We often look for

mean,median,mode,and

range

when analyzing lists of data.

5, 2, 7, 8, 6, 2, 3

5, 2, 7, 8, 6, 2, 3Mean:

Divide the sum of the numbers by the number of numbers in the list.

5, 2, 7, 8, 6, 2, 3Mean:

Divide the sum of the numbers by the number of numbers in the list.

5 + 2 + 7 + 8 + 6 + 2 + 3 =

5, 2, 7, 8, 6, 2, 3Mean:

Divide the sum of the numbers by the number of numbers in the list.

5 + 2 + 7 + 8 + 6 + 2 + 3 = 33

5, 2, 7, 8, 6, 2, 3Mean:

Divide the sum of the numbers by the number of numbers in the list.

5 + 2 + 7 + 8 + 6 + 2 + 3 = 33

33 ÷ 7 =

5, 2, 7, 8, 6, 2, 3Mean:

Divide the sum of the numbers by the number of numbers in the list.

5 + 2 + 7 + 8 + 6 + 2 + 3 = 33

33 ÷ 7 = 4 57

5, 2, 7, 8, 6, 2, 3Mean:

Divide the sum of the numbers by the number of numbers in the list.

5 + 2 + 7 + 8 + 6 + 2 + 3 = 33

33 ÷ 7 = 4 57

5, 2, 7, 8, 6, 2, 3Median:

Find the middle number in the list.

5, 2, 7, 8, 6, 2, 3Median:

Find the middle number in the list.

2, 2, 3, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3Median:

Find the middle number in the list.

2, 2, 3, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3, 1Median:

Find the middle number in the list.

5, 2, 7, 8, 6, 2, 3, 1Median:

Find the middle number in the list.

1, 2, 2, 3, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3, 1Median:

Find the middle number in the list.

1, 2, 2, 3, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3, 1Median:

Find the middle number in the list.

1, 2, 2, 3, 5, 6, 7, 8(3 + 5) ÷ 2 =

5, 2, 7, 8, 6, 2, 3, 1Median:

Find the middle number in the list.

1, 2, 2, 3, 5, 6, 7, 8(3 + 5) ÷ 2 = 8 ÷ 2 =

5, 2, 7, 8, 6, 2, 3, 1Median:

Find the middle number in the list.

1, 2, 2, 3, 5, 6, 7, 8(3 + 5) ÷ 2 = 8 ÷ 2 = 4

5, 2, 7, 8, 6, 2, 3, 4Median:

Find the middle number in the list.

5, 2, 7, 8, 6, 2, 3, 4Median:

Find the middle number in the list.

2, 2, 3, 4, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3, 4Median:

Find the middle number in the list.

2, 2, 3, 4, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3, 4Median:

Find the middle number in the list.

2, 2, 3, 4, 5, 6, 7, 8(4 + 5) ÷ 2 =

5, 2, 7, 8, 6, 2, 3, 4Median:

Find the middle number in the list.

2, 2, 3, 4, 5, 6, 7, 8(4 + 5) ÷ 2 = 9 ÷ 2 =

5, 2, 7, 8, 6, 2, 3, 4Median:

Find the middle number in the list.

2, 2, 3, 4, 5, 6, 7, 8(4 + 5) ÷ 2 = 9 ÷ 2 = 4.5

5, 2, 7, 8, 6, 2, 3, 5Median:

Find the middle number in the list.

5, 2, 7, 8, 6, 2, 3, 5Median:

Find the middle number in the list.

2, 2, 3, 5, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3, 5Median:

Find the middle number in the list.

2, 2, 3, 5, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3, 5Median:

Find the middle number in the list.

2, 2, 3, 5, 5, 6, 7, 8

5

5, 2, 7, 8, 6, 2, 3Mode:

Find the number or numbers that occur most often in the list.

5, 2, 7, 8, 6, 2, 3Mode:

Find the number or numbers that occur most often in the list.

