Algebra Examples

$540$ , $630$ , $540$ , $650$ , $480$ , $620$ , $650$ , $540$ , $500$ , $580$ , $390$ , $480$ , $510$ , $520$ , $460$ , $530$

Step 1

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

$\frac{540 + 630 + 540 + 650 + 480 + 620 + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2

Cancel the common factor of $540 + 630 + 540 + 650 + 480 + 620 + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530$ and $16$ .

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Step 2.1

Factor $2$ out of $540$ .

$\frac{2 (270) + 630 + 540 + 650 + 480 + 620 + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.2

Factor $2$ out of $630$ .

$\frac{2 \cdot 270 + 2 \cdot 315 + 540 + 650 + 480 + 620 + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.3

Factor $2$ out of $2 \cdot 270 + 2 \cdot 315$ .

$\frac{2 \cdot (270 + 315) + 540 + 650 + 480 + 620 + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.4

Factor $2$ out of $540$ .

$\frac{2 \cdot (270 + 315) + 2 (270) + 650 + 480 + 620 + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.5

Factor $2$ out of $2 \cdot (270 + 315) + 2 (270)$ .

$\frac{2 \cdot (270 + 315 + 270) + 650 + 480 + 620 + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.6

Factor $2$ out of $650$ .

$\frac{2 \cdot (270 + 315 + 270) + 2 (325) + 480 + 620 + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.7

Factor $2$ out of $2 \cdot (270 + 315 + 270) + 2 (325)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325) + 480 + 620 + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.8

Factor $2$ out of $480$ .

$\frac{2 \cdot (270 + 315 + 270 + 325) + 2 (240) + 620 + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.9

Factor $2$ out of $2 \cdot (270 + 315 + 270 + 325) + 2 (240)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240) + 620 + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.10

Factor $2$ out of $620$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240) + 2 (310) + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.11

Factor $2$ out of $2 \cdot (270 + 315 + 270 + 325 + 240) + 2 (310)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310) + 650 + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.12

Factor $2$ out of $650$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310) + 2 (325) + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.13

Factor $2$ out of $2 \cdot (270 + 315 + 270 + 325 + 240 + 310) + 2 (325)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325) + 540 + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.14

Factor $2$ out of $540$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325) + 2 (270) + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.15

Factor $2$ out of $2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325) + 2 (270)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270) + 500 + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.16

Factor $2$ out of $500$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270) + 2 (250) + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.17

Factor $2$ out of $2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270) + 2 (250)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250) + 580 + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.18

Factor $2$ out of $580$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250) + 2 (290) + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.19

Factor $2$ out of $2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250) + 2 (290)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290) + 390 + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.20

Factor $2$ out of $390$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290) + 2 (195) + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.21

Factor $2$ out of $2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290) + 2 (195)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195) + 480 + 510 + 520 + 460 + 530}{16}$

Step 2.22

Factor $2$ out of $480$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195) + 2 (240) + 510 + 520 + 460 + 530}{16}$

Step 2.23

Factor $2$ out of $2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195) + 2 (240)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240) + 510 + 520 + 460 + 530}{16}$

Step 2.24

Factor $2$ out of $510$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240) + 2 (255) + 520 + 460 + 530}{16}$

Step 2.25

Factor $2$ out of $2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240) + 2 (255)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255) + 520 + 460 + 530}{16}$

Step 2.26

Factor $2$ out of $520$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255) + 2 (260) + 460 + 530}{16}$

Step 2.27

Factor $2$ out of $2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255) + 2 (260)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260) + 460 + 530}{16}$

Step 2.28

Factor $2$ out of $460$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260) + 2 (230) + 530}{16}$

Step 2.29

Factor $2$ out of $2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260) + 2 (230)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230) + 530}{16}$

Step 2.30

Factor $2$ out of $530$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230) + 2 (265)}{16}$

Step 2.31

Factor $2$ out of $2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230) + 2 (265)$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230 + 265)}{16}$

Step 2.32

Cancel the common factors.

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Step 2.32.1

Factor $2$ out of $16$ .

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230 + 265)}{2 (8)}$

Step 2.32.2

Cancel the common factor.

$\frac{2 \cdot (270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230 + 265)}{2 \cdot 8}$

Step 2.32.3

Rewrite the expression.

$\frac{270 + 315 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230 + 265}{8}$

Step 3

Simplify the numerator.

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Step 3.1

Add $270$ and $315$ .

$\frac{585 + 270 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230 + 265}{8}$

Step 3.2

Add $585$ and $270$ .

$\frac{855 + 325 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230 + 265}{8}$

Step 3.3

Add $855$ and $325$ .

$\frac{1180 + 240 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230 + 265}{8}$

Step 3.4

Add $1180$ and $240$ .

$\frac{1420 + 310 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230 + 265}{8}$

Step 3.5

Add $1420$ and $310$ .

$\frac{1730 + 325 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230 + 265}{8}$

Step 3.6

Add $1730$ and $325$ .

$\frac{2055 + 270 + 250 + 290 + 195 + 240 + 255 + 260 + 230 + 265}{8}$

Step 3.7

Add $2055$ and $270$ .

$\frac{2325 + 250 + 290 + 195 + 240 + 255 + 260 + 230 + 265}{8}$

Step 3.8

Add $2325$ and $250$ .

$\frac{2575 + 290 + 195 + 240 + 255 + 260 + 230 + 265}{8}$

Step 3.9

Add $2575$ and $290$ .

$\frac{2865 + 195 + 240 + 255 + 260 + 230 + 265}{8}$

Step 3.10

Add $2865$ and $195$ .

$\frac{3060 + 240 + 255 + 260 + 230 + 265}{8}$

Step 3.11

Add $3060$ and $240$ .

$\frac{3300 + 255 + 260 + 230 + 265}{8}$

Step 3.12

Add $3300$ and $255$ .

$\frac{3555 + 260 + 230 + 265}{8}$

Step 3.13

Add $3555$ and $260$ .

$\frac{3815 + 230 + 265}{8}$

Step 3.14

Add $3815$ and $230$ .

$\frac{4045 + 265}{8}$

Step 3.15

Add $4045$ and $265$ .

$\frac{4310}{8}$

Step 4

Cancel the common factor of $4310$ and $8$ .

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Step 4.1

Factor $2$ out of $4310$ .

$\frac{2 (2155)}{8}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $8$ .

$\frac{2 \cdot 2155}{2 \cdot 4}$

Step 4.2.2

Cancel the common factor.

$\frac{2 \cdot 2155}{2 \cdot 4}$

Step 4.2.3

Rewrite the expression.

$\frac{2155}{4}$

Step 5

Divide.

$538.75$

Step 6

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.

$538.8$