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Descriptive Statistics

Descriptive Statistics is broken down into Tendency and Variability.

Tendency is about Center Measures:

  • The Mean (the average value)
  • The Median (the mid point value)
  • The Mode (the most common value)

The Mean

The Mean Value is the Average of all values.

This table contains 11 values:

7889991011141415

To find the Mean Value: Add all values and divide by the number of values.

The Mean Value is:
(7+8+8+9+9+9+10+11+14+14+15)/11 = 10.3636363636.

The Mean is the Sum divided by the Count.

Calculate the Mean Value:

let mean = (7+8+8+9+9+9+10+11+14+14+15)/11;

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Or use a math library like math.js:

const values = [7,8,8,9,9,9,10,11,14,14,15];
let mean = math.mean(values);

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The Median

A list of speed values:

99,86,87,88,111,86,103,87,94,78,77,85,86

The Median is the value in the middle (after the values are sorted):

77,78,85,86,86,86,87,87,88,94,99,103,111

Calculate the median:

const speed = [99,86,87,88,111,86,103,87,94,78,77,85,86];
let median = math.median(speed);

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If there are two numbers in the middle, divide the sum of them by two.

77,78,85,86,86,86,87,87,88,94,99,103
(86 + 87) / 2 = 86.5

Calculate the median:

const speed = [99,86,87,88,86,103,87,94,78,77,85,86];
let median = math.median(speed);

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The Mode

The Mode Value is the value that appears the most number of times:

99,86,87,88,111,86,103,87,94,78,77,85,86

Calculate the mode:

const speed = [99,86,87,88,86,103,87,94,78,77,85,86];
let mode = math.mode(speed);

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Outliers

Outliers are values "outside" the other values:

99,86,87,88,111,86,103,87,94,78,300,85,86

Outliers can change the mean a lot. Sometimes we don't use them (they might be an error), or we use the median or the mode instead.

Calculate the Mean:

const values = [99,86,87,88,111,86,103,87,94,78,300,85,86];
let mean = math.mean(values);

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