# Averages And Range Homework Online

## Statistical Average Calculator

for Mean, Median, Mode, and Range

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The Statistical Average Calculator on this page will instantly calculate the mean, median, mode, and range from an entered or pasted-in data set.

This free online statistics calculator will calculate the mean, median, mode, minimum, maximum, and range of a data set.

You can either enter the numbers in the data set one at a time, or you can copy and paste an existing data set (if separated by spaces, commas, line returns, or any combination thereof), or you can enter a number and its frequency (12x4, 8x6, 9x4) to get the weighted average from grouped data within a data set.

Plus, unlike other online statistics calculators, this calculator will generate and display a distribution table in the results so you can see how many times each of the numbers is repeated within the data set.

### Example Data Set

To show how to calculate mean, median, mode, and range, I will use the following data set:

**36, 3, 8, 12, 15, 18, 22, 34, 8, 25, 17, 13, 23**

### How Do You Calculate the Mean?

The *mean* is the average of all numbers in a data set. To calculate the mean of set of numbers, you add all of the numbers together and then divide that sum by the number of elements within the set.

Data set: 36, 3, 8, 12, 15, 18, 22, 34, 8, 25, 17, 13, 23 |

Data set contains 13 numbers |

Mean = (36 + 3 + 8 + 12 + 15 + 18 + 22 + 34 + 8 + 25 + 17 + 13 + 23) ÷ 13 |

Mean = 234 ÷ 13 |

Mean = 18 |

### How Do You Calculate the Median?

The *median* is the middle number in a data set after sorting the data set from smallest to largest. To calculate the median of a data set, you count the number of elements and then sort the elements from smallest to largest. Next, for an **odd** number of elements, you add 1 to the number of elements and then divide by 2 to get position of the middle number. From our example data set, the median is the 7th number in the sorted list, which is the number 17.

Odd numbered data set: 36, 3, 8, 12, 15, 18, 22, 34, 8, 25, 17, 13, 23 | |||||||||||||

Number of elements in set is 13 | |||||||||||||

Middle Position = ((count + 1) ÷ 2) | |||||||||||||

Middle Position = ((13 + 1) ÷ 2) | |||||||||||||

Middle Position = (14 ÷ 2) | |||||||||||||

Middle Position = 7 | |||||||||||||

Count | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |

Data Set | 3 | 8 | 8 | 12 | 13 | 15 | 17 | 18 | 22 | 23 | 25 | 34 | 36 |

Median = 17 (7th number in sorted data set) |

Note that for an **even** number of elements, you find the average of the two middle numbers. The first middle position would be equal to number of elements divided by 2 less 1. The second middle position would be the first middle position plus 1. You then add the two middle numbers together and divide by 2 to find the average. From our revised example data set, this gives you a medium of 16 -- which is the average of the 6th and 7th elements (15 and 17).

Even numbered data set: 36, 3, 8, 12, 15, 18, 22, 34, 8, 25, 17, 13 | ||||||||||||

Number of elements in set is 12 | ||||||||||||

1st Middle Position = (count ÷ 2) - 1 | ||||||||||||

1st Middle Position = (12 ÷ 2) - 1 = 6 | ||||||||||||

1st Middle Number = 15 | ||||||||||||

2nd Middle Position = 1st Middle Position + 1 | ||||||||||||

2nd Middle Position = 6 + 1 = 7 | ||||||||||||

2nd Middle Number = 17 | ||||||||||||

Average of Middle Numbers = (15 + 17) ÷ 2 = 16 | ||||||||||||

Count | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

Data Set | 3 | 8 | 8 | 12 | 13 | 15 | 17 | 18 | 22 | 25 | 34 | 36 |

Median = 16 (average of 15 and 17) |

### How Do You Calculate the Mode?

The *mode* is the number in a data set that is repeated the most often within the set. To find the mode, you simply count the number of times each unique number appears within the data set. The number that appears most often is the mode. In our example data set, the number that appears the most often is 8, therefore the mode of the data set is 8.

Example data set: 36, 3, 8, 12, 15, 18, 22, 34, 8, 25, 17, 13, 23 | |||||||||||||

Sorted Data Set | 3 | 8 | 8 | 12 | 13 | 15 | 17 | 18 | 22 | 23 | 25 | 34 | 36 |

Mode = 8 (8 appears the most often) |

Note that a data set can have more than 1 mode. For example, if the above data set included another 3, then the set would have two modes: 3 and 8. A data set having two modes is referred to as a *bimodal* set, whereas a data set having more than two modes is referred to as a *multimodal* set.

### How Do You Calculate the Range?

The *range* is the difference between the largest number within the set and the smallest number in the set. To find the range, you sort the range from smallest to largest to determine the minimum and maximum values. You then subtract the minimum value from the maximum value to find the range. In our example set the minimum is 3 and the maximum is 36, which would result in a range of 33 (36 - 3).

Example data set: 36, 3, 8, 12, 15, 18, 22, 34, 8, 25, 17, 13, 23 | |||||||||||||

Sorted Data Set | 3 | 8 | 8 | 12 | 13 | 15 | 17 | 18 | 22 | 23 | 25 | 34 | 36 |

Range = 33 (difference between maximum of 36 and minimum of 3) |

With that, let's use the Statistical Average Calculator to calculate the mean, median, mode, and range for a set of data.

### Statistical Average Calculator Glossary of Terms

Data set: Enter each element of the data set (or paste a copied data set) into this text box. Be sure each number is separated by a space, a comma, a line return, or any combination of the three. Also, if you wish to enter a frequency for each number, enter the number, followed by a lowercase x, followed by the multiplier (for 3 number twos, enter 2x3).

Total numbers in set: This is the total number of elements detected in the data set field.

Sum of numbers: This is the sum of elements detected by the statistical average calculator.

Average (mean): This is the average or mean of the elements within the data set. This is calculated by summing the elements within the set, and then dividing the sum by the number of elements.

Median: This is the median of the elements detected in the data set. If the number of elements in the set is odd, this is the middle number when sorted from smallest to largest. In the case of an even number of elements in the set, this result will be the average of the middle two numbers.

Minimum: This is the smallest of the elements entered into the data set.

Maximum: This is the largest of the elements entered into the data set.

Range: This is the difference between the largest number in the data set and smallest number in the data set.

Mode: This is the mode of elements entered in the data set, which is the element(s) with the highest frequency of occurrences within the set.

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## Mean Mode Median Worksheets

## Mean, Mode, Median, and Range Worksheets

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**Mean Mode Median and Range Definition Worksheets**

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