2, 2, 3, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3Mode:

Find the number or numbers that occur most often in the list.

2, 2, 3, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3Mode:

Find the number or numbers that occur most often in the list.

2, 2, 3, 5, 6, 7, 8

2

5, 2, 7, 8, 6, 2, 3, 5Mode:

Find the number or numbers that occur most often in the list.

5, 2, 7, 8, 6, 2, 3, 5Mode:

Find the number or numbers that occur most often in the list.

2, 2, 3, 5, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3, 5Mode:

Find the number or numbers that occur most often in the list.

2, 2, 3, 5, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3, 5Mode:

Find the number or numbers that occur most often in the list.

2, 2, 3, 5, 5, 6, 7, 8

Two modes: 2 and 5

2, 7, 8, 6, 3, 5Mode:

Find the number or numbers that occur most often in the list.

2, 7, 8, 6, 3, 5Mode:

Find the number or numbers that occur most often in the list.

2, 3, 5, 6, 7, 8

2, 7, 8, 6, 3, 5Mode:

Find the number or numbers that occur most often in the list.

2, 3, 5, 6, 7, 8

No mode

5, 2, 6, 7, 8, 6, 3, 6, 5, 2

Mode:Find the number or numbers that

occur most often in the list.

5, 2, 6, 7, 8, 6, 3, 6, 5, 2

Mode:Find the number or numbers that

occur most often in the list.

2, 2, 3, 5, 5, 6, 6, 6, 7, 8

5, 2, 6, 7, 8, 6, 3, 6, 5, 2

Mode:Find the number or numbers that

occur most often in the list.

2, 2, 3, 5, 5, 6, 6, 6, 7, 8

5, 2, 6, 7, 8, 6, 3, 6, 5, 2

Mode:Find the number or numbers that

occur most often in the list.

2, 2, 3, 5, 5, 6, 6, 6, 7, 8

5, 2, 6, 7, 8, 6, 3, 6, 5, 2

Mode:Find the number or numbers that

occur most often in the list.

2, 2, 3, 5, 5, 6, 6, 6, 7, 8

6

5, 2, 7, 8, 6, 2, 3Range:

Find the difference between the highest and lowest numbers in the list.

5, 2, 7, 8, 6, 2, 3Range:

Find the difference between the highest and lowest numbers in the list.

2, 2, 3, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 3Range:

Find the difference between the highest and lowest numbers in the list.

2, 2, 3, 5, 6, 7, 8 8 – 2 =

5, 2, 7, 8, 6, 2, 3Range:

Find the difference between the highest and lowest numbers in the list.

2, 2, 3, 5, 6, 7, 8 8 – 2 = 6

5, 2, 7, 8, 6, 2, 3

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Mean:

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Number of #'s = 7

Mean:

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Number of #'s = 7 Sum of #'s = 33

Mean:

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Number of #'s = 7 Sum of #'s = 33

Mean: 33 ÷ 7

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Number of #'s = 7 Sum of #'s = 33

Mean: 33 ÷ 7

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Mean: 33 ÷ 7

Median:

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Mean: 33 ÷ 7

Median:

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Mean: 33 ÷ 7

Median: 5

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Mean: 33 ÷ 7

Median: 5

Mode:

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Mean: 33 ÷ 7

Median: 5

Mode:

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Mean: 33 ÷ 7

Median: 5

Mode: 2

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Mean: 33 ÷ 7

Median: 5

Mode: 2

Range:

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Mean: 33 ÷ 7

Median: 5

Mode: 2

Range:

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Mean: 33 ÷ 7

Median: 5

Mode: 2

Range: 8 – 2 =

5, 2, 7, 8, 6, 2, 32, 2, 3, 5, 6, 7, 8

Mean: 33 ÷ 7

Median: 5

Mode: 2

Range: 8 – 2 = 6

Chicago high and low

temperatures for each day in Feb. 2014.

