You may get two to three questions from Descriptive Statistics in the GMAT quant section - in both variants viz., problem solving and data sufficiency. The concepts tested include Averages or simple arithmetic mean, weighted average, median, mode, range, variance and standard deviation.
Sample GMAT practice questions from statistics & averages is given below. Attempt these questions and check whether you have got the correct answer. If you face difficulty with arriving at the answer to any question, go to the explanatory answer or the video explanations (provided for all questions) to learn how to crack the GMAT sample question in this question bank.
Ideally, you should start by watching these two GMAT Math lesson videos in Statistics and Averages to help you get better traction when solving the questions given below.
If the mean of numbers 28, x, 42, 78 and 104 is 62, what is the mean of 48, 62, 98, 124 and x ?
'x' is common to both the sets of numbers. Therefore, 'x' will not impact the average of the second set of numbers.
Step 1: Find out the sum of the 4 numbers other than x in both scenarios.
Step 2: Apportion the difference between the two sums obtained in step 1 equally to all the 5 numbers to find the difference in average.
Step 3: Add or subtract the difference to the average of the first set, i.e., 62 to find the answer.
The explanatory answer to this GMAT Averages practice question walks you through two different methods to find the answer. An easy GMAT 600 level quant question.
The arithmetic mean of the 5 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s + 2 ?
This GMAT practice question is an Averages question - an easy GMAT 550 to 600 level quant question.
The easiest way to solve this averages problem is to assume values for the 5 consecutive integers. Do not look too far. Let the 5 numbers be 1, 2, 3, 4, and 5. Determine values for 's', and 'a' with respect to the values assumed and apply it to the set of 9 consecutive integers starting from (s + 2).
The average weight of a group of 30 friends increases by 1 kg when the weight of their football coach was added. If average weight of the group after including the weight of the football coach is 31 kg, what is the weight of their football coach ?
This GMAT question is a statistics and averages question - An easy GMAT 550 level quant practice question.
The question is an ideal candidate to apply and consolidate the standard framework to solve an averages question.
Step 1: Find the sum of the weights of the 30 friends after deducing the average weight of the 30 friends.
Step 2: Compute the sum of the weights of 30 friends and the football coach from the information about the average given in the question.
Step 3: The difference between answers obtained in steps 2 and 1 is the weight of the coach.
The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87/day and the average wages during the last 7 days was $92 /day. What was his wage on the 8^{th} day ?
This GMAT question is an easy averages question that can be solved using the standard framework to solve GMAT averages problems.
Step 1: Compute the sum of wages received for all 15 days using the verage wages for 15 days.
Step 2: Compute sum of wages for first 7 days using average wages for the first 7 days.
Step 3: Compute sum of wages for last 7 days using average wages for the last 7 days.
The sum of the second and third step gives the sum of wages for 14 of the 15 days. Compute the difference between wages for 15 days and 14 days to find wage on 8th day.
The average of 5 numbers is 6. The average of 3 of them is 8. What is the average of the remaining two numbers ?
This GMAT averages problem is a vey easy question.
Step 1: Compute sum of all 5 numbers using the average of the 5 numbers.
Step 2: Compute sum of 3 of the 5 numbers using the average of the 3 numbers.
Step 3: The difference between values obtained in step 1 and step 2 will give the sum of the remaining 2 numbers. Use this information to compute the average of the remaining two numbers.
The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group ?
Step 1: Set up the standard framework table and populate it with available data about number of students and their average age before the two students join the group and after two students join the group
Step 2: Compute sum of ages of the group before and after the students join the group
Step 3: The difference between the sum of the ages after the 2 students join and that before the 2 students join gives the sum of the ages of the 2 new students
Step 4: Divide the value computed in Step 3 by 2 to find the answer.
If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0 ?
Step 1: Decoding the Question: Standard deviation is a non-negative number. So, it can either be zero or positive.
So, the question boils down to figuring out whether 's' is zero or is it positive.
Step 2: Evaluate statement 1 alone to determine whether 's' is zero or positive
Step 3: Evaluate statement 2 alone to determine whether 's' is zero or positive
Step 4: If the statements are independently not sufficient, combine the statements to determine whether answer is C or E
Positive integers from 1 to 45, inclusive are placed in 5 groups of 9 each. What is the highest possible average of the medians of these 5 groups ?
Step 1: To maximize the average of the medians of the 5 sets, we have to maximize the median in each set.
Step 2: Try to divide the given numbers into sets of 9 each such that the median is as high as possible. Start with the set where the 5 largest numbers are 41, 42, 43, 44, and 45.
Step 3: Note, to maximize median in each set, it is imperative that the first 4 numbers of each set is as small as possible so that the 5 larger numbers in any set gets maximized.
Step 4: After you have identified the maximized medians for each set, compute the average of the medians to find the answer.
If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers ?
Step 1: Compute the sum of the 5 integers using information about the average of these numbers.
Step 2: Because the range is 10, the largest number is 10 more than the smallest number.
Step 3: If the largest number has to be maximized, the remaining 4 numbers have to be minimized.
Step 4: Find the condition that will minimize the remaining 4 numbers and consquently find the maximum value of the largest of the 5 numbers.
An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest incentive received by the 5 salesmen in the month ?
Step 1: Compute the sum of the incentives.
Step 2: Median incentive is $7000. So, the 3rd highest is $7000.
Step 3: Only mode is $12,000. Because third highest is $7000, highest and second highest have to be the same value = $12,000
Step 4: Now that we have details about the incentives for the 3 highest salesman and we also know the sum of their incentive, we can find the sum of the incentives of the two salesmen who got the least incentive.
Step 5: Use the information that there is only one mode to find the lowest incentive.
Step 6: Compute the difference between the highest and lowest incentives - essentially the range of incentives.
Is 'b' the median of 3 numbers a, b, and c ?
Step 1: The given question is an "IS" question. The answer should be yes or no. Data is sufficient when we get a definite yes or definite no.
Step 2: Evaluate statement 1 alone. We know the numbers are in GP. Check whether 'b' is the median of the 3 numbers. Points to check are - will 'b' be the median if the common ratio is negative.
Step 3: Evaluate statement 2 alone. Look for a counter example.
Step 4: Combine the statements if you did not get a conclusive answer using either statements alone.
What is the standard deviation (SD) of the four numbers p, q, r, and s?
Step 1: The given question is a "What is" question. The answer is a value. Data is sufficient if we get a unique value for the standard deviation of the 4 numbers.
Step 2: Evaluate statement 1 alone. Will the sum of the 4 numbers help find the SD? If not, will it help in determining the average of the 4 numbers?
Step 3: Evaluate statement 2 alone. Sum of squares alone is of not much use.
Step 4: Combine the statements. Revisit formula (alternative method) to find SD and determine whether we have a unique value for the SD of the 4 numbers.
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