# Mean Median Mode Problems And Solutions Pdf

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*While the calculation of statistics is pretty uniform, the application of statistics can be very diverse. Answer: Dispersion is the extent to which values in a distribution differ from the avarage of the distribution.*

- Mean/Median/Mode/Range Worksheets
- Statistics Concepts – Mean, Median, Mode and Solved Examples
- Mean, Median, Mode and Range
- Central Tendency Worksheets: Mean, Median, Mode and Range

*Here you will find another series of progressive worksheets, filled with step-by-step examples, that will help students master the art of analyzing data sets.*

## Mean/Median/Mode/Range Worksheets

In this post, we will be discussing mean, median, mode concepts and their solved examples which is a frequently asked topic in XAT and SNAP examination. We will start our discussion with basic concepts of statistics followed by some examples that will help you get a better understanding of the concept.

The short tricks to solve some particular questions are discussed during the solution of the question. To find the median, your numbers have to be listed in numerical order from smallest to largest, so you may have to rewrite your list before you can find the median.

If no number in the list is repeated, then there is no mode for the list. Let us understand the concepts better by use of some examples. We can just count in from both ends of the list until you meet in the middle, if you prefer, especially if your list is short. The formula works when the number of terms in the series is odd.

In case there are even number of numbers, median will be average of two middle numbers in the list. The simplest way to find the mean is sum of all the values in the set divided by total number of values in the set. To calculate median, the data has to be sorted in ascending or descending order. As we can see, the given sequence is an Arithmetic progression An arithmetic progression is a sequence of terms where any two consecutive terms differ by a constant difference.

To find out the median, we need to know the number of terms. Then, depending on whether n is odd or even we can find out the media. The entire process will take up a lot of time. It quantifies the amount of variation of a set of data values. But, this might not always be the case.

In question with different number of terms and varying differences between consecutive terms, we need to use the formula for S. Enroll Now Rs. In simple terms, to calculate the Variance, you need to square the S.

To understand weighted average, let us take two groups G1 group of N1 rice packets and G2 group of N2 wheat packets , with number of items in G1 as N1 and number of items in G2 as N2. The average quantity of group 1 is W1 and the average quantity of group 2 is W2.

When we combine both the groups the average quantity in each packet becomes the weighted average. Let us understand this concept with the help of an example.

Some of the bottles are 1-liter and some are 2-liter bottles. The average cold drink of the bottles is ml. Find the number of 2-liter bottles.

Let us say number of 2-lit bottles is N1 and number of 2-lit bottles is N2. The average of group 1 W1 is ml as all the bottles are of equal quantity, i.

Similarly, the average of group 2 W2 is ml. With the help of weighted average formula we can calculate N1 and N2. The weighted average here is ml.

Let us put the values in the equation. Thus, the shopkeeper has 10 bottles of 2-lit. This is a common result. You should not assume that your mean will be one of your original numbers.

The mean value of the sequence is Find the difference between K and the original mean. As you might have noticed in this example that the mean value is directly changed by any operation done on the values of the sequence. Example 11 : A sequence consists of 9 terms. The standard deviation of the sequence is If 10 is added to each term, and then each term is multiplied by Find the new S.

Solution: As we have discussed, the S. D does not change when we add or subtract a number to the terms of the sequence. So after adding 10 to each term, S. D remains as In the second operation, each term is multiplied by When me multiply a constant to each term, we multiply the S.

D by modulus of that number, thus the new S. Example Find the mean, median, mode, and range for the following list of values: 1, 2, 4, 7. The median is the middle number. Because of this, the median of the list will be the mean that is, the usual average of the middle two values within the list. The mode is the number that is repeated most often, but all the numbers in this list appear only once, so there is no mode.

Mean: 3. What is the minimum grade he must get on the last test in order to achieve that average? Solution: The minimum grade is what we need to find. To find the average of all his grades the known ones, plus the unknown one , we have to add up all the grades, and then divide by the number of grades.

Then computation to find the desired average is:. Example In a sequence of 25 terms, can 20 terms be below the average? Can 20 terms be between median and average? Solution: Yes. We can have 24 zeroes and as the 25 numbers. In this case, there are 24 numbers below the average number. No, in a sequence of 25 numbers, 12 will be greater than or equal to the median and 12 will be lesser than or equal to the median. We cannot have 20 terms in between the average and median Correct Answer: 24 numbers below the average, 0 numbers between the average and median.

Example The median of n distinct numbers is greater than the average, does this mean that there are more terms above the average than below it? So, there will. However, this need not be the case when there are an even number of terms.

