 Statistics is a method of collecting data and summarizing the data. The study of the collection, analysis, interpretation, presentation, and organization of data is called Statistics. Now a days Statistics is very important because today we live in the information world and much of this information is determined mathematically by Statistics. The statistics concept is necessary for informing correct data. Go through the entire article to be well versed with Statistical Terms and Concepts along with Examples.

## Statistical Terms and Definitions

The various terms related to statistics such as Data, Mean, Mode, Raw data, Observation, Array, Range are explained clearly. Let us discuss them in detail by considering few examples.

### Data

Statistical refers to the set of numerical facts collected for the purpose of an investigation is called Statistical data. There are two types of statistical data,

1. Primary Statistical data
2. Secondary Statistical data

The data can be about population, birth, death, the temperature of place during a week marks scored in the class runs scored in different matches, etc.

Primary Statistical Data: The data which are naturally obtained by the investigator himself for the first time for his own use is called Primary Statistical data. Primary data also called First Handed Data.

Secondary Statistical Data: The data which was collected by someone with the help of primary data is called secondary data, which is artificial in nature. Secondary Statistical data is also called Second Handed Data in nature. They are two types of Secondary Statistical Data,

1. Raw data (or) ungrouped data.
2. Array

Example:

The below table is an example of statistical data, in this, the data will be regarding the number of students opting for different subjects like English, Maths, Science, Social.

 Subjects English Maths Science Social No. of students 25 30 40 20

Based on the above table, we can easily calculate the total numbers of the students, average of the students. Therefore the total number of students is 115. If we want to calculate two subjects total then we can add that two subjects student numbers.

### Raw Data (or) Ungrouped Data

Raw data is also called ungrouped data. These types of data are obtained in their original form. When some information is randomly and presented is called Raw Data.

Example:

The example of Raw data (or) ungrouped data is given below. The students in class VII A are 15 and marks obtained by them out of 25 in the English Test. Based on the given data we can know each student’s marks, this means a student is one data and marks is another data we are knowing the marks based on the student. In some marks will be given more students but student strength gives less at that time we are comparing both then choose the predict or collect values.

Given the marks (out of 25) obtained by 15 students of class VII A in English in a test.

16, 13, 20, 21, 15, 25, 14, 19, 10, 20, 22, 12, 18, 15, 23

### Array

Generally, Arrays are the data that are put in the form of a table which is also called the presentation of data. simply, Array refers to the arrangement of data in ascending or descending of data order. If the number of times an observation occurs, then it is called frequency distribution. Array data is also called Arrayed data.

Example:

In this example, the main concept is array is putting the raw data in ascending order or descending order. The below data is given, we can arrange them in ascending order,

Given data is 12, 10, 10, 12, 8, 3, 7, 2, 17, 20, 15

The given data is arranged in ascending and represented as,

2, 3, 7, 8, 10, 10, 12, 12, 15, 17, 20

### Observation

The observation is defined as every entry is collected as a numerical fact in the given data. In other words, an observation in statistics means a value of something of interest you are measuring or counting during a study or experiment ‘like a person’s height, a bank account value at a certain point in time, or a number of animals like that. The observation unit measures the same thing in the context.

For example, let’s say you are measuring how well your savings perform over the period of one year. You record one measurement that is your bank account balance for every three months for a total.

### Range

Statistics Range means the difference between the highest value and the lowest value of the observation is called the range of the data. In other words, statistics the range of a set of data is the difference between the largest and smallest values. The formulae of Range is,

Range (X) = Max(X) – Min(X)

The above range formula is used for calculating the same value, the minimum range is subtracted from the maximum range value to get the Range Value. X is denoted as the value of data.

Example:

In an exam, the highest marks obtained are 20 and the lowest marks are 5 then what is the range?

Highest marks obtained = 20

Lowest marks obtained = 4

Range (X) = Max(X) – Min(X)

Therefore, range = highest marks – lowest marks = 20 – 5 = 16

Another example is, in {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9 − 3 = 6.
The range can also mean all the output values of a function.

### Mean

Mean and mode is used to measure the central tendency. Mean is defined as the average or the most common value in a collection of numbers. The mean or average of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

If x, x1, x3, ……… xn are n observations then
Arithmetic mean = (x1 + x2 + xn, ……………. xn)/n = (∑xi)/n.
∑ is the Greek letter sigma and is used to denote summation.

### Mode

In Statistics, the mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. The mode can be the same value as the mean and/or median, but this is usually not the case.

A Mode in statistics is defined as the value that has a higher frequency in a given set of data. It is the value that appears the most number of times.  Two modes in a given set of data, such values are called Bimodal. A set of numbers with three modes is called Trimodal, and any set of numbers with more than one mode is called Multimodal.

The advantages of mode in statistics are below,

• The mode is equal to understand and calculate.
• The mode is not affected by extreme values.
• The mode is easy to identify in a data set and in a discrete frequency distribution
• The mode is useful for Qualitative data.
• The mode can be located graphically.
• The mode can be computed in an open- Ended frequency table.

Example:

In the following list of numbers, 12 is the mode since it appears more times in the set than any other numbers:

3, 3, 4, 5, 5, 6, 8, 9, 12, 12, 12, 24, 27, 37

### Solving Problems on Statistical Terms

Example 1:

The height of 12 girls was measured in cm and the results are as follows:

149, 144, 126, 138, 145, 130, 145, 150, 133 ,129, 131, 151

(i) What is the height of the tallest girl?

(ii) What is the Height of the shortest girl?

(iii) What is the range of data?

Solution:

Given the 12 girls heights in cm

To finding the tallest girl height and shortest height and range.

(i) The height of the tallest girl is 151 cm

(ii) The height of the shortest girl is 126

(iii) We know the Range Formula,

Range (X) = Max (X) – Min (X )

Substitute the given values in above formula, we get

Range = 151 cm – 126 cm

= 25 cm

Therefore, Range = 25 cm.

Example 2:

Find the Mean of the given data

5, 6, 9, 10, 15, 17, 19, 20, 25, 30

Solution :

Given the data is 5, 6, 9, 10, 15, 17, 19, 20, 25, 30

Now, we can calculate the Mean

Mean = Total sum / no. of terms

Mean = 156 / 10 = 15. 6

Therefore, the Mean of a given data is 15.6

Example 3:

Find the Mode of a given data.

3, 3, 5, 6, 13, 15, 15, 19, 20 , 15

Solution:

Given the data is 3, 3, 5, 6, 13, 15, 15, 19, 20, 15

Now, we are finding the Mode of a given data.

Mode means the value that has the higher frequency in a given set of data.

In this given data the higher frequency data is 15.

Therefore the Mode of a given data is 15.