11.05 Describing data distributions

Describe the shape of each of the following data sets as positively skewed, negatively skewed or symmetrical:

a

b

c

d

e

1

2

3

4

5

6

7

8

x

3

6

9

12

15

18

21

y

f

	Leaf
1	6\ 7\ 7
2	2\ 2\ 2\ 2\ 3\ 3\ 3
3	3\ 3\ 3\ 6\ 6\ 6\ 7\ 7\ 7\ 7\ 7
4	4\ 4\ 4\ 4\ 4\ 4
5	7\ 7

Key: 1 \vert 6 = 16

g

h

1

2

3

4

5

6

7

8

5

10

15

20

25

i

1

2

3

4

5

6

7

8

5

10

15

20

25

Describe the distribution of the following graphs:

a

b

The table shows the number of crime novels in a bookshop for different price ranges.

Consider the dot plot below:

Temperatures were recorded over a period of time and presented as a dot plot:

a

Are there any outliers?

b

Is there any clustering of data? If so, in what interval?

c

What is the modal temperature?

d

Describe the shape of the distribution of the data.

If a set of data is strongly positively skewed and the median is 70, what can we conclude about the mean?

State whether each of the following statements are true or false:

Which of the following dot plots has the highest median?

A

B

Determine whether the following sets of data have equal median and mean:

a

b

c

d

Consider the frequency distribution table below:

For the following scenarios, determine the value of the x:

The six numbers 6, 2, 7, 18, 17 and an unknown number x have a median of 8.5. Find the value of x.

Five numbers have a range of 16, a mode of 2, a median of 7 and a mean of 8. The minimum number in the set is 2. Calculate:

Three numbers have a mode of 10 and a mean of 10. Write the three numbers of the data set.

Four numbers have a range of 5, a median of 9 and a mode of 11. Write the four numbers of this data set.

State the measure of centre which more accurately describes the centre of each of the following data sets:

Consider the histogram below:

Determine the measure of centre that would be most appropriate to use to represent the data in this graph. Explain your answer.

Find the most appropriate measure of centre for the following data sets:

a

b

c

Carl has been recording his spelling test scores for the past semester:14,\, 16,\, 2,\, 15,\, 15,\, 16,\, 15

The stem and leaf plot below shows the age of people to enter through the gates of a concert in the first 5 seconds:

The following stem plot shows the ages of 20 employees in a company:

\text{VO}_2 \text{Max} is a measure of how efficiently your body uses oxygen during exercise. The more physically fit you are, the higher your \text{VO}_2 \text{Max}. Here are some people's results, listed in ascending order, when their \text{VO}_2 \text{Max} was measured:

21,\, 21,\, 23,\, 25,\, 26,\, 27,\, 28,\, 29,\, 29,\, 29,\, 30,\, 30,\, 32,\, 38,\, 38,\, 42,\, 43,\, 44,\, 48,\, 50,\, 76

Susanah has been growing watermelons. The weight of the watermelons (in kilograms) are shown below:15,\, 6,\, 5,\, 2,\, 4,\, 4,\, 5

A timed quiz consists of 6 puzzles. The data below shows the times (in seconds) that it took Sophia to complete each question on her first and second attempts of the quiz:

• Times in first attempt: \, 11,\, 15,\, 17,\, 20,\, 23,\, 34

• Times in second attempt: \, 20,\, 20,\, 20,\, 19,\, 21,\, 20

The price of petrol at a petrol station was recorded each day for two weeks. The results are presented in the table below:

The mean petrol price across the 14 days of records is \$1.54 per litre. For which week is this mean a better indication of the price of petrol? Explain your answer.

Every week over 45 weeks, a kayaking club ran social sessions and the number of people who attended each session was recorded in the table:

Explain why the mean and the median are equally accurate indicators of the typical number of people who attended each session.

The histograms below represents the luggage weight of each passenger on board an airline's morning and afternoon flight:

The airline wants to get an indication of how much luggage each passenger is checking in. For which flight's data would the median be a more precise indicator of a typical passenger's luggage weight than the mean? Explain your answer.