Date High Low Date High Low

1 32 23 15 24 6

2 23 7 16 28 18

3 22 1 17 29 22

4 25 10 18 45 23

5 25 9 19 45 32

6 12 -1 20 51 35

7 11 -3 21 37 28

8 17 6 22 35 23

9 20 7 23 29 16

10 13 -2 24 25 13

11 15 -4 25 24 7

12 23 2 26 29 1

13 34 15 27 29 6

14 22 13 28 32 6

Low temperatures

Date High Low Date High Low

1 32 23 15 24 6

2 23 7 16 28 18

3 22 1 17 29 22

4 25 10 18 45 23

5 25 9 19 45 32

6 12 -1 20 51 35

7 11 -3 21 37 28

8 17 6 22 35 23

9 20 7 23 29 16

10 13 -2 24 25 13

11 15 -4 25 24 7

12 23 2 26 29 1

13 34 15 27 29 6

14 22 13 28 32 6

Low temperatures

Date High Low Date High Low

1 32 23 15 24 6

2 23 7 16 28 18

3 22 1 17 29 22

4 25 10 18 45 23

5 25 9 19 45 32

6 12 -1 20 51 35

7 11 -3 21 37 28

8 17 6 22 35 23

9 20 7 23 29 16

10 13 -2 24 25 13

11 15 -4 25 24 7

12 23 2 26 29 1

13 34 15 27 29 6

14 22 13 28 32 6

Low temperatures

-4,

Date High Low Date High Low

1 32 23 15 24 6

2 23 7 16 28 18

3 22 1 17 29 22

4 25 10 18 45 23

5 25 9 19 45 32

6 12 -1 20 51 35

7 11 -3 21 37 28

8 17 6 22 35 23

9 20 7 23 29 16

10 13 -2 24 25 13

11 15 -4 25 24 7

12 23 2 26 29 1

13 34 15 27 29 6

14 22 13 28 32 6

Low temperatures

-4, -3,

Date High Low Date High Low

1 32 23 15 24 6

2 23 7 16 28 18

3 22 1 17 29 22

4 25 10 18 45 23

5 25 9 19 45 32

6 12 -1 20 51 35

7 11 -3 21 37 28

8 17 6 22 35 23

9 20 7 23 29 16

10 13 -2 24 25 13

11 15 -4 25 24 7

12 23 2 26 29 1

13 34 15 27 29 6

14 22 13 28 32 6

Low temperatures

-4, -3, -2,

Date High Low Date High Low

1 32 23 15 24 6

2 23 7 16 28 18

3 22 1 17 29 22

4 25 10 18 45 23

5 25 9 19 45 32

6 12 -1 20 51 35

7 11 -3 21 37 28

8 17 6 22 35 23

9 20 7 23 29 16

10 13 -2 24 25 13

11 15 -4 25 24 7

12 23 2 26 29 1

13 34 15 27 29 6

14 22 13 28 32 6

Low temperatures

-4, -3, -2, -1,

Date High Low Date High Low

1 32 23 15 24 6

2 23 7 16 28 18

3 22 1 17 29 22

4 25 10 18 45 23

5 25 9 19 45 32

6 12 -1 20 51 35

7 11 -3 21 37 28

8 17 6 22 35 23

9 20 7 23 29 16

10 13 -2 24 25 13

11 15 -4 25 24 7

12 23 2 26 29 1

13 34 15 27 29 6

14 22 13 28 32 6

Low temperatures

-4, -3, -2, -1, 1, 1,

Date High Low Date High Low

1 32 23 15 24 6

2 23 7 16 28 18

3 22 1 17 29 22

4 25 10 18 45 23

5 25 9 19 45 32

6 12 -1 20 51 35

7 11 -3 21 37 28

8 17 6 22 35 23

9 20 7 23 29 16

10 13 -2 24 25 13

11 15 -4 25 24 7

12 23 2 26 29 1

13 34 15 27 29 6

14 22 13 28 32 6

Low temperatures

-4, -3, -2, -1, 1, 1, 2,

Date High Low Date High Low

1 32 23 15 24 6

2 23 7 16 28 18

3 22 1 17 29 22

4 25 10 18 45 23

5 25 9 19 45 32

6 12 -1 20 51 35

7 11 -3 21 37 28

8 17 6 22 35 23

9 20 7 23 29 16

10 13 -2 24 25 13

11 15 -4 25 24 7

12 23 2 26 29 1

13 34 15 27 29 6

14 22 13 28 32 6

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6,

Date High Low Date High Low

1 32 23 15 24 6

2 23 7 16 28 18

3 22 1 17 29 22

4 25 10 18 45 23

5 25 9 19 45 32

6 12 -1 20 51 35

7 11 -3 21 37 28

8 17 6 22 35 23

9 20 7 23 29 16

10 13 -2 24 25 13

11 15 -4 25 24 7

12 23 2 26 29 1

13 34 15 27 29 6

14 22 13 28 32 6

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Date High Low Date High Low

