Mean, Median, Mode Calculator

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Mean-Median-Mode Calculator

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Answer:

Mean \( \overline{x} \)

16.75

Median \( \widetilde{x} \)

15.5

Mode

Range

Minimum

Maximum

Count n

Sum

268

Quartiles

Quartiles:
Q₁ --> 13
Q₂ --> 15.5
Q₃ --> 22.5

Interquartile
Range IQR

9.5

Outliers

none

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Calculator Use

Calculate mean, median, mode along with the minimum, maximum, range, count, and sum for a set of data.

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

Add up all data values to get the sum
Count the number of values in your data set
Divide the sum by the count

The mean is the same as the average value in a data set.

Mean Formula

The 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 Median

The median \( \widetilde{x} \) is the data value separating the upper half of a data set from the lower half.

Arrange data values from lowest to highest value
The median is the data value in the middle of the set
If there are 2 data values in the middle the median is the mean of those 2 values.

Median Example

For 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 Formula

Ordering a data set x₁ ≤ x₂ ≤ x₃ ≤ ... ≤ x_n 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 Mode

Mode 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 Range

IQR = Q₃ - Q₁

Outliers

Potential Outliers are values that lie above the Upper Fence or below the Lower Fence of the sample set.
Upper Fence = Q₃ + 1.5 × Interquartile Range
Lower Fence = Q₁ − 1.5 × Interquartile Range

Related Statistics and Data Analysis Calculators

Acceptable Data Formats

Type
Unit

Your Format Input
Options

Actual Input Processed

Column (New Lines)

42
54
65
47
59
40
53

42, 54, 65, 47, 59, 40, 53

Comma Separated

42,
54,
65,
47,
59,
40,
53,

or

42, 54, 65, 47, 59, 40, 53

42, 54, 65, 47, 59, 40, 53

Spaces

42 54
65 47
59 40
53

or

42 54 65 47 59 40 53

42, 54, 65, 47, 59, 40, 53

Mixed Delimiters

42
54 65,,, 47,,59,
40 53

42, 54, 65, 47, 59, 40, 53