Calculator UseCalculate mean, median, mode along with the minimum, maximum, range, count, and sum for a set of data. Show
Enter values separated by commas or spaces. You can also copy and paste lines of data from spreadsheets or text documents See all allowable formats in the table below. What are Mean Median and Mode?Mean, median and mode are all measures of central tendency in statistics. In different ways they each tell us what value in a data set is typical or representative of the data set. The mean is the same as the average value of a data set and is found using a calculation. Add up all of the numbers and divide by the number of numbers in the data set. The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number. This is the median. If there are 2 numbers in the middle, the median is the average of those 2 numbers. The mode is the number in a data set that occurs most frequently. Count how many times each number occurs in the data set. The mode is the number with the highest tally. It's ok if there is more than one mode. And if all numbers occur the same number of times there is no mode. How to Find the Mean
The mean is the same as the average value in a data set. Mean FormulaThe mean x̄ of a data set is the sum of all the data divided by the count n. \[ \text{mean} = \overline{x} = \dfrac{\sum_{i=1}^{n}x_i}{n} \] How to Find the MedianThe median \( \widetilde{x} \) is the data value separating the upper half of a data set from the lower half.
Median ExampleFor the data set 1, 1, 2, 5, 6, 6, 9 the median is 5. For the data set 1, 1, 2, 6, 6, 9 the median is 4. Take the mean of 2 and 6 or, (2+6)/2 = 4. Median FormulaOrdering a data set x1 ≤ x2 ≤ x3 ≤ ... ≤ xn from lowest to highest value, the median \( \widetilde{x} \) is the data point separating the upper half of the data values from the lower half. If the size of the data set n is odd the median is the value at position p where \[ p = \dfrac{n + 1}{2} \] \[ \widetilde{x} = x_p \] If n is even the median is the average of the values at positions p and p + 1 where \[ p = \dfrac{n}{2} \] \[ \widetilde{x} = \dfrac{x_{p} + x_{p+1}}{2} \] How to Find the ModeMode is the value or values in the data set that occur most frequently. For the data set 1, 1, 2, 5, 6, 6, 9 the mode is 1 and also 6. Interquartile RangeIQR = Q3 - Q1 OutliersPotential Outliers are values that lie above the Upper Fence or below the Lower Fence of the sample set. Related Statistics and Data Analysis Calculators
Acceptable Data Formats Column (New Lines) 42 42, 54, 65, 47, 59, 40, 53 Comma Separated 42, or 42, 54, 65, 47, 59, 40, 53 42, 54, 65, 47, 59, 40, 53 Spaces 42 54 or 42 54 65 47 59 40 53 42, 54, 65, 47, 59, 40, 53 Mixed Delimiters 42 42, 54, 65, 47, 59, 40, 53 Mean Median Mode: Contents (Click to skip to that section): Watch the video for an overview and how to find the mean, median, and mode: The mean median mode are measurements of central tendency. In other words, it tells you where the “middle” of a data set it. Each of these statistics defines the middle differently: Of the three, the mean is the only one that requires a formula. I like to think of it in the other dictionary sense of the word (as in, it’s “mean” as opposed to nice!). That’s because, compared to the other two, it’s not as easy to work with because of the formula. Having trouble with the mean median mode differences? Here’s a couple of hints that can help. When you first started out in mathematics, you were probably taught that an average was a “middling” amount for a set of numbers. You added up the numbers, divided by the number of items you can and voila! you get the average. For example, the average of 10, 6 and 20 is: 10 + 6 + 20 = 36 / 3 = 12. The you started studying
statistics and all of a sudden the “average” is now called the mean. What happened? The answer is that they have the same meaning(they are synonyms). However there is a caveat. Technically, the word mean is short for the arithmetic mean. We use different words in stats, because there are multiple different
types of means, and they all do different things. You’ll probably come across these in an elementary stats class. They have very narrow meanings: There are other types of means, and you’ll use them in various branches of math. However, most have very narrow applications to fields like finance or physics; if you’re in elementary statistics you probably won’t work with them.
These are some of the most common types you’ll come across. These are fairly common in statistics, especially when studying populations. Instead of each data point contributing equally to the final average, some data points contribute more than others. If all the weights are equal, then this will equal the arithmetic mean. There are certain circumstances when this can give incorrect information, as shown by
Simpson’s Paradox. The harmonic mean is used quite a lot in physics. In some cases involving rates
and ratios it gives a better average than the arithmetic mean. In addition, you’ll also find uses in geometry, finance and computer science. Arithmetic-Geometric MeanThis is used mostly in calculus and in machine computation (i.e. as the basis for many computer calculations). It’s related to the perimeter of an ellipse and when it was first developed by Gauss, it was used to calculate planetary orbits. The arithmetic-geometric is (perhaps not surprisingly) a blend of the arithmetic and geometric averages. The math is quite complicated but you can find a relatively simple explanation of the math here. Root-Mean SquareIt is very useful in fields that study sine waves, like electrical engineering. This particular type is also called the quadratic average. See: Quadratic Mean / Root Mean Square. Heronian MeanUsed in geometry to find the volume of a pyramidal frustum. A pyramidal frustum is basically a pyramid with the tip sliced off. Graphic MeanAnother name for the slope of the secant line: the equivalent of the average rate of change between two points. 2. What is the Mode?The mode is the most common number in a set. For example, the mode in this set of numbers is 21: 21, 21, 21, 23, 24, 26, 26, 28, 29, 30, 31, 33 3. What is the Median?The median is the middle number in a data set. To find the median, list your data points in ascending order and then find the middle number. The middle number in this set is 28 as there are 4 numbers below it and 4 numbers above: 23, 24, 26, 26, 28, 29, 30, 31, 33 Note: If you have an even set of numbers, average the middle two to find the median. For example, the median of this set of numbers is 28.5 (28 + 29 / 2): 23, 24, 26, 26, 28, 29, 30, 31, 33, 34 How to find the mean median mode by hand: StepsHow to find the mean median mode: MODE
How to find the mean median mode: MEAN
How to find the mean median mode: MEDIANIf you had an odd number in step 3, go to step 5. If you had an even number, go to step 6.
