Describing Data : Summary Measures

Describing Data : Summary Measures

Published by: Anu Poudeli

Published date: 20 Jun 2023

Describing data : Summary measures

Summary measures are statistical methods for succintly and meaningfully describing and summarizing data. They give a quick overview of a dataset's key features, enabling researchers and analysts to make inferences and learn more about the data.

Here are a few typical summary metrics :

1. Central Tendency Measures

a. Mean : The mean of a database is determined by adding up all the values and dividing the total by the number of observations.

b.  Median : When a dataset is sorted in either ascending or descending order, the median is the midway value. It serve as the data's midway.

c. Mode : The most prevalent value (s) inside a  dataset is/ are the mode.

2. Dispersion measures 

a. Range : The difference between a database maximum and minimum values, which shows how evenly distributed the data are.

b. Variance : The average of the squared deviations from the mean, which gives an indication of how widely apart data points are from one another.

c. Standard Deviation : The avarage deviation of data points from the mean, calculated as the aquare root of variance.

3. Dimensions of Form

a. Skewness : Describes the asymmetries in the distribution of a dataset. A longer tail on the right is indicated by positive skewness, whereas a longer tail on the left is indicated by negative skewness.

b. Kurtosis : Determine if a distribution is flat or peaks . A sharper peak and heavier tails are indicated by high kurtosis, whereas a flatter peak and lighter tails are indicated by low Kurtosis.

4. Quartiles and Percentiles

a.  Percentiles : Divide the data into hundredths or hundredths (percentiles) to detrmine the percentiles. The value below  which 25% of the data falls, for instance, is represented by the first quartile's 25th percentile.

b. Quartiles : Divide the data into quarters using quartiles. The median is represented by the second quartile (Q2) , the 75th percentile is re[presented by the third quartile (Q3) and the first quartile (Q1) is the 25th percentile. 

5.  Interquartile Range (IQR) : The range between the first and third  quartiles, or interquartile range (IQR), provides a measurement of the spread of the middle 50% of the data.

6. Outliers : Values that are noticeably outside the normal distribution of the data and may point to mistakes or irrational findings.

Analysts can better grasp  the distribution, central tendency, variability, and form of the data with the use of these summary metrics. They are helpful for comparing things, finding patterns, seeing abnormalities, and coming at intelligent judgements. When evaluating statistics, it is crucial to take the context and constraints of these metrics into account.