Week 4 Discussion: Frequency and Descriptive Statistics

Descriptive analysis is a critical concept in statistics that helps develop meaning by
summarizing, describing, and showing data to define study variables and reveal sample
characteristics. According to Gray & Grove (2020), the process of descriptive analysis allows
researchers to present data in a simplified and meaningful manner. Descriptive statistics are
metrics that summarize data by representing either sample of a population or the entire
population. They are classified into (1) measures of variability, such as variance, standard
deviation, skewness, maximum and minimum variables, and variance and (2) measures of central
tendency, including mode, median, and mean. This assignment summarizes Week Four’s
descriptive statistics SPSS output document.
Summary

I. Respondent’s Age
These descriptive statistics show that the maximum and minimum ages of the
respondents or study participants when they were interviewed were 49.430 and 19.378,
respectively. The sample size (N) was 1000 people. The mean age was 36.63733, while the
standard deviation from the mean was 6.198741. The skewness was -0.374, with a standard error
of 0.077. Skewness measures the symmetricalness of distribution, and the negative value implies
that the fatter/longer tail is located on the distribution’s left part (Illowsky & Dean, 2017).
II. Highest School Grade Completed
These descriptive statistics indicate that the maximum and minimum highest school
grades completed (N=1000) are 16 and 1, respectively. The letter N denotes the total population
of the items (high school grades completed) sampled. The mean, standard deviation, and

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skewness are 11.28, 1.561, and -0.727, respectively. The standard error of skewness is 0.78. A
skewness to standard error ratio is often used to examine the normality of data.
III. Race and Ethnicity
The frequency distribution table shows frequencies, valid percentages, percentages, and
cumulative percentages based on race/ethnicity. Frequency describes the number of times an
event/item repeats itself (Carlberg, 2014). Cumulative rates are estimated by multiplying the
ratio of the cumulative frequency and sum of observations by 100. Valid percentages are
calculated by excluding “missing data.” In this case, the missing data excluded in ‘valid’ percent
calculations are two people: one DK (default knowledge) and one who refused.
The results show that the frequencies of Black (not Hispanic), Hispanic, White (not
Hispanic), and Other are 803, 128, 53, and 14, respectively. This brings the total to 998,
excluding the two missing individuals. Their percentages are 80.3, 12.8, 5.3, and 1.4,
respectively. This amounts to 99.8%, excluding 0.2% of the missing data. Valid rates are 80.5%,
12.8%, 5.3%, and 1.4%, respectively. This brings the total to 100%. On the other hand, the
cumulative percentages for Black, Hispanic, and White communities are 80.5, 93.3, and 98.6.
IV. Currently Employed
The “currency employed” distribution table shows the frequencies, valid percentages,
percentages, and cumulative percentages of people (N=1000) employed (Yes) and those
unemployed (No), as well as those whose employment information is missing in the system (2).
The total “valid” population is 998. Currently, there are 452 employed and 546 unemployed
individuals, representing 45.2% and 54.6% of the valid population, respectively. The ‘valid’
percentages are 45.3% and 54.7%, respectively. The cumulative proportions are 100% and
54.7%, respectively.

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V. Family Income from Prior Month
The family income distribution table shows the sample size (N=895) of the families
sampled, the minimum family income received last month (0$), and the maximum income
($6,593). The data also shows the mean income ($1,172.59 with a standard error of $26.345),
standard deviation ($788.153), and skewness ($2.030 with a standard error of 0.082). The
positive skewness value implies that the fatter/longer tail is located on the distribution’s right
side.

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References

Carlberg, C. (2014). Statistical analysis: Microsoft Excel 2013. Que Publishing.
Gray, J. R., & Grove, S. K. (2020). Burns and Grove’s the practice of nursing research:
Appraisal, synthesis, and generation of evidence (9 th ed.). Elsevier.
Illowsky, B., & Dean, S. (2017). Introductory statistics. Samurai Media Limited.