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Statistics

Mean

The mean is the average of a group of numbers.

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Mean = Sum ÷ Number of values
Statistics

Median

The median is the middle number after arranging the values in order.

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Median = Middle value
Statistics

Mode

The mode is the number that appears most often.

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Mode = Most frequent value
Statistics

Range

The range shows the difference between the greatest and smallest values.

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Range = Greatest − Smallest

Mean

Add all the numbers. Then divide by how many numbers there are.
Solved Examples
Example 1: Find the mean of 8, 12, 10, 15, 5
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  1. Add all numbers: 8 + 12 + 10 + 15 + 5 = 50.
  2. Count the numbers: there are 5 numbers.
  3. Mean = 50 ÷ 5 = 10.
Answer: 10
Example 2: Find the mean of 4, 6, 8, 6, 10, 12, 6
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  1. Add all numbers: 4 + 6 + 8 + 6 + 10 + 12 + 6 = 52.
  2. Count the numbers: there are 7 numbers.
  3. Mean = 52 ÷ 7 = 7.43.
Answer: 7.43
Example 3: Find the mean of 20, 30, 40, 50
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  1. Add all numbers: 20 + 30 + 40 + 50 = 140.
  2. Count the numbers: there are 4 numbers.
  3. Mean = 140 ÷ 4 = 35.
Answer: 35

Auto-Checked Practice

Median

Arrange the numbers from smallest to greatest. Then choose the middle number.
Solved Examples
Example 1: Find the median of 7, 2, 9, 5, 1

Original:

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Ordered:

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  1. Arrange the numbers: 1, 2, 5, 7, 9.
  2. The middle number is 5.
  3. Median = 5.
Answer: 5
Example 2: Find the median of 4, 6, 6, 6, 8, 10, 12
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  1. The numbers are already in order.
  2. There are 7 numbers, so the 4th number is the middle.
  3. Median = 6.
Answer: 6
Example 3: Find the median of 3, 9, 12, 20, 25
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  1. The numbers are already arranged.
  2. The middle number is 12.
  3. Median = 12.
Answer: 12

Auto-Checked Practice

Mode

Count how many times each number appears. The number that appears most often is the mode.
Solved Examples
Example 1: Find the mode of 4, 6, 2, 6, 8, 6, 5
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  1. Count each number.
  2. The number 6 appears 3 times.
  3. 6 appears more than all other numbers.
Answer: 6
Example 2: Find the mode of 3, 3, 5, 7, 9
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  1. Count each number.
  2. 3 appears 2 times.
  3. All other numbers appear once.
Answer: 3
Example 3: Find the mode of 10, 12, 12, 14, 14, 14
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  1. 12 appears 2 times.
  2. 14 appears 3 times.
  3. The most frequent number is 14.
Answer: 14

Auto-Checked Practice

Range

Find the greatest number and the smallest number. Then subtract: greatest − smallest.
Solved Examples
Example 1: Find the range of 14, 18, 9, 22, 11
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  1. Greatest number = 22.
  2. Smallest number = 9.
  3. Range = 22 − 9 = 13.
Answer: 13
Example 2: Find the range of 5, 10, 15, 20
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  1. Greatest number = 20.
  2. Smallest number = 5.
  3. Range = 20 − 5 = 15.
Answer: 15
Example 3: Find the range of 32, 18, 45, 21, 10
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  1. Greatest number = 45.
  2. Smallest number = 10.
  3. Range = 45 − 10 = 35.
Answer: 35

Auto-Checked Practice