Basic Statistics

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Quick recall

• Sort values before finding the median.
• A data set may have more than one mode or no unique mode.

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Formula Cards

1. Mean

$$\bar{x}=\frac{\sum x}{n}$$

2. Median

Sort first. Odd count: take the middle value. Even count: average the two middle values.

3. Mode

The most frequent value; more than one mode may occur.

4. Range

$$\text{Range}=\text{Maximum}-\text{Minimum}$$

Worked Examples

Example 1

Question: Find the mean and range of 2, 3, 7.

Step 1: Find the mean.

$$\bar{x}=\frac{2+3+7}{3}=4$$

Step 2: Subtract minimum from maximum.

$$\text{Range}=7-2=5$$

Answer: Mean 4; range 5.

Example 2

Question: Find the median of 3, 7, 2, 9, 5.

Step 1: Sort the data.

$$2,\ 3,\ 5,\ 7,\ 9$$

Step 2: Select the middle, third value.

$$\text{Median}=5$$

Answer: 5.

Example 3

Question: Find the median of 4, 8, 2, 6.

Step 1: Sort the data.

$$2,\ 4,\ 6,\ 8$$

Step 2: Average the two middle values.

$$\text{Median}=\frac{4+6}{2}=5$$

Answer: 5.

Example 4

Question: Find the mode of 2, 3, 3, 5, 5, 5, 7.

Step 1: Count the frequencies.

$$f(2)=1,\ f(3)=2,\ f(5)=3,\ f(7)=1$$

Step 2: Choose the most frequent value.

$$\text{Mode}=5$$

Answer: 5.

Drill

Try each question before opening its answer.

Question 1

Find mean of 4,8,6,10,12.

• Show answer

  8

Question 2

Find median of 9,3,7,1,5.

• Show answer

  5

Question 3

Find mode of 1,1,2,3,3,3,4.

• Show answer

  3

Question 4

Find range of 12,45,3,67,9.

• Show answer

  64

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