GMAT quant section is quite expansive and intricate too. It comprises the majority of the main topics that we had in high school. Thinking it to be easy, therefore? Not really. It is GMAT after all, an exam that leads MBA aspirants to pursue their degree in the world’s best institutes. The syllabus of the quant section of GMAT holds a place for statistics too. Statistics, a quite dealt with the topic during school and for college days as well (for few). It is generally stated that students who did practice maths during their +2s in a meticulous way, for them it is easier to cope with. But, it is often witnessed that certain commonplace mistakes are done by the majority of the students. So, today let us revisit the topic from the beginning along with discussing a few rules which when recollected will help them score high.
Mean or the arithmetic mean or the average is probably the simplest of the lot which states finding the ordinary average: adding up all the objects on the queue/number of items or
Average = sum of items/number of items
For example, Peter scored 86 in English, 70 in Maths, 75 in Science, and 80 in Economics. Let us calculate his average score.
Solution: 86+70+75+80/4 = 77.75.
The next term to be familiar with is median. Median is the process of finding the middle value when the digits are structured in either ascending or descending order. When the data set has an odd setting, the middle value will be chosen. If it has even set, the mean of both of the middle numbers is chosen.
For example: Find the median of the set – 7, 9, 5, 3, 2.
Let us first set it in order: 2, 3, 5, 7, 9
As this is an odd setting the median is 5.
Let us take another set of numbers: 5, 6, 8, 9, 7, 3
Let’s arrange it in order: 3,5,6,7,8,9.
This is an even setting so the median will be – 6+7 =13.
The mode is the most used value in a set of data. A set may have more than one or no mode at all.
Example 1: 1,2,9,8,3,9,7
Here, the mode is 9.
Example 2: 7, 9, 3, 86, 45, 94, 86, 3
Here, the answer is bimodal set as there are two modes – 86 and 3 respectively.
Example 3: 5, 4, 3, 2, 1
This one has no mode.
Measures of Dispersion
Here, we will be explaining two measures of dispersion - Range and Standard Deviation
The easiest way of calculating the dispersion is by range. One can just find it out by finding the difference between the highest and the lowest values in a set of numbers.
For example: 5, 6, 9, 3, 7. Here, the highest value is 9 and the lowest is 3. So the range will be 9-3 = 6
The standard deviation measures how distant are the data set from the mean or in other words, the deviation from the mean. To explain it let us first count the mean-
Let us take into account two data sets – 0, 2, 4 and 1, 2, 3
As we can see after adding both the data sets and dividing them by the number of data in each set, it is coming 3.
Now, the mean 3 is distant from the first set (0, 2, 4) than the second set (1, 2, 3). This means the standard deviation of 0, 2, 4 is greater than 1, 2, 3.
Ground Rules for Preparation of GMAT Statistics
From the definitions discussed earlier, the standard deviation has proved to be the most complicated one. Now, as we already know GMAT quant section is itself tricky so to cope with the statistics part, it is really needed from the student’s part to work hard.
You cannot have a negative standard deviation
In a given data set, if all the values are equal, this means the mean will also be equal. The standard deviation, in that case, will be zero. It is to be noted that the standard deviation can never be zero and if you are getting the same then it is time you do it all over again.
Adding the same numbers with the values of the data set either by subtracting or adding will result in same standard deviation
To understand this let us take an example – let us take a set of data set – 2, 3, 4 and add it with 5. So, the answers will be 7, 8, 9. The standard deviation will also be the same for both the sets.
Multiplication always changes standard deviation except when multiplied by 1 or -1
If the case needs a rise in the data set by power then the standard deviation will always change.
A change in mean because of the addition of number is the same with a standard deviation
When any new number is added to a set of data the mean changes and so does the standard deviation.
Fathoming the Standard Deviation Formula
Though it is not mandatory to learn the formula while solving the sums but it is advised to keep it in mind for the concerned situation. Learning the standard deviation formula will undoubtedly provide you with a precise way of understanding the sum and easily solve it with ease considering the trivial 2 minutes for solving the GMAT quant section.
The formula can be learned anyhow but knowing exactly how the formula can be utilized is by answering these questions – finding the mean of a set of value, find the differences between every value and the mean, squaring all the differences and taking out the average differences which eventually will result in the variance, discovering the square root of the variance.
Figuring out the effect of fluctuating numbers on data sets
Putting on numbers to a data set will not only result in a difference in standard deviation but also in mean, median, mode, and range. Further addition of numbers states that the mean will always be effected. But if the number is similar to that of the value-added then the mean will be the same. The same action is incorporated for the median and mode. So, it is always advised while solving a multi-part question which is quite common in the GMAT quant section, one should ship a new value to the whole set and then continue.
Eventually, the problems will be solved
In a GMAT exam, no calculator is allowed. The student will have their old-school pen, pencil, paper and that is how they will be solving the sums. So, in case you are coming across a magnanimous decimal number then you are probably heading in the wrong direction. Mostly the answers are in whole or simply fractions or decimals at the most.