# Descriptive Statistics with its statistical approach

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## What are Descriptive Statistics and their use?

Descriptive Statistics, as the name suggests, is used to summarize or describe the data set. As per the data sets, it is a set of observations or responses that are gathered from a population or a sample of a population. Where a population is an entire group from whom data is collected, a sample is much lesser than a population and generally represents an entire population. Now, the population doesn’t always have to be dealing with people, rather it can be any other entity such as companies, cities, countries, etc.

As for descriptive statistics, as it is quantitative research while working on the datasets there are various statistical operations used on variables such as mean, standard deviation, frequency, etc. This descriptive statistics in turn helps us describe the characters of a variable and the relations between them.

Example:

You are taking a survey about what genre of books a population likes.

This will give you all sorts of genres but you will have to prepare a visualization of it, to simply get a readable picture showing how many percentages of people like what genre. Well, as we talk about a graphical representation, it can be a bar graph, pie chart, etc. with various colour codes and labels.

For the next step and an application for the descriptive statistics, there are inferential statistics that help us conclude that our hypothesis matches the data sets and check whether we can generalize it over to a larger population.

## What are Descriptive Statistics Types:

There are statistical ways to

### Distribution- focuses on the frequency of each value

• Frequency Distribution

It indicates how many times a particular value occurs in a data set. This can be represented using graphs and tables and can be counted in numbers or percentages.

Example 1: A survey of 20 people choosing their favourite book genre. The frequency distribution table would look something like this;

 Genre Number Romance 7 Mystery 5 Philosophy 5 Horror 3

These tables indicate all the genres and the number of times they occurred in the survey. This is called Simple Frequency Distribution.

Example 2: A survey of students’ marks in mathematics. The frequency distribution table would look something like this;

 Marks Percentage 0-25 2% 26-50 8% 51-75 50% 76-100 40%

The above tables give us the range of marks of students in mathematics out of 100 and their corresponding percentage of students scoring that many marks. Let’s say for the marks ranging from 51-75 there are 50% of students who scored between 51-75. This is called Grouped Frequency Distribution.

### Central Tendency

Focuses on calculating the centre or average of a gathered sample dataset. Let’s take the first 5 responses of a survey of people giving their age.

• Mean

Calculates the average of the data. Mean is denoted by ‘M’. to calculate the mean, just add all the age responses and divide them by the total number of responses denoted by ‘N’.

Example:

 Data Set 6,45,23,13,67 Sum of all responses 154 Total number of responses (N) 5 Mean (M) 154/5= 30.8

That means, 30 years and 8 months is the average age according to the above data set.

• Median

It gives the value that is exactly at the centre of the data set. Arrange the responses in ascending order and manually find their middle.

Example 1: For the above data set (where the response is in odd count), the median would be.

 Data Set 6,13,23,45,67 Median 23

Example 2: For the above data set, let’s take the response in even numbers. For this we will have two middle values, hence calculate their mean and it is the median.

 Data Set 6,13,23,45,67,80 Middle two values 23,45 Mean of two values (23+45)/2 =34

### Hence the median is 34.

• Mode

It gives the most occurred response value. A data set can have from zero to multiple modes.

Example: For the above survey there are zero modes since no age number is repeating. But if we modify it as;

 Data Set 6,13,13,23,45,67,80 Mode 13

### Variability

Variability describes how scattered the data set is. This diversity of values in a dataset is given by the following measures of variability.

• Range

It gives a depiction of how far apart the two extremes of a range are. It is calculated by simply subtracting the lowest number in ranger with the highest one.

Example: For the above survey of ages;

 Data Set 6,13,23,45,67 Range 67-6= 61
• Standard Deviation

It is the average amount of variability in the dataset. Concerning the mean, it shows how far each value lies from it. Hence, standard deviation represents how large the variation in the data is.

Example: For the above survey of ages.

It has six steps

Step1) Write each score and its mean

Step2) To get its deviation, Score – Mean

Step3) Square each deviation

Step4) Add all the squared deviation

 Raw data Deviation from mean Squared deviation 6 6 – 39 = -33 1089 13 13 – 39 = -26 676 23 23 – 39 = -16 256 45 45 – 39 = 6 36 80 80– 39 = 41 1681 67 67-39 = 28 784 M = 39 Sum = 0 Sum of squares = 4522

Step5) Divide square of deviations by N-1

4522- (6-1) = 4517

Step6) Now find the square root of the found number.

√4517 = 67.2 is the Standard Deviation.

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• Variance

It is simply the square of the standard deviation. It gives about how much degree the data is scattered. Denoted by ‘s2’

Example: For the above example of standard deviation, its variance will be;

s = 67.2

s2 = 4515

With all of those calculations, it is certain that now it would be easy to work with Descriptive Statistics and derive the necessary outcomes regarding data sets.

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