Descriptive statistics

Qualitative variables : dichotomous/binary

Two possible values

What is frequency? What is relative frequency?

Frequency : Number of times a specific event, value, or category occurs within a dataset

Relative frequency: proportion or percentage of a specific value or category compared to the total number of observations

Qualitative variables : nominal/ categorical

Data that consist of names, labels, or categories and cannot be ordered

Example would be marital status : married, separated, widowed, etc.

Qualitative variables: ordinal

Data can be ordered but the differences between data values are meaningless

Example is self reported health status: poor, good, excellent

What is cumulative frequency? Cumulative relative frequency?

Cumulative frequency : totally frequencies in a data set, add up frequencies with the final one equaling the total

Cumulative relative frequency: proportion or percentage

How to describe data distribution?

• shape

• central tendency

• Variability

What is central tendency?

The mean

The median

The mode

What is the mean and its equation?

Arithmetic average (population mean\mu )

Sample mean :

\overline{x}=\frac{\left(\sum X\right)}{N}

Sensitive to outliers

In a normal bell-shaped distribution, all three indexes (mean, median, mode) coincide in the middle.

What is the median?

Middle score when scores are ordered

Not influenced by outliers

What is the mode?

Most frequent score

Bimodal, multimodal

Describe variability. What are the measures of variability?

High variability(platykurtic), low variability (leprokurtic)

Shape of distribution

Measures of variability:

1. Range

2. Interquartile range IQR

3. Variance

4. Standard deviation

5. Coefficient of variation CV

What is the measure of variability RANGE?

The smallest score subtracted from the largest

Sensitive to outliers

What is the measure of variability INTERQUARTILE RANGE?

3 quartiles that split sorted data into 4 equal parts

Q1, Q2(median), Q3

Reduces influenced of outliers

What is the measure of variability DEVIANCE?

Looking at different each score is from the center of distribution(Mean)

Deviance =x-\overline{x}

Total deviance=\sum\left(x-\overline{x}\right)

What is the measure of variability VARIANCE?

Indicated the total dispersion, or total deviance of scores from the mean=\frac{\left(\sum\left(x-\overline{x}\right)^2\right)}{N-1}

What is the measure of variability STANDARD DEVIATION?

Average deviation

Square root of variance

=\sqrt{\frac{\left(\sum\left(x-\overline{x}\right)^2\right)}{N-1}}

What is the measure of variability COEFFICIENT OF VARIATION?

CV=\frac{S.D}{\overline{x}}\cdot100 %

No need for specific units of measurement

Data presentations?

Graphs include bar chart, histograms, boxplot (box and whisker plot), scatter plots

Quantitative variables : discrete

Distinct, separate, countable values

Quantitative variables : continuous

Any value within a given range or interval

Measured, not counted