Exams K12 Statistics: Types of Stats Formulas, Concepts and More

Written By Vaibhav_Raj_Asthana
Last Modified 25-01-2023

Statistics: Types of Stats Formulas, Concepts and More

Statistics deals with the analysis, collection, interpretation, and organisation of data. The word Statistics may have different meanings depending upon the use and department. But here we will talk about the term in relation to Mathematics subject. Much of the early push for the subject of statistics came from government needs for census data as well as information on a variety of economic operations. The current requirement to convert vast volumes of data available in a variety of applied domains into valuable information has sparked both theoretical and practical breakthroughs in statistics.

The facts and figures that are gathered, evaluated, and summarised for presentation and interpretation are referred to as data. Quantitative and qualitative data are two types of information. Quantitative data is used to determine how much or how many of something, whereas qualitative data is used to assign labels or names to groups of similar items.

In this article, we will provide you with all the information on Statistics definition, sample questions, formulas, concepts as well as the NCERT solutions for the same.

Statistics Definition

As per the definition, the word ‘statistics’ appears to have been derived from the Latin word ‘status’ meaning ‘a (political) state’. It is a branch of mathematics that deals with the study of meaningful information and how to use it.

Statistics Method

Using statistics for analysis, prediction, management and interpretation of data or datum involves some basic steps. These are:

i) Collection of Data
ii) Presentation of Data
iii) Graphical Representation of Data
iv) Measures of Central Tendency

We will discuss the above topics in detail in the next few sections along with examples.

Collection of Data: Statistical Data Collection

In this step, all the data is gathered like heights of 20 students of your class or heights of 15 plants in or around your school or number of absentees in each day in your class for a month.

Here two types of data are collected i.e. primary data that refers to data collected by the investigator herself or himself with a definite objective and secondary data that is information was gathered from a source that already had the information stored.

Presentation of Data

Once you have gathered your data you need to express it in a form that is easy to understand, meaningful & gives its main features at a glance. Consider the below case:

We can use the concept of frequency to present the above data in a structured and easy manner.

Marks	Number ofStudents (i.e., the frequency)
10	1
20	1
36	3
40	4
50	3
56	2
60	4
70	4
72	1
80	1
88	2
92	3
95	1

Graphical Representation of Data

The representation of data using tables was explained in the previous section now let us look at the other way of representing data i.e. graphical representation. Here we can present data in 3 formats i.e.

1. Bar Graphs
2. Histograms
3. Frequency Polygons

Bar Graphs

A bar graph is a pictorial representation of data where usually bars of uniform width are drawn with equal spacing between them on one axis (say, the x-axis), depicting the variable. The values of the variable are shown on the other axis (say, the y-axis) and the heights of the bars depend on the values of the variable.

Histograms of uniform width, & of varying widths

A histogram is the same as a bar graph but it is used for continuous class intervals. consider the table below that represents the weight of 36 students of a class.

Weights (in kg)	Number of Students
30.5 – 35.5	9
35.5 – 40.5	6
40.5 – 45.5	15
45.5 – 50.5	3
50.5 – 55.5	1
55.5 – 60.5	2
Total	36

Taking the scale as 1 cm = 5 kg, we get the following histogram:

In case of a varying with histogram, the with of the distribution varies and rest everything is the same.

Frequency Polygons

To draw a frequency polygon we require the mid-points of the class intervals used in the data or we can first draw a histogram and find the midpoint on the bars and connect them. These mid-points of the class intervals are called class-marks.

Frequency Polygon without Histogram in Statistics — Frequency Polygon without Histogram

Formulas In Statistics

Here are some formulas that are used to calculate various values:

Sample Mean (x̅)	( Σ x_i ) / n.
Population Mean (μ)	( Σ x_i ) / N.
Sample Standard Deviation (s)	\(\sigma=\sqrt{\frac{1}{N}\sum_{i=1}^{n} (x_i-\bar x)^2}\)
Population Standard Deviation (σ)	sqrt[ Σ ( X_i – μ )² / N ]
Sample Variance (s²)	Σ ( x_i – x̅ )² / ( n – 1 )
Population Variance (σ²)	Σ ( X_i – μ )²/ N
Range (R)	Largest data value – smallest data value

Measures of Central Tendency in Statistics

By using measures of central tendency or averages we can find out if the representation of data using various forms like frequency distribution, bar graphs, etc was worth or not and do we need to study all of the data or some specific points.

Let us consider a case where two students scored some marks in a test having 5 questions of 10 marks each:

Question Number	Diana’s Score	Clark’s Score
1	10	4
2	8	7
3	9	10
4	8	10
5	7	10

After receiving their test copies, both of them found their average scores as:

Diana’s average score = 42 ÷ 5 = 8.4

Clark’s average score = 41 ÷ 5 = 8.2

Now arranging the score in ascending order we get;

Diana’s Score	Clark’s Score
7	4
8	7
8	10
9	10
10	10

Based on the above table Clark made some assumptions and these are:

Clark said that since his middle-most score was 10, which was higher than Diana’s middle-most score, which is 8, his performance should be rated better. But Diana was not convinced.
To convince Diana, Clark tried out another strategy. He said he had scored 10 marks more often (3 times) as compared to Diana who scored 10 marks only once.

To settle the dispute between the two we can use the concepts of Mean, Median, and Mode.

Sample Questions on Statistics

Here are some questions that are based on the concepts studied on this page:

Q1. Give five examples of data that you can collect from your day-to-day life

Q2. The blood groups of 30 students of Class VIII are recorded as follows: A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,
A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students?

Q3. The relative humidity (in %) of a certain city for a month of 30 days was as follows:
98.1, 98.6, 99.2, 90.3, 86.5, 95.3, 92.9, 96.3, 94.2, 95.1
89.2, 92.3, 97.1, 93.5, 92.7, 95.1, 97.2, 93.3, 95.2, 97.3
96.2, 92.1, 84.9, 90.2, 95.7, 98.3, 97.3, 96.1, 92.1, 89
(i) Construct a grouped frequency distribution table with classes 84 – 86, 86 – 88, etc.
(ii) Which month or season do you think this data is about?
(iii) What is the range of this data?

Q4. The following number of goals were scored by a team in a series of 10 matches: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3. Find the mean, median and mode of these scores.

Q5. The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95.

FAQs

Look below the questions that are mostly asked on the topic:

Q1. What are the two types of statistics?
Ans. The 2 types are:
i) Descriptive Statistics
ii) Inferential Statistics

Q2. What is the importance of Statistics in real life?
Ans. It is being widely used in data analysis to formulate strategies for the better growth of a company. We can also use it to identify patterns, doing predictive analysis & make forecasts as well.

Q3. How is statistics applied in Maths?
Ans. Statistics is used for data collection, representation, analysis and prediction.

Q4. Where do I find Statistics Formula?
Ans. Students can refer to this article for Statistics Formula.

Q5. What is the definition of statistics?
Ans. As per the definition, the word ‘statistics’ appears to have been derived from the Latin word ‘status’ meaning ‘a (political) state’. It is a branch of mathematics that deals with the study of meaningful information and how to use it.