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## Class 10 (Foundation)

### Course: Class 10 (Foundation)>Unit 5

Lesson 2: Mean, median, mode

# Statistics intro: Mean, median, & mode

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set. Created by Sal Khan.

## Want to join the conversation?

• I've heard of both the arithmetic mean and the geometric mean. What's the difference?
• Think about it this way. The arithmetic mean of a bunch of numbers is the number a that satisfies
x₁ + x₂ + x₃ + .... = a + a + a + ... + a

The geometric mean is the number b that satisfies
x₁ * x₂ * x₃ * ... = b * b * b * ... * b

There is also a harmonic mean, which is the number h that satisfies

1/x₁ + 1/x₂ + 1/x₃ + ... = 1/h + 1/h + ... + 1/h.
If the set of numbers were (2 , 4 , 6 , 8 , 10) , how would you find the mode?
(There are no numbers repeated in the above question.)
• The mode is 'No Mode' or 'None'.
Mode is used to find the number of times a number appears for statistics.
• is centeral tendancy the same thing as mean?? What is the difference??
• The arithmetic mean is one example of a statistic that describes the central tendency of a dataset. But any other formula or process that takes a dataset and generates a single number that represents a "typical" value is also a measure of central tendency. That includes the median and mode as well as more exotic things like the midrange or the arithmetic mean when you ignore the largest and smallest value. All of these numbers attempt to capture the spirit of a dataset by giving you a sense of a single "usual" value, and that is what makes them measures of central tendency..
• if there is a question such as:
what is the mode of 2,2,3,5,6,5?
would it be 2 or 5?
• It's always possible that there are two modes, and sometimes there is no mode at all. So since 2 and 5 are both repeated the same time, they are both modes of your data set.
• If two numbers are the most common in a set ( example: 1,2,3,3,4,5,6,6,7), what would be the mode?
• A data set can have more than one mode. Unlike the mean, the mode is not necessarily unique. Your example is "bimodal" - it has two modes: 3 and 6.
• Here are some quick definitions.

Statistics: the study and manipulation of data (basically it's just data)

Descriptive statistics: Showing data while summarizing or using a smaller set of numbers.

Average: (these are just words to describe average) In general, mean, typical, middle, central tendency.

Arithmetic mean (or just mean, I just like arithmetic mean more): The process of adding a set of numbers, then dividing by the amount of numbers. (Example: 4+3+1+6+1+7= 22 divided by 6. The answer to that is 3 2/3.)

Median: The "middle" number in a set. Rule: When faced with a set of numbers where the amount of numbers in it are all even, you take the two middle numbers and add them. Then you divide them by two to get the median. (In the set of numbers we had earlier [1, 1, 3, 4, 6, 7], 3 and 4 were the middle numbers. We add them together to get 7, then divide it by 2 to get a median of 3.5.) However, this DOES NOT apply to a set of numbers with an odd set of numbers in it.

Mode: The most common number in a set (the number that repeats itself the most). Rule: If all the numbers are represented equally (basically if there are the same amount of each number, if that makes sense,) there is no mode. For example, in the set of numbers from earlier (1, 1, 3, 4, 6, 7), the mode would be 1. But if we remove one of the ones, since every number would be represented equally, there would be no mode.

Hope this helped.
• How would you use average in real life?
• There are countless applications. I'll give some examples. The normal body temperature is 98.6 degrees Fahrenheit. How was this exact temperature chosen?This number was given by a German doctor Carl Reinhold August Wunderlich, after examining millions of readings taken from 25,000 German patients and taking their average. The mileage of automobiles is calculated by finding the average volume of fuel consumed by the automobile. Each and every science experiment done in the lab involves calculation of the average reading after repeating the experiment many times, so that error is minimized. In fact, calculating the average is one of the most essential mathematical skills. One would need this knowledge regardless of which field he/she works in.
• What if the numbers are 1,3,5,6,7,8,23,42,76,83,93 how do you find the median
• You put the numbers in order (as you've done) and count how many numbers there are. If there's an odd number of numbers (as in this case), you pick the number in the middle of the list, and that's the median. If there's an even number of numbers, you take the two numbers in the middle, add them together, and divide them by two.