Mean & Median & Mode & Range Calculators

Knowledge

Definitions of mean, median, mode and range

•What is the mean in math?

The mean of a list of numbers, is the sum of all of the numbers divided by the number of numbers. Similarly, the mean of a sample X1, X2,...,Xn. Usually written as the sum of the sampled values divided by the number of items in the sample.

m = sum of the terms number of terms

•What is the median?

The median of a finite list of numbers is the "middle" number, when those numbers are listed in order from smallest to greatest.

If the data set has an odd number of observations, the middle one is selected.

If the data set has an even number of observations. In this case, we find the two numbers in the middle. Then calculate the half value between them.

•What is the mode?

The mode is the value that appears most often in a set of data values. It is a way of expressing, in a (usually) single number, important information about a random variable or a population. Finding the mode requires the least amount of mathematical computation of all the measurements. Instead, since the mode is just the most frequent score in the distribution, all you have to do is look at all the scores and choose the most common score.

•What is the range?

The range of a set of data is the difference between the largest and smallest values. It has to be mentioned that there is also a concept called midrange. Midrange and range are different. Midrange refers to the average value between two figures in a group of data.

How to calculate the mean, median, mode and range?

•How to calculate the mean?

To calculate the mean, first we need to add all the values together, then divide the sum by the number of values used.

Example: What is the mean of 10, 2, 38, 23, 38, 23, 21?

Answer: 10+2+38+23+38+23+21 7 = 155 7 = 22.14

•How to calculate the median?

The steps for finding the median differ depending on whether you have an odd or an even number of data points. If there are two numbers in the middle of a dataset, their mean is the median. We can use these two formulas to find the median or we can just use the UpStudy mean median mode range calculator to get the answer quickly.

Example: What is the median of 10, 2, 38, 23, 38, 23, 21?

Answer:

Step1 - Order the values from low to high.

2, 10, 21, 23, 23, 38, 38

Step2 - Use the formulan+12 to calculate the values. (n is the number of values in your dataset).

n+1 2 = 7+1 2 = 4

The median is the value at the 4th position.

Step3 - find the value in the 4th position.

2, 10, 21, 23, 23, 38, 38

So, the final answer is 23.

•How to calculate the mode?

As mentioned above, finding the mode does not require too much mathematical calculation. We only need to use very simple methods - just look at all the data scores and find the data score that appears most often. However, it can also be calculated by formula, that is, the following seemingly complex one.

Estimated Mode = L + (f_m-f_m-1) (f_m-f_m-1)+(f_m-f_m+1) × W

Example: find the mode of of 10, 2, 38, 23, 38, 23, 21.

Answer:

2, 10, 21, 23, 23, 38, 38

The answers are 23 and 38 because they are tied in frequency (both occur twice).

•How to calculate the range?

The range in math is the difference between the lowest and the highest value. To work it out, simply subtract the lowest value from the highest.

Range = Maximum value - Minimum value

Example: find the range of of 10, 2, 38, 23, 38, 23, 21.

Answer:

38 - 2 = 36