# Basic Statistics for Dummies 1

**statistics** is a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of masses of numerical data to make inference and reach decisions in the face of uncertainty in economics , agriculture, education e.t.c

statistics can be subdivided into descriptive **statistics** and inferential **statistics**

**Descriptive Statistics**

Descriptive statistics are brief descriptive coefficients that summarize and describe a given data set, The most recognized types of descriptive statistics are measures of center: the **mean**, **median**, and **mode****,** which are used at almost all levels of math and statistics.

**Mean:** The “average” number; found by adding all data points and dividing by the number of data points. (∑x)/N

Here,

∑ represents the summation

X represents observations

N represents the number of observations .

Example: The mean of 3, 2, and 7 is (3+2+7)/3 = 12/3 = 4

**Median:** The middle number; found by ordering all data points and picking out the one in the middle (or if there are two middle numbers, taking the mean of those two numbers).

Example: The median of 2, 1, and 5 is 2 because when the numbers are put in order (1, 2, 5), the number 2 is in the middle

**Mode:** The most frequent number — that is, the number that occurs the highest number of times.

Example: The mode of {4, 2, 4, 3, 3, 3}, is 3because it occurs three times, which is more than any other number.

# inferential **statistics**

**Inferential statistics** allows you to make predictions (“inferences”) from that data. With inferential statistics, you take data from samples and make generalizations about a population.

**Population:** is the entire pool from which a **statistical** sample is drawn. A **population** may refer to an entire group of people, objects, events, hospital visits, or measurements.

**Sample**: is a set of element selected from a given population, **Samples** are also used in **statistical** testing when population sizes are too large for the test to include all possible members or observations.

# Important Terms in Statistics

**Average**

also called mean; a number that describes the central tendency of the data

**Parameter**

a number that is used to represent a population characteristic and that generally cannot be determined easily

**Population**

all individuals, objects, or measurements whose properties are being studied

**Probability**

a number between zero and one, inclusive, that gives the likelihood that a specific event will occur

**Proportion**

the number of successes divided by the total number in the sample

**Sample**

a subset of the population studied

**Variable**

a characteristic of interest for each person or object in a population

**Data**

a set of observations (a set of possible outcomes); most data can be put into two groups: **qualitative** (an attribute whose value is indicated by a label) or **quantitative** (an attribute whose value is indicated by a number). Quantitative data can be separated into two subgroups: **discrete** and **continuous**. Data is discrete if it is the result of counting (such as the number of students of a given ethnic group in a class or the number of books on a shelf). Data is continuous if it is the result of measuring (such as distance traveled or weight of luggage)

**Quantitative data**

**Quantitative data** is defined as the value of **data** in the form of counts or numbers where each **data**-set has an unique numerical value associated with it, **Quantitative** Information — Involves a measurable quantity — numbers are used. Some **examples** are length, mass, temperature, and time.

**Qualitative data**

Qualitative data is non-numerical data that is observed, descriptive, and subjective. **Examples of qualitative data** include sex (male or female), name, state of origin, citizenship, etc. A more practical **example** is a case whereby a teacher gives the whole class an essay that was assessed by giving comments on spelling, grammar, and punctuation rather than score.

**Types of Quantitative data**

(1) DISCRETE DATA

(2)CONTINUOUS DATA

**DISCRETE DATA**

**Discrete data is** information that can only take certain values (countable or finite) **examples :**

- The number of students in a class.
- The number of workers in a company.
- The number of parts damaged during transportation.
- Shoe sizes.
- Number of languages an individual speaks.
- The number of test questions you answered correctly.

**CONTINUOUS DATA**

Continuous data are data that can take any value (within a range).

Example: People’s heights could be any value (within the range of human heights), not just certain fixed heights.

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