1 32 23 15 24 6

2 23 7 16 28 18

3 22 1 17 29 22

4 25 10 18 45 23

5 25 9 19 45 32

6 12 -1 20 51 35

7 11 -3 21 37 28

8 17 6 22 35 23

9 20 7 23 29 16

10 13 -2 24 25 13

11 15 -4 25 24 7

12 23 2 26 29 1

13 34 15 27 29 6

14 22 13 28 32 6

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean:

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28Median:

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28Median:

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28Median: 8

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28Median: 8Mode:

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28Median: 8Mode:

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28Median: 8Mode:

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28Median: 8Mode: 6

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28Median: 8Mode: 6Range:

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28Median: 8Mode: 6Range:

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28Median: 8Mode: 6Range: 35 – -4 =

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28Median: 8Mode: 6Range: 35 – -4 = 35 + 4 =

Low temperatures

-4, -3, -2, -1, 1, 1, 2, 6, 6, 6, 6, 7, 7, 7, 9, 10, 13, 13, 15, 16, 18, 22, 23, 23, 23, 28, 32, 35

Mean: 319 ÷ 28Median: 8Mode: 6Range: 35 – -4 = 35 + 4 = 39

Chicago high and low

temperatures for each day in Feb. 2014.

Date High Low Date High Low

1 32 23 15 24 6

2 23 7 16 28 18

3 22 1 17 29 22

4 25 10 18 45 23

5 25 9 19 45 32

6 12 -1 20 51 35

7 11 -3 21 37 28

8 17 6 22 35 23

9 20 7 23 29 16

10 13 -2 24 25 13

11 15 -4 25 24 7

12 23 2 26 29 1

13 34 15 27 29 6

14 22 13 28 32 6

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean:

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 =

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 = 27.0

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 = 27.0Median:

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 = 27.0Median:

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 = 27.0Median: 25

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 = 27.0Median: 25Mode:

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 = 27.0Median: 25Mode:

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 = 27.0Median: 25Mode:

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 = 27.0Median: 25Mode: 29

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 = 27.0Median: 25Mode: 29Range:

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 = 27.0Median: 25Mode: 29Range:

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 = 27.0Median: 25Mode: 29Range: 51 – 11 =

High temperatures

11, 12, 13, 15, 17, 20, 22 ,22, 23, 23, 24, 24, 25, 25, 25, 28, 29, 29, 29, 29, 32, 32, 34, 35, 37, 45, 45, 51

Mean: 756 ÷ 28 = 27.0Median: 25Mode: 29Range: 51 – 11 = 40

We often look for mean, median, mode, and range when analyzing lists of data. The mean, median,

and mode are all measures of central tendency. A measure of central tendency is sometimes

called the average. The mean is probably referred to as the

average of a list of numbers more often than the median or mode.