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Raw Data Sorted Stem Leaf

30 4 0 4

25 24 1

45 25 2 4 5 6 8

4 26 3 0 2 8 8

38 28 4 0 5 6

46 30

28 32

40 38

38 38

32 40

24 45

26 46

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Topic 2 - Presenting Data (Class Activity)

Temperature Freq. % Cum. Freq. Cum. %

10-20 1 6.67% 1 6.67%

20-30 3 20.00% 4 26.67%

30-40 5 33.33% 9 60.00%40-50 4 26.67% 13 86.67%

50-60 2 13.33% 15 100.00%

15 100.00%

0

2

4

6

10-20 20-30 30-40 40-50 50-60

Fre

quency

Temperature

Temperature

0.00%

20.00%

40.00%

60.00%

80.00%

100.00%

120.00%

10-20

20-30

30-40

40-50

50-60

Ogive

Cu

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m. %

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Raw Data Sorted

342 264

426 266

317 298

545 317

264 342

451 426

1049 451 Median Value or "=median(range of values)"

631 492 451

512 512

266 545

492 562 Mean

562 631 Sum up the observations "sum(range of values)"

298 1049 Divide by number of observations "=count(range of value

473.462 or 473.462 "=average(range of val

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s)"

ues)"

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Calculating Mean, Mode and Median

440 280 Mean = 423.3333

490 390

550 390 Median = 415

390 440

280 490 Mode = 390

390 550

Calculating Mean, Variance and Standard Deviation

7 Mean = 11.16667 Xi (Xi - )

9 7 11.16667 -4.16667

10 Variance = 12.16667 9 11.16667 -2.16667

11 10 11.16667 -1.16667

13 Std Dev = 3.488075 11 11.16667 -0.16667

17 13 11.16667 1.833333

17 11.16667 5.833333

S.Var =

S.Std Dev =

Measures of Variation: Comparing Standard Deviations

(Notice that although the mean values for all 3 samples are the same but the spread of the dat

- Standard Deviation - is very different as evident from the diagrams in the slides)

Sample A Xi (Xi - )

11 Mean = 15.5 11 15.5 -4.5

12 12 15.5 -3.5

13 Variance = 11.14286 13 15.5 -2.5

16 16 15.5 0.5

16 Std Dev = 3.338092 16 15.5 0.5

17 17 15.5 1.5

18 18 15.5 2.5

21 21 15.5 5.5

S.Var =

S.Std Dev =

Sample B Xi (Xi - )

14 Mean = 15.5 14 15.5 -1.5

15 15 15.5 -0.5

15 Variance = 0.857143 15 15.5 -0.5

15 15 15.5 -0.5

16 Std Dev = 0.92582 16 15.5 0.5

Calculating variance and standa

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16 16 15.5 0.5

16 16 15.5 0.5

17 17 15.5 1.5

S.Std Dev =

Sample C Xi (Xi - )

11 Mean = 15.5 11 15.5 -4.5

11 11 15.5 -4.5

11 Variance = 20.85714 11 15.5 -4.5

12 12 15.5 -3.5

19 Std Dev = 4.566962 19 15.5 3.5

20 20 15.5 4.5

20 20 15.5 4.5

20 20 15.5 4.5

S.Var =

S.Std Dev =

Calculate Q1 (First Quartile), Q2 (Second Quartile or Median), Q3 (Third Quartile)

44 28 Q1 = 39.00

49 38

55 39 Q2 = 46.5

39 39

28 44 Q3 = 55.75

39 49

38 55

56 56

59 59

64 64

Simulating Quartile calculations using Excel with constant ascending numbers

1 Q1 = 3.25

2 Q2 = 5.5

3 Q3 = 7.754 Q4 = 10

5

6

7

8

9

10

NOTE: Excel uses a different

formula for calculating quartiles:

Q1 = 1/4 * (n + 3)Q2 = 2/4 * (n + 1)

Q3 = 1/4 * (3n + 1)

Note the slight difference in the way

Excel (and different types of

statistical software) calculates thequartiles... Just remember, follow

the quartile position rules based

on the slides for exam purposes.

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Question 3-121 (Textbook - Weiss, Page 124) Question 3

Raw Data

Sorted

Data

Position

Number Raw Data

79 45 1 352

80 48 2 445

73 64 3 374

48 70 4 43480 73 5 400

80 74 6 400

78 74 7 426

80 78 8 354

80 78 9 396

79 79 10 374

74 79 11 427

82 80 12 349

80 80 13

64 80 14

45 80 15

82 80 16

74 80 17

78 81 18

81 82 19

70 82 20

Also, if you are interested, you can visit this website

http://peltiertech.com/WordPress/excel-box-and-whisker-diagrams-box-plots/

to give you an idea how to construct a Boxplot from scratch... (good for people with insomi

A Boxplot gives a pictorial description of the upper and lower limits as well as Q1, Q2, Q3 all

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(Xi - )2

17.36111

4.694444

1.361111

0.027778

3.361111

34.02778

60.83333

12.16667

3.488075

a

(Xi - )2

20.25

12.25

6.25

0.25

0.25

2.25

6.25

30.25

78

11.14286

3.338092

(Xi - )2

2.25

0.25

0.25

0.25

0.25

rd

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0.25

0.25

2.25

6

0.92582

(Xi - )2

20.25

20.25

20.25

12.25

12.25

20.25

20.25

20.25

146

20.85714

4.566962

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126 (Textbook - Weiss, Page 124)

Sorted

Data

Position

Number

349 1

352 2

354 3

374 4374 5

396 6

400 7

400 8

426 9

427 10

434 11

445 12

a)

l on the

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Class Activity

x P(x) xP(x) (x - ) (x - )2

(x - )2

P(x)

0 0.4 0 -1.15 1.3225 0.529

1 0.3 0.3 -0.15 0.0225 0.00675

2 0.1 0.2 0.85 0.7225 0.072253 0.15 0.45 1.85 3.4225 0.513375

4 0.05 0.2 2.85 8.1225 0.406125

= 1.15 2

= 1.5275

= 1.23592071