Basic Math Examples

4.5

$4.5$ ,

3

$3$ ,

1

$1$ ,

2

$2$ ,

4

$4$ ,

3

$3$ ,

6

$6$ ,

4.5

$4.5$ ,

4

$4$ ,

5

$5$ ,

2

$2$ ,

1

$1$ ,

3

$3$ ,

4

$4$ ,

3

$3$ ,

2

$2$

Step 1

The mean of a set of numbers is the sum divided by the number of terms.

\frac{4.5 + 3 + 1 + 2 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}

$\frac{4.5 + 3 + 1 + 2 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}$

Step 2

Simplify the numerator.

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Step 2.1

Add

4.5

$4.5$ and

3

$3$ .

\frac{7.5 + 1 + 2 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}

$\frac{7.5 + 1 + 2 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}$

Step 2.2

Add

7.5

$7.5$ and

1

$1$ .

\frac{8.5 + 2 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}

$\frac{8.5 + 2 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}$

Step 2.3

Add

8.5

$8.5$ and

2

$2$ .

\frac{10.5 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}

$\frac{10.5 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}$

Step 2.4

Add

10.5

$10.5$ and

4

$4$ .

\frac{14.5 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}

$\frac{14.5 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}$

Step 2.5

Add

14.5

$14.5$ and

3

$3$ .

\frac{17.5 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}

$\frac{17.5 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}$

Step 2.6

Add

17.5

$17.5$ and

6

$6$ .

\frac{23.5 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}

$\frac{23.5 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}$

Step 2.7

Add

23.5

$23.5$ and

4.5

$4.5$ .

\frac{28 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}

$\frac{28 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}$

Step 2.8

Add

28

$28$ and

4

$4$ .

\frac{32 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}

$\frac{32 + 5 + 2 + 1 + 3 + 4 + 3 + 2}{16}$

Step 2.9

Add

32

$32$ and

5

$5$ .

\frac{37 + 2 + 1 + 3 + 4 + 3 + 2}{16}

$\frac{37 + 2 + 1 + 3 + 4 + 3 + 2}{16}$

Step 2.10

Add

37

$37$ and

2

$2$ .

\frac{39 + 1 + 3 + 4 + 3 + 2}{16}

$\frac{39 + 1 + 3 + 4 + 3 + 2}{16}$

Step 2.11

Add

39

$39$ and

1

$1$ .

\frac{40 + 3 + 4 + 3 + 2}{16}

$\frac{40 + 3 + 4 + 3 + 2}{16}$

Step 2.12

Add

40

$40$ and

3

$3$ .

\frac{43 + 4 + 3 + 2}{16}

$\frac{43 + 4 + 3 + 2}{16}$

Step 2.13

Add

43

$43$ and

4

$4$ .

\frac{47 + 3 + 2}{16}

$\frac{47 + 3 + 2}{16}$

Step 2.14

Add

47

$47$ and

3

$3$ .

\frac{50 + 2}{16}

$\frac{50 + 2}{16}$

Step 2.15

Add

50

$50$ and

2

$2$ .

\frac{52}{16}

$\frac{52}{16}$

\frac{52}{16}

$\frac{52}{16}$

Step 3

Cancel the common factor of

52

$52$ and

16

$16$ .

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Step 3.1

Factor

4

$4$ out of

52

$52$ .

\frac{4 (13)}{16}

$\frac{4 (13)}{16}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

4

$4$ out of

16

$16$ .

\frac{4 \cdot 13}{4 \cdot 4}

$\frac{4 \cdot 13}{4 \cdot 4}$

Step 3.2.2

Cancel the common factor.

$\frac{4 \cdot 13}{4 \cdot 4}$

Step 3.2.3

Rewrite the expression.

$\frac{13}{4}$

Step 4

Divide.

$3.25$

Step 5

The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$3.3$