To accomplish your dream of acquiring an MBA degree from an esteemed university abroad, the GMAT (Graduate Management Admission Test) is the essential gateway that one needs to clear. It is an international entry-level exam predominantly for the MBA programs in which aspirants have to qualify. It is conducted by the Graduate Management Admission Council (GMAC) and is a computer-based adaptive test. There are majorly four sections in the exam Quantitative, Verbal Reasoning, Analytical Writing Section, and Integrated Reasoning and together they hold a weightage of 800 marks. As the quant section encompasses hardcore calculations and maths, students often struggle with their preparation. If you are planning to appear for the GMAT exam this year, here is a blog which aims to elucidate the basic Statistics formulas to help you ace the quant section with good scores.

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Mean 

Mean is the average calculated by adding the sum of numbers given and then dividing it by the sum of values i.e., the number of values. In our list of Statistics Formulas, Mean is calculated as:

For Example:

Let us consider a data set of the values 10, 20 and 30. Calculate the mean value of the set. 

We will calculate the sum of the values given (Σx)= 10+20+30= 60 

The number of values is (N)= 3
x= 603=20
Hence, the mean of the given data set is 20.

Median 

The median is the middlemost number of a given data set of values. 

Statistics Formulas for Median are as follows: 

For Example: 

1. Here is a set of numbers 11, 13, 10, 18, 19. Calculate the median of the given set of values.

= Let us consider the data set: 11, 13, 10, 18, 19

Begin with arranging the numbers in ascending order: 10,11,13,18,19  
Now, the middle-most term is 13.

Hence, the mean of the given data set 10,11,13,18,19  = 13

But, what if the data set that has been provided to you has an even number of values like 8,6,10,4?

Let’s have a look at the distinct formula for calculating the median using the statistics formulas of a given data set having an even number of values.

Start with arranging the numbers in ascending order: 4,6,8,10 

Calculate the sum of the two middlemost values: (6+8)= 14

Divide the sum of the digits by 2= 14/2 = 7

Hence, 7 is the median of the data set 8,6,10,4.

The situation now arises, what if it is not feasible to calculate the median of the given data set by observation especially when the given data set is bulky? In that case, students can use the statistical formulas for the Median which are mentioned above.

Hence, 7 is the median of the data set 8,6,10,4.

The situation now arises, what if it is not feasible to calculate the median of the given data set by observation especially when the given data set is bulky? In that case, students can use the statistical formulas for the Median which are mentioned above.

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Mode  

Mode is basically the frequency (term) that occurs most frequently. 

Talking about statistics formulas, there is as such no set method to find out the Mode of a given set of data. It is generally calculated through observation. But if the data is bulky, students can use tally marks for frequency. 

For Example: 

6,6,3,8,9,1,3,6,8,7,6,9,5,2,6  is a given data set. Find the mode of this set of values. 

Clearly, we can see that the frequency 6 is occurring for the maximum times thus, it is the mode of the given data set. 

Range 

The range of given data set is calculated by subtracting the minimum term from the maximum term in a particular set. 

Range= Maximum Value- Minimum Value

For Example:

Calculate the range of the given data set 25, 10, 8, 60, 35, 82, 100. 

The maximum value in this set is= 100
The minimum value in this set is= 8 
Applying the above-given statistics formula, 
Maximum Value- Minimum Value= 100-8= 92
Hence, the range of the set is 92.

Also Read: Algebra Formulas for GMAT Quantitative Section

Standard Deviation 

Standard Deviation helps us in calculating how far the data in a given set have deviated from the mean. 

Statistics Formulas for Standard Deviation is as follows: 

For Example,

The step-wise calculation for finding the standard deviation of 1,2,2,4,6 is:

Variance

Variance quantifies the deviation of the given data from the mean. It is the expectation of a random variable’s squared deviation from its sample mean. The square of standard deviation equals variance. The formula for calculating variance is as follows:

Variance (σ²) = 

Where x is the observations given

 is the mean of the given data

n represents the total count of observations.

Practice Question

Now that you are through with statistics formulas, here are some of the important questions for you to practice this topic-

1. A manufacturing unit if toys X mentors such that the range of their weekly wages is rupees 5000. The estimated monthly salary is 10,000 above the lowest salary while the median monthly salary is rupees 7000 above the lowest salary. What is the minimum value of x? 
2. if the average of five positive integers is 40 where are the difference between the smallest and the largest of these five numbers is 10, what is the maximum value possible for the largest of these integers?
3. In a group of 30 friends, the average weight of one person increased by 1 kg then the weight of their cricket coach was added. If the average weight of a person including the weight of the cricket coach is 31 kg, determine the weight of their cricket coach? 
4. If the mean of numbers 104, 78, 42, x is 62. Then, find the mean of 48, 62, 124, 98. 
5. The estimated salary of a vehicle during the night shift for 15 consecutive days is rupees 90 per day. In the first seven days his average salary is 87 rupees birthday and for the last 7 days, the average salary increased to 92 rupees per day. What will be the salary of the worker on 8th day? 
6. All the positive integers from 1 to 45 are placed in groups of 5 and 9 each. What is the highest possible average of the medians of these five groups? 
7. Calculate median, mode and range of the set {31, 56,78, 98, 23, 39}.
8. Calculate the median of the set {x,y, 56, 28, 67} if x
9. Is ‘b’ the median of 3 numbers a, b, c? 
10. If m & s are the average and standard deviation of integers a, b, c and d, then, is s>0? 

Things to Remember

• The arithmetic mean is calculated by taking the sum of all observations and dividing it by the number of items.
• The median value is the value that is exceeded and exceeded by the same amount of observations.
• The mode of a set of observations is the value of the observations that appear the most frequently.
• Mode= 3 Median -2 Mean
• Variance is a statistic that shows how a piece of data differs from the mean. The difference in deviation from the actual value is referred to as variance.
• The standard deviation is equal to the square root of the variance.

Also check:

FAQs

Thus, we hope that this blog has helped you comprehend the essential statistics formula that you need to practice thoroughly for GMAT. If you are gearing up for the GMAT this year and need assistance regarding different sections, reach out to our experts at Leverage Edu and we will help you prepare for this exam with the best study materials and guides to ensure that you crack it with flying colours and get into your dream university!

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