Statistics Examples

$3$ , $4$ , $8$ , $8$ , $10$ , $11$ , $12$ , $13$ , $14$ , $15$ , $15$ , $16$ , $16$ , $17$ , $17$ , $18$ , $21$ , $22$ , $22$ , $24$ , $24$ , $25$ , $26$ , $26$ , $27$ , $27$ , $29$ , $29$ , $31$ , $32$ , $33$ , $33$ , $34$ , $34$ , $35$ , $37$ , $40$ , $44$ , $44$ , $47$

Step 1

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

$\frac{3 + 4 + 8 + 8 + 10 + 11 + 12 + 13 + 14 + 15 + 15 + 16 + 16 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2

Simplify the numerator.

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Step 2.1

Add $3$ and $4$ .

$\frac{7 + 8 + 8 + 10 + 11 + 12 + 13 + 14 + 15 + 15 + 16 + 16 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.2

Add $7$ and $8$ .

$\frac{15 + 8 + 10 + 11 + 12 + 13 + 14 + 15 + 15 + 16 + 16 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.3

Add $15$ and $8$ .

$\frac{23 + 10 + 11 + 12 + 13 + 14 + 15 + 15 + 16 + 16 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.4

Add $23$ and $10$ .

$\frac{33 + 11 + 12 + 13 + 14 + 15 + 15 + 16 + 16 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.5

Add $33$ and $11$ .

$\frac{44 + 12 + 13 + 14 + 15 + 15 + 16 + 16 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.6

Add $44$ and $12$ .

$\frac{56 + 13 + 14 + 15 + 15 + 16 + 16 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.7

Add $56$ and $13$ .

$\frac{69 + 14 + 15 + 15 + 16 + 16 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.8

Add $69$ and $14$ .

$\frac{83 + 15 + 15 + 16 + 16 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.9

Add $83$ and $15$ .

$\frac{98 + 15 + 16 + 16 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.10

Add $98$ and $15$ .

$\frac{113 + 16 + 16 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.11

Add $113$ and $16$ .

$\frac{129 + 16 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.12

Add $129$ and $16$ .

$\frac{145 + 17 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.13

Add $145$ and $17$ .

$\frac{162 + 17 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.14

Add $162$ and $17$ .

$\frac{179 + 18 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.15

Add $179$ and $18$ .

$\frac{197 + 21 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.16

Add $197$ and $21$ .

$\frac{218 + 22 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.17

Add $218$ and $22$ .

$\frac{240 + 22 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.18

Add $240$ and $22$ .

$\frac{262 + 24 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.19

Add $262$ and $24$ .

$\frac{286 + 24 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.20

Add $286$ and $24$ .

$\frac{310 + 25 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.21

Add $310$ and $25$ .

$\frac{335 + 26 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.22

Add $335$ and $26$ .

$\frac{361 + 26 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.23

Add $361$ and $26$ .

$\frac{387 + 27 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.24

Add $387$ and $27$ .

$\frac{414 + 27 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.25

Add $414$ and $27$ .

$\frac{441 + 29 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.26

Add $441$ and $29$ .

$\frac{470 + 29 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.27

Add $470$ and $29$ .

$\frac{499 + 31 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.28

Add $499$ and $31$ .

$\frac{530 + 32 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.29

Add $530$ and $32$ .

$\frac{562 + 33 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.30

Add $562$ and $33$ .

$\frac{595 + 33 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.31

Add $595$ and $33$ .

$\frac{628 + 34 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.32

Add $628$ and $34$ .

$\frac{662 + 34 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.33

Add $662$ and $34$ .

$\frac{696 + 35 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.34

Add $696$ and $35$ .

$\frac{731 + 37 + 40 + 44 + 44 + 47}{40}$

Step 2.35

Add $731$ and $37$ .

$\frac{768 + 40 + 44 + 44 + 47}{40}$

Step 2.36

Add $768$ and $40$ .

$\frac{808 + 44 + 44 + 47}{40}$

Step 2.37

Add $808$ and $44$ .

$\frac{852 + 44 + 47}{40}$

Step 2.38

Add $852$ and $44$ .

$\frac{896 + 47}{40}$

Step 2.39

Add $896$ and $47$ .

$\frac{943}{40}$

Step 3

Divide.

$23.575$

Step 4

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.

$23.6$