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Level 2

Functional SkillsMathematics

Learning Resource 15Statistics

HD1/L2.1-4

STATISTICS LEVEL 2

©West Nottinghamshire College 2

Excellence in skills development

15

Contents Extracting Data HD1/L2.1 Page 3

Discrete Data HD1/L2.1 Page 4 - 6

Continuous Data HD1/L2.1 Page 7 - 8 Collect, Organise and Represent Data HD1/L2.2 Page 12

Discrete Data HD1/L2.2 Page 9 – 10

Continuous Data HD1/L2.2 Page 11 Mean, Median and Mode HD1/L2.3 Page 13 - 15 Range HD1/L2.4 Page 16 Mean, Median, Mode and Range HD1/L2.3 Page 17 HD1/L2.4

15 STATISTICS LEVEL 2

HD1/L2.1 Excellence in skills development Information Extracting Data Data can be either discrete or continuous. Discrete data is something that you can count and classify, it is quick and easy to collect, e.g. the number of people, parts, animals etc. Discrete data can be illustrated by pictograms, bar charts or pie charts.

Comparative bar charts are used to compare two or more different sets of data; the bars are drawn next to each other to make the comparison easy.

Component bar charts are similar to comparative bar charts but the bars are drawn on top of one another; the full height of the bar shows the total number of items.

Pie charts usually represent percentage values. Each slice shows a share of the total, e.g. 50% of people questioned said they had blue eyes; 35% brown; 15% green. To represent information in a pie chart you need to turn the percentages into the degree of angle needed for representing each piece of data. The angles must total 360°. Continuous data can have a value on a continuous scale. It can be compared with similar data; it changes over a period of time, e.g. a child’s height, the exchange rate of sterling, the heart rate of a patient. Continuous data can be illustrated by line graphs.

Line graphs use a line to connect measurements to show data changing over time. They can be used to show a comparison of two or more different sets of data, e.g. temperatures for different countries. It is sometimes best to draw a line graph as a curve when things change gradually over a period of time, rather than points connected with a ruler. Example Drawing a Pie Chart This example uses the data, given in the information above. Colour of eyes; 50% blue; 35% brown; 15% green. First work out the number of degrees for each sector, then use a protractor to draw the angles:

Green, 15%

Brown, 35%

54º

126º 180º

50% of 360° = 10050 × 360° = 180°

35% of 360° =

10035 × 360° = 126°

Blue, 50% 15% of 360° =

10015 × 360° = 54°



