Descriptive Statistics
Descriptive statistics uses data that provides a description of the population either through numerical calculated graphs or tables. It provides a graphical summary of data.
It is simply used for summarizing objects, etc. There are two categories in this as follows.
- Measure of Central Tendency
- Measure of Variability
Let’s discuss both categories in detail.
Measure of Central Tendency
Measure of central tendency is also known as summary statistics that are used to represent the center point or a particular value of a data set or sample set. In statistics, there are three common measures of central tendency that are:
- Mean
- Median
- Mode
Statistics formula
Statistic | Formula | Definition | Example |
---|---|---|---|
Mean | x̄=∑ x/n | The arithmetic average of a set of values. It’s calculated by adding up all the values in the data set and dividing by the number of values. | Example: Consider the data set {2, 4, 6, 8, 10}. (2+4+6+8+10/ 5) Mean = 5 |
Median | Middle value in an ordered data set | The middle value of a data set when it is arranged in ascending or descending order. If there’s an odd number of observations, it’s the value at the center position. If there’s an even number, it’s the average of the two middle values. | Example: Data set {3, 6, 9, 12, 15}. Median = 9 |
Mode | Value that appears most frequently in a data set | The value that occurs most frequently in a data set. There can be one mode (unimodal), multiple modes (multimodal), or no mode if all values occur with the same frequency. | Example: Data set {2, 3, 4, 4, 5, 6, 6, 6, 7}. Mode = 6 |
Mean
It is the measure of the average of all values in a sample set. The mean of the data set is calculated using the formula:
Mean = ∑x/n
For example:
Cars |
Mileage |
Cylinder |
---|---|---|
Swift |
21.3 |
3 |
Verna |
20.8 |
2 |
Santra |
19 |
5 |
Mean = (Sum of all Terms)/(Total Number of Terms)
⇒ Mean = (21.3 + 20.8 + 19) /3 = 61.1/3
⇒ Mean = 20.366
Median
It is the measure of the central value of a sample set. In these, the data set is ordered from lowest to highest value and then finds the exact middle. The formula used to calculate the median of the data set is, suppose we are given ‘n’ terms in s data set:
If n is Even
- Median = [(n/2)th term + (n/2 + 1)th term]/2
If n is Odd
- Median = (n + 1)/2
For example:
Cars |
Mileage |
Cylinder |
---|---|---|
Swift |
21.3 |
3 |
Verna |
20.8 |
2 |
Santra |
19 |
5 |
i 20 | 15 | 4 |
Data in Ascending order: 15, 19, 20.8, 21.3
⇒ Median = (20.8 + 19) /2 = 39.8/2
⇒ Median = 19.9
Mode
It is the value most frequently arrived in the sample set. The value repeated most of the time in the central set is actually mode. The mode of the data set is calculated using the formula:
Mode = Term with Highest Frequency
- For example: {2, 3, 4, 2, 4, 6, 4, 7, 7, 4, 2, 4}
- 4 is the most frequent term in this data set.
- Thus, mode is 4.
Measure of Variability
The measure of Variability is also known as the measure of dispersion and is used to describe variability in a sample or population. In statistics, there are three common measures of variability as shown below:
1. Range of Data
It is a given measure of how to spread apart values in a sample set or data set.
Range = Maximum value – Minimum value
2. Variance
In probability theory and statistics, variance measures a data set’s spread or dispersion. It is calculated by averaging the squared deviations from the mean. Variance is usually represented by the symbol σ2.
S2= ∑ni=1 [(xi – ͞x)2 / n]
- n represents total data points
- ͞x represents the mean of data points
- xi represents individual data points
Variance measures variability. The more spread out the data, the greater the variance compared to the average.
There are two types of variance:
- Population variance: Often represented as σ²
- Sample variance: Often represented as s².
Note: The standard deviation is the square root of the variance.
Dispersion
It is the measure of the dispersion of a set of data from its mean.
σ= √ (1/n) ∑ni=1 (xi – μ)2
Introduction of Statistics and its Types
Statistics and its Types: Statistics is a branch of math focused on collecting, organizing, and understanding numerical data. It involves analyzing and interpreting data to solve real-life problems, using various quantitative models. Some view statistics as a separate scientific discipline rather than just a branch of math. It simplifies complex tasks and offers clear insights into regular activities. Statistics finds applications in diverse fields like weather forecasting, stock market analysis, insurance, betting, and data science.
In this article, we will learn about, What is Statistics, Types of Statistics, Models of Statistics, Statistics Examples, and others in detail.
Table of Content
- What are Statistics?
- Types of Statistics
- Descriptive Statistics
- Inferential Statistics
- Hypothesis Testing
- Data in Statistics
- Representation of Data
- Models of Statistics
- Data Analysis
- Types of Data Analysis
- Coefficient of Variation
- Applications of Statistics
- Business Statistics
- Scope of Statistics
- Limitations of Statistics
- Solved Problems – Statistics
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