with a long tail to the left. In particular, the variable is positively skewed.
The gender distribution is as summarized in Table 2.
| Table2:
Gender |
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| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | Male | 141 | 47.0 | 47.0 | 47.0 |
| Female | 159 | 53.0 | 53.0 | 100.0 | |
| Total | 300 | 100.0 | 100.0 | ||
The composition of the whole sample is 47% whereas the female proportion is 53%. Notably, the distribution is uniformly distributed.
The sample education distribution is as illustrated in Table 3.
| Table 3:
Education |
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| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | high school | 46 | 15.3 | 15.3 | 15.3 |
| College | 101 | 33.7 | 33.7 | 49.0 | |
| Masters | 90 | 30.0 | 30.0 | 79.0 | |
| Professional | 63 | 21.0 | 21.0 | 100.0 | |
| Total | 300 | 100.0 | 100.0 | ||
The sample has a large population of people with college education qualification (33.7%), followed by Masters qualified with a proportion of 30%, followed by professional with a percentage of 21%; the smallest percentage is of those with high school qualifications 15.3%.
The frequency distribution of those with a history of diabetes is as summarized in Table 4.
| Table 4:
Diabetes |
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| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | No | 191 | 63.7 | 63.7 | 63.7 |
| Yes | 109 | 36.3 | 36.3 | 100.0 | |
| Total | 300 | 100.0 | 100.0 | ||
A larger proportion of 63.7% in the sample population has no record of being sick of diabetes while as only 36.3 percent has a suffered from this disease.
The frequency distribution of those with a history of allergies is as summarized in Table 5.
| Table 5:
Allergies |
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| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | No | 120 | 40.0 | 40.0 | 40.0 |
| Yes | 180 | 60.0 | 60.0 | 100.0 | |
| Total | 300 | 100.0 | 100.0 | ||
In the sample, 60% has suffered from allergies, whereas 40% has not.
The proportion of families that have diabetes is as summarized in Table 6.
| Table 6:
Family has diabetes |
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| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | No | 188 | 62.7 | 62.7 | 62.7 |
| Yes | 112 | 37.3 | 37.3 | 100.0 | |
| Total | 300 | 100.0 | 100.0 | ||
The results indicate that 62.7% of the sample population has no history of family members with diabetes whereas 37.3% has a history of a family member with diabetes.
The proportion of families that have allergies is as summarized in Table 7.
| Table7:
Family has allergies |
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| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | No | 152 | 50.7 | 50.7 | 50.7 |
| Yes | 148 | 49.3 | 49.3 | 100.0 | |
| Total | 300 | 100.0 | 100.0 | ||
The results illustrate that in the sample 50.7% of the respondent had family members that have not suffered from allergies. On the other hand, 49.3% of the sample had members that have suffered from allergies.
The distribution of sample population depression during winter is as summarized in Table 8.
| To feel depressed during the winter | |||||
| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | 1.00 | 38 | 12.7 | 12.7 | 12.7 |
| 2.00 | 75 | 25.0 | 25.0 | 37.7 | |
| 3.00 | 75 | 25.0 | 25.0 | 62.7 | |
| 4.00 | 75 | 25.0 | 25.0 | 87.7 | |
| 5.00 | 37 | 12.3 | 12.3 | 100.0 | |
| Total | 300 | 100.0 | 100.0 | ||
These results deduce that the distribution of people feeling being depressed during winter is normally distributed, with a plot that is symmetrical (skewedness is 0.002 which is close to zero).
The distribution of how people behave (overreact) when stressed is as illustrated in Table 9.
| Table 9:
To overreact when stressed out |
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| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | 1 | 67 | 22.3 | 22.3 | 22.3 |
| 2 | 67 | 22.3 | 22.3 | 44.7 | |
| 3 | 67 | 22.3 | 22.3 | 67.0 | |
| 4 | 66 | 22.0 | 22.0 | 89.0 | |
| 5 | 33 | 11.0 | 11.0 | 100.0 | |
| Total | 300 | 100.0 | 100.0 | ||
These results deduce that the sample population has a positive skewedness in regard to how they overreact when stressed, in other words, the high proportion is on the lower values. Thus, the data has a positive skewness.
The distribution of preference of exercise during summer is tabulated below.
| Table 10:
To exercise during the summer |
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| Frequency | Percent | Valid Percent | Cumulative Percent | ||
| Valid | 1 | 27 | 9.0 | 9.0 | 9.0 |
| 2 | 54 | 18.0 | 18.0 | 27.0 | |
| 3 | 54 | 18.0 | 18.0 | 45.0 | |
| 4 | 110 | 36.7 | 36.7 | 81.7 | |
| 5 | 55 | 18.3 | 18.3 | 100.0 | |
| Total | 300 | 100.0 | 100.0 | ||
This data shows that the sample population preference of exercise during summer is negatively skewed (more people on the higher values).
The summary table 11 shows the distribution of continuous variables.
| Statistics | ||||||
| Age | Salary | weight | height | BMI | ||
| N | Valid | 300 | 300 | 300 | 300 | 300 |
| Missing | 0 | 0 | 0 | 0 | 0 | |
| Mean | 50.46 | 54498.02 | 159.1133 | 66.9833 | 24.6387 | |
| Median | 50.00 | 50012.00 | 161.0000 | 67.0000 | 25.0000 | |
| Mode | 18 | 15000a | 145.00a | 65.00a | 25.40 | |
| Std. Deviation | 20.020 | 28923.783 | 31.66517 | 3.75010 | 2.23138 | |
| Variance | 400.797 | 836585198.715 | 1002.683 | 14.063 | 4.979 | |
| Skewness | .085 | .407 | .495 | -.060 | .583 | |
| Std. Error of Skewness | .141 | .141 | .141 | .141 | .141 | |
| Kurtosis | -1.133 | -.913 | .112 | -.743 | .653 | |
| Std. Error of Kurtosis | .281 | .281 | .281 | .281 | .281 | |
| Minimum | 18 | 10123 | 110.00 | 60.00 | 21.30 | |
| Maximum | 91 | 117878 | 235.00 | 74.00 | 30.20 | |
| a. Multiple modes exist. The smallest value is shown | ||||||
The table illustrates that on average the sample population has a mean of 50.46, with a standard deviation of 20.020. Nevertheless, the minimum age of the participants is 18, and the maximum age is 91 years. The most repeated frequency in the sample is 18, and the median is 50 years.
On average the sample population has a salary of 54498.02 with the maximum receiving $ 117,878 and the minimum is $10,123. The salary data has a positive skewedness, implying that most of the people in the sample receive the lower values.
The average weight of the sample population is 159.1133, with a standard deviation of 31.66517. The minimum weight in the sample data is 110 and the maximum 235, further the data has a positive skewness.
The mean height of the sample is 66.9833, and notably, the median of the height is 67. The height variable has a standard deviation of 3.75010, and the minimum height is 60, and the maximum is 74.
The average BMI of the sample population is 24.6387, with a mode of 25.4 and the median 25. The standard deviation of BMI data is 2.23138. The minimum BMI is 21.3, and the maximum BMI is 30.2.
