Descriptive Statistics
Descriptive statistics summarize and describe data. It represents a population’s mean, standard deviation, and shape. Descriptive statistics may tell different people and samples (Sard et al., 2020, p. 1469). Descriptive statistics may uncover outliers, trends, and odd numbers. It also helps compare datasets or test a hypothesis or theoretical model. According to Chiang et al. (2015), descriptive statistics organize, summarize, and display data. Descriptive statistics may help in decision-making by providing a summary of the facts. Descriptive statistics may show a dataset’s central tendency (mean or median) and dispersion (as indicated by the standard deviation or range). Descriptive statistics may test hypotheses, compare data sets, and find irregularities.
Variables’ Distribution
Moreover, there are additional specifications and descriptions. Chiang et al. (2015) and Bhattacherjee (2012) examine numerous elements that affect a 1000-word research study. Chiang et al. (2015) underline the relevance of independent variables unaffected by other factors in the study. Age, gender, ethnicity, education, employment, income, and psychological and social aspects, including attitudes, views, and values, are demographic variables. Health and mobility are the examples: Chiang et al. (2015) highlight independent factors and the dependent variables they affect. Quantify health, quality, and happiness; treatment adherence, health service use, and exercise are examples.
Another mediating factor that bridges the independent and dependent variables: self-efficacy, self-esteem, and social support. Environmental implications include resource availability, service accessibility, and social norms. Bhattacherjee (2012) also highlights the need for control variables, which are kept constant to check for external effects. Date, location, and research kind are factors. Chiang et al. (2015) and Bhattacherjee (2012) suggest using covariates to explain study variables. Age, gender, ethnicity, education, occupation, money, and psychological variables, including views, beliefs, attitudes, and lifestyle, may all play a role.
Presentation of the Variables’ Distribution
A histogram or frequency table is a graphical representation of data that illustrates the distribution of distinct variables. The distribution of a variable’s values in a data collection may be depicted graphically using frequency tables and histograms. A frequency table or histogram may aid in identifying data trends and outliers that may skew the findings. Histograms and frequency tables may be used to investigate the distribution of data points within a collection. When examining a dataset, it might be helpful to determine the frequency of specific values. The first column of a frequency table gives the variable’s values, while the second column indicates the occurrence frequency of each significance. The frequency of a significance reflects its occurrence within a particular dataset.
Distribution, Symmetrical or Asymmetrical, Dispersion
For symmetry, values must be distributed symmetrically around the mean. The mean, median, and mode are equal. The exact number of observations below and above the mean shows the curve is symmetrical around the mean. Extreme values have equal probability around the mean. The most common symmetrical distribution is the normal distribution (bell curve). Uniform, Binomial, Chi-Square, and Student-t Distributions are also balanced. Skewed distributions have data values not evenly distributed around the mean. Values are unequal, with more data points on one side of the mean. This occurs when one or a few dataset values diverge greatly from the rest. Right-skewed distributions have a large right tail and are the most common asymmetrical distributions. Left-skewed, bimodal, and log-normal distributions are asymmetrical. Data dispersion is assessed by standard deviation. Variance measures data differences. Range, the most basic dispersion statistic, indicates data gathering extremes. Dispersion is better measured by interquartile content.
Central Tendency
Mean
To establish the central tendency of a set, statisticians compute a statistic known as the mean by adding all the numbers in the group and dividing by the total number of digits. As a measure of such tendency, the most common alternative is the mean, or average (Corea et al., 2021). If five individuals’ test results varied from 50 to 90 (or 60 to 80), the mean score would be 70.
Median
Another measure of the centralized tendency, the median, is the number in the center of a set of numbers ordered from lowest to highest. The five persons in the above example would get a median score of 70 if they retook the test and received scores of 10, 20, 70, 80, and 90, respectively.
Mode
By selecting the value that occurs most often within a collection, one may derive a measure of central tendency known as the mode. The mode is most useful for nominal or ordinal data, whereas it is less useful for interval or ratio data. Consequently, if the same five individuals took the third exam and received 1, 2, 3, and 4, the mean would be 4.
Variability
Variability is the degree to which individual values in a data set differ. Take the difference between the lowest and highest numbers to get the range. The interquartile range is determined by subtracting the 25th percentile from the 75th percentile. The variance and standard deviation may be calculated by quadrupling the sum of the squared differences between each value and the mean. The range of scores would be 40, the interquartile field would be 25, the standard deviation would be 14.14, and the variance would be 200 if the same five individuals took the fourth exam and received 10, 20, 30, 40, and 50 points.
Reference List
Bhattacherjee, A. (2012) Social science research: Principles, methods, and practices, University of Florida.
Chiang, J.J. et al. (2018) “Affective reactivity to daily stress and 20-year mortality risk in adults with chronic illness: Findings from the National Study of Daily Experiences.“ Health Psychology, 37(2), p.170.
Corea, F. et al. (2021) “Telemedicine during the Coronavirus disease (COVID-19) pandemic: A Multiple Sclerosis (MS) outpatients service perspective,” Neurology international, 13(1), pp. 25–31.
Sard, N. M. et al. (2020) “RAPTURE (RAD capture) panel facilitates analyses characterizing sea lamprey reproductive ecology and movement dynamics,” Ecology and evolution, 10(3), pp. 1469–1488.