Statistics basics can be learned easily and quickly and are the basic requirement in every competitive exam and day-to-day life.
Attempting any statistics basics-related questions requires a correct understanding of the question and what is asked for. A wrong interpretation will lead to incorrect answers and a waste of time.
Nowadays, statistics basics questions asked in IBPS, SBI, or other competitive exams are not direct calculations but it’s derived from questions that we’ve to take the help of statistics basics to get the answers.
Table of Contents
What is Statistics?
The word ‘Statistics’ is used as a singular noun, meaning the subject that deals with the collection, presentation, and analysis of data as well as drawing meaningful conclusions from the data.
As soon as the work related to the collection of data is over, the data analyst has to find out ways to present them in a form that is meaningful, easily understood, and gives its main features at a glance.
It is well said that one picture is better than a thousand words. Usually, comparisons among the individual items are best shown by means of graphs. The representation then becomes easier to understand than the actual data.
What are Statistics Basics?
Statistics Basics consists of some of the basic knowledge on analyzing the data. There are a few important concepts to remember as a part of Statistics Basics. Below are the few Statistics Basics that we’ll cover in this article:
- Range
- Frequency
- Mean
- Median
- Mode
What is Range?
The difference between the highest and the lowest values in the data is called the range of the data. When the data collection is over then the first thing done by the analyst is to find out the range of data. This makes it easier to understand, interpret and present the data.
What is Frequency?
Frequency is the number of repetitions of a particular type of data in the whole collection. Finding frequency is also helpful in representing the processed data.
For example, if a class has written a test for 10 maths questions. And we to find out how many students gave the wrong answer to any particular question. So finding this number can be interpreted as frequency.
What is Mean?
The Mean (or average) of a number of observations is the sum of the values of all the observations divided by the total number of observations. It’s similar to Mathematical Average. Click here to find out more on average.
What is the Median?
The Median is the value of the given number of observations, which divides it into exactly two parts. So, when the data is arranged in ascending (or descending) order the median of ungrouped data is calculated.
What is Mode?
The Mode is the value of the observation which occurs most frequently, i.e., an observation with the maximum frequency is called the mode.
Example of Statistics basics
Below is the example of Statistics basics that will help in understanding Range, Frequency, Mean, Median, and Mode:
Example 1: Below are the marks obtained by 30 students of a Class out of 100: 60, 88, 36, 92, 95, 40, 50, 56, 60, 36, 40, 36, 40, 92, 40, 50, 50, 56, 60, 10, 20, 70, 92, 88, 80, 70, 72, 70, 70, 60. Find Range and Frequency of Marks?
Solution 1: On scanning the above marks we can clearly find out the range which is the smallest and the biggest number.
Range = 10 to 95
Frequency is to find out the number of occurrences of a number, as shown below:
| S.No. | Marks | Frequency |
| 1 | 10 | 1 |
| 2 | 20 | 1 |
| 3 | 36 | 3 |
| 4 | 40 | 4 |
| 5 | 50 | 3 |
| 6 | 56 | 2 |
| 7 | 60 | 4 |
| 8 | 70 | 4 |
| 9 | 72 | 1 |
| 10 | 80 | 1 |
| 11 | 88 | 2 |
| 12 | 92 | 3 |
| 13 | 95 | 1 |
Example 2: Find the mean (or average) of the given data in the above question?
Solution: To calculate mean we need to find out the total or sum of all marks obtained by 30 students:
Sum = 60 + 88 + 36 + 92 + 95 + 40 + 50 + 56 + 60 + 36 + 40 + 36 + 40 + 92 + 40 + 50 + 50 + 56 + 60 + 10 + 20 + 70 + 92 + 88 + 80 + 70 + 72 + 70 + 70 + 60
Sum = 1779
Mean or Average = Sum / 30
Mean = 1779 / 30 = 59.3
Example 3: Marks obtained by 9 students in a class is as below:
55, 60, 45, 49, 50, 47, 52, 44, 48. Find the median?
Solution 3: As the number of students is 9 which is an odd number so the median can be calculated as
Median Position = (Number of Students + 1) / 2
Median Position = (9 + 1) / 2
Median Position = 10 / 2 = 5
Now first we need to sort the numbers to see which number is at a median position. Sorted Marks are: 44, 45, 47, 48, 49, 50, 52, 55, 60
Hence in the 5th Position, we’ve 49, which is the Median.
Example 4: Below are the marks obtained by 30 students of a Class out of 100: 60, 88, 36, 92, 95, 40, 50, 56, 60, 36, 40, 70, 40, 92, 40, 50, 50, 56, 60, 10, 20, 70, 92, 88, 80, 70, 72, 70, 70, 60. Find Mode of Marks?
Solution 4: As from the above-given data we can see that 70 is repeated for the maximum number of times. Hence 70 is the Mode.
Practice Questions on Statistics
Below are Practice Questions on Statistics:
- Marks obtained by 10 Students in a Class out of 10: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3. Find Range, Frequency, Mean, and Mode?
- Marks obtained by 10 Students in a Class out of 10: 7, 8, 4, 6, 9, 7, 3, 3, 4, 3. Find Range, Frequency, Mean, and Mode?
- Marks obtained by 15 Students in a Class out of 10: 41, 39, 48, 52, 46, 62, 54, 42, 52, 60, 40, 96, 52, 98, 40. Find Range, Frequency, Mean, and Mode?
- Marks obtained by 15 Students in a Class out of 10: 71, 89, 48, 82, 56, 62, 54, 40, 52, 60, 50, 96, 52, 98, 40. Find Range, Frequency, Mean, and Mode?
- Marks obtained by 15 Students in a Class out of 10: 71, 89, 48, 82, 56, 62, 54, 40, 52, 60, 50, 96, 52, 98, 40. Find Median?
- Marks obtained by 10 Students in a Class out of 10: 7, 8, 4, 6, 9, 7, 3, 3, 4, 3. Find Range, Frequency, Mean, and Mode?
- Find the mode of below numbers: 14, 25, 14, 28, 18, 17, 18, 14, 25, 22, 14, 18.
- Marks obtained by 10 Students in a Class out of 100: 49, 52, 78, 56, x, x + 2, 72, 88, 64, 91. If the Median is 77 then find the value of x and Mean?
Final Words
Practicing the above questions for Statistics basics is not the end of your practice, but it’s the start of a new journey to apply Statistics basics with multiple approaches for a correct and faster way. For cracking competitive exams one must practice Statistics basics without a calculator is a must.