From the Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997

Stemplots

1. In 1798, Henry Cavendish measured the density of the earth using an instrument called a torsion balance. While the density is obviously not uniform, the value of the mean density is important in determining the earth’s composition. The units are grams / cm3.

a. Construct a stemplot of this data.

b. Find the centre of the data.

c. Comment on the distribution.

Density of the Earth

5.5 5.57 5.42 5.61 5.53 5.47 4.88 5.62 5.63 4.07 5.29 5.34
5.26 5.44 5.46 5.55 5.34 5.3 5.36 5.79 5.75 5.29 5.1 5.86
5.58 5.27 5.85 5.65 5.39              

 

2. Shortly after metric units were introduced in Australia, a group of 44 students was asked to guess, to the nearest metre, the width of the lecture hall in which they were sitting. The true width of the hall was 13.1 metres.

a. Construct a stemplot of this data.

b. Find the centre of this dataset.

c. Describe the distribution.

d. A second group of students in the same room were asked to guess the width of the room in feet, measured to the nearest foot. (1 metre = 3.28 feet, to 2 decimal places). Construct a back to back stemplot from these two datasets. How will you overcome the problem that different units are used in the two datasets?

Source: Hills, M. etal, Statistical Methods, Unit 1: Data, distributions and uncertainty, Open University, England.

Guesses (Metres)

8 9 10 10 10 10 10 10 11 11 11 11 12
12 13 13 13 14 14 14 15 15 15 15 15 15
15 15 16 16 16 17 17 17 17 18 18 20 22
25 27 35 38 40                

Guesses (Feet)

24 25 27 30 30 30 30 30 30 32 32 33 34
34 34 35 35 36 36 36 37 37 40 40 40 40
40 40 40 40 40 41 41 42 42 42 42 43 43
44 44 44 45 45 45 45 45 45 46 46 47 48
48 50 50 50 51 54 54 54 55 55 60 60 63
70 75 80 94                  

 

3. Researchers at the Purdue University School of Vetinary Medicine deposited 25 female and 10 male fleas in the fur of a cat, in order to study the egg production of the flea. The number of eggs produced by the fleas over 27 consecutive days was:

Source: Moore D., McCabe G, Introduction to the Practice of Statistics, p.27

Fleas Dataset

Day

No. of eggs

Day

No of eggs

1

436

15

550

2

495

16

487

3

575

17

585

4

444

18

549

5

754

19

475

6

915

20

435

7

945

21

523

8

655

22

390

9

782

23

425

10

704

24

415

11

590

25

450

12

411

26

395

13

547

27

405

14

584

    

a. Discussing these questions will help decide on how the stemplot should be drawn:

How many rows will there be if:

b. Draw a stemplot to illustrate this data.

c. Describe the shape of the distribution, and discuss any unusual features.

d. What value is the centre of this dataset?