When there are 2n distinct terms, n of them will be greater than the median and n will be lesser than the median. Also, the average of these two terms can be such that there are n terms above the average and n below it. For instance, if the numbers are 0, 1, 7, 7. The median is 4, average is 3. Average is less than the median. And there are more 2 numbers above the average and 2 below the average. So, answer is it is not necessary that if median is greater than average, there will be more terms above average than below it, specifically in the scenario that there are even number of terms.

Example In a class of 5 students, average weight of the 4 lightest students is 40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is the difference between the maximum and minimum possible average weight overall? The average of a, b, c and d is 40 kg, whereas the average of b, c, d and e is 45 kg. The sum of a, b, c and d is kg, and the sum of b, c, d and e is kg.

What is the total weight of all the students? There are two ways of looking at this. So, the highest value of e will correspond to the highest possible average. The highest possible value of e occurs when it is 20 higher than the highest possible value for a, which is 40 a is lightest and here we assume that all a, b, c and d is Conversely, the least possible value for the average occurs when a is the least.

This happens when e is the least too since a is 20 less than e. So, the least possible value for a would be This will be the case when the weights are 25 kgs, 45kgs, 45 kgs, 45 kgs and 45 kgs.

Example The average of 5 distinct positive integers if What are the maximum and minimum possible values of the median of the 5 numbers if the average of the three largest numbers within this set is 39? Solution: Let the numbers be a, b, c, d, e in ascending order. We need to find the maximum and minimum possible values of c. For minimum value, a and b have to be minimum. Example Consider 4 numbers a, b, c and d. Ram figures that the smallest average of some three of these four numbers is 30 and the largest average of some three of these 4 is What is the range of values the average of all 4 numbers can take?

So, this will be minimum when a is minimum. So, this will be maximum when d is maximum. All the salary figures are in integer lakhs.

## Statistics Concepts – Mean, Median, Mode and Solved Examples

In these lessons, we will learn how to calculate the median of a given set of data. We will also learn how to solve some mean, median, mode SAT questions. The following diagrams show how to obtain the median from a given set of data. Scroll down the page for examples and solutions. Given a set of observations, the median is the middle value among the observations.

Simplify comparisons of sets of number, especially large sets of number, by calculating the center values using mean, mode and median. Use the ranges and standard deviations of the sets to examine the variability of data. The mean identifies the average value of the set of numbers. For example, consider the data set containing the values 20, 24, 25, 36, 25, 22, To find the mean, use the formula: Mean equals the sum of the numbers in the data set divided by the number of values in the data set.

Learn how to find the group median, group mode and group mean with practice problems.

## Mean, Median, Mode and Range

Mean, median, mode and range worksheets contain printable practice pages to determine the mean, median, mode, range, lower quartile and upper quartile for the given set of data. The pdf exercises are curated for students of grade 3 through grade 8. Interesting word problems are included in each section.

In statistics, mode, median and mean are typical values to represent a pool of numerical observations. They are calculated from the pool of observations. Mode is the most common value among the given observations.

*In this post, we will be discussing mean, median, mode concepts and their solved examples which is a frequently asked topic in XAT and SNAP examination. We will start our discussion with basic concepts of statistics followed by some examples that will help you get a better understanding of the concept.*

### Central Tendency Worksheets: Mean, Median, Mode and Range

In previous sections introducing the concept of mean, median and mode, we discussed how descriptive statistics are generally divided between measures of central tendency and of variability. Here, we will expand upon what you learned about measures of central tendency by showing you how to calculate the mean, median and mode for grouped data. Measures of central tendency are used to capture and describe the centre of a variable. Divide that summed value by the sample size, Median The midpoint of the data, where half the observations fall above and below No standard formula 1. Order the observations from least to greatest.

The measure of Central Tendency is a topic that has high weightage in maths and to solve the questions correctly, the students can take help from our RD Sharma Solutions for Class 9 Maths Chapter 24 PDF, which will help them tremendously throughout the chapter. If three of the numbers are 58, 76, and 88, what is the value of the fourth number? It tells the variation of the data from one another and gives a clear idea about the distribution of the data. Solution: D 3. You just add up all of the values and divide by the number of observations in your dataset. While the calculation of statistics is pretty uniform, the application of statistics can be very diverse. Functions of Average: i] Presents complex data in a simple form.

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Solutions: Finding the Mean, Median, Mode. Now that you have completed the practice problems, review the solutions to see how well you did. 1. What is the.

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The mean, median and mode are three different ways of describing the average. (a) the mean (b) the median (c) the mode (d) the range. Solution. (a) The mean is The survey in question 1 also asked how many TV sets there were in each.

To calculate the arithmetic mean of a set of data we must first add up (sum) all of the Calculate the mean, median, and mode of this data. Answers. 1. a) 5, 6, 7.