4 descriptive statistics and its measurements

Descriptive statistics

refers to the branch of statistics that deals with the collection, organization, presentation, and summarization of data. Its main purpose is to describe the basic features of data in a study, providing simple summaries about the sample and the measures.

• It does not draw conclusions or inferences beyond the data analyzed; instead, it presents information in a clear and understandable way

central tendency

describe the typical or central value of a dataset. They provide an idea of where the "center" of the data lies.

mean

median

mode

Measures of central tendency

mean

The sum of all data values divided by the number of observations.

Example: The average test score of a class.

MEDIAN

The middle value when data are arranged in order. If there is an even number of values, the median is the average of the two middle numbers. Example: The median income in a community.

MODE

The most frequently occurring value in the dataset. A dataset may have no mode, one mode, or multiple modes. Example: The most common blood type in a group of patients.

measures of dispersion

show how spread out or variable the data are. They help us understand whether data values are closely clustered or widely scattered.

range

variance

standard deviation

coefficient of variation

measures of dispersion

RANGE

The difference between the highest and lowest values.

VARIANCE

The average of the squared differences from the mean; shows overall variability.

STANDARD DEVIATION (SD)

The square root of variance; indicates how far values deviate from the mean on average.

COEFFICIENT OF VARIATION

The ratio of standard deviation to the mean, expressed as a percentage, useful for comparing variability between datasets.

Measures of location

identify the position of a particular value within a dataset. They divide the data into equal parts or indicate specific ranks.

percentile

quartiles

deciles

z-scores

measures of location

PERCENTILE

Divide the data into 100 equal parts. The 50th percentile is the median.

Example: A student who scored at the 90th percentile performed better than 90% of classmates.

QUARTILES

Divide the data into four equal parts (Q1, Q2, 03). Q2 is the median.

DECILES

Divide the data into 10 equal parts.

Z-SCORES

Indicate how many standard deviations a value is from the mean

Kurtosis

describes the shape of the distribution, specifically the "peakedness" or "flatness" of the data compared to a normal distribution. It tells us how data are concentrated around the mean.

MESOKURTIC

Normal distribution (bell-shaped curve).

LEPTOKURTIC

Data are more peaked; values cluster tightly around the mean, with heavier tails (more extreme values).

PLATYKURTIC

Data are flatter; values are spread more evenly, with fewer extreme values.