Tip: You can have more than one mode. For example, the three modes of 1, 1, 5, 5, 6, 6 are 1, 5, and 6.
SPSS Mean mode medianIn order to find the SPSS mean mode median, you’ll need to use the Frequency table. It seems a little counter-intuitive, but the Descriptive Statistics tab does not give you the option to find the mode or the median. SPSS has a very similar interface to Microsoft Excel. Therefore, if you’ve used Microsoft Excel before, you will quickly adapt to SPSS. SPSS Mean Median Mode: StepsWatch the video for the steps: Example question: Find the SPSS mean mode median for the following data set: 20,23,35,66,55,66 Step 1: Open SPSS. In the “What would you like to do?” dialog box, click the “type in data” radio button and then click “OK.” A new worksheet will open. Note: If you have opted out of the first help screen, you may not see this option. In that case, just
start at Step 2. Step 2: Type your data into the worksheet. You can type the data into one column or multiple columns if you have multiple data sets. For this example, type 20, 23, 35, 66, 55, 66 into column 1. Do not leave spaces between the data (i.e., don’t leave any empty rows). Step 2: Click “Analyze,” hover over “Descriptive Statistics” and then click “Frequencies.” Step 3: Click “Statistics” and then check the boxes “mean”, “mode” and “median.” Click “Continue” twice (select “none” as the chart type in the second window). Note: In some versions of SPSS, you may only have to click “Continue” once and it may not give you an option for chart type. The frequency results will appear as output. The top part of the output will display the mean median mode. If you scroll down, the frequency table will also show you the mode. The mode is defined in statistics as the number with the highest frequency (for this sample data set, the number appearing the most is 66, with two results in the frequency column). TI 83 Mean Median ModeFinding the TI 83 mean or TI 83 median from a list of data can be accomplished in two ways: by entering a list of data, or by
using the home screen to type the commands. Using the list feature is just as easy as entering the data onto the home screen, and it has the added advantage that you can use the data for other purposes after you have calculated the mean median mode (for example, you might want to create a TI 83 histogram). Steps for the Mean Median Mode on the TI 83Watch the video for the mean and median on the TI 83: Example problem: Find the mean and the median for the height of the top 20 buildings in NYC. the heights, (in feet) are: 1250, 1200, 1046, 1046, 952, 927, 915, 861, 850, 814, 813, 809, 808, 806, 792, 778, 757, 755, 752, and 750. Step 1: Enter the above data into a list. Press the STAT button and then press ENTER. Enter the first number (1250), and then press ENTER. Continue entering numbers, pressing the ENTER button after each entry. Step 2: Press the STAT button. Step 3: Press the right arrow button to highlight “Calc.” Step 4: Press ENTER to choose “1-Var Stats” and then type in the list name. For example, to enter L1 press [2nd] and [1]. Step 5: Press ENTER again. The calculator will return the mean, x̄. For this list of data, the TI 83 mean is 884.05 feet (rounded to 3 decimal places). Step 6: Arrow down until you see “Med.” This is the TI 83 median; for the above data, the median is 813.05 feet. Note: The TI-83 plus doesn’t have a built in mode function, but once you’ve entered your list, it’s pretty easy to spot the mode: it’s just the number that occurs most often in the set. Not sure? Read more about the mode here. That’s it! Lost your guidebook? Download a new one here at the TI website. Find the Mean in RWatch the video to learn how to find the mean in R: Can’t see the video? Click here. Mean Median Mode ReferencesKenney, J. F. and Keeping, E. S. “The Mode,”
“Relation Between Mean Median Mode,” and “Relative Merits of Mean Median Mode.” §4.7-4.9 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 50-54, 1962.
Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free! Comments? Need to post a correction? Please Contact Us. How do you find the mean and median?To find the mean, add up the values in the data set and then divide by the number of values that you added. To find the median, list the values of the data set in numerical order and identify which value appears in the middle of the list.
How do you calculate mean with examples?For example, take this list of numbers: 10, 10, 20, 40, 70. The mean (informally, the “average“) is found by adding all of the numbers together and dividing by the number of items in the set: 10 + 10 + 20 + 40 + 70 / 5 = 30.
What is an mean in math?mean, in mathematics, a quantity that has a value intermediate between those of the extreme members of some set. Several kinds of means exist, and the method of calculating a mean depends upon the relationship known or assumed to govern the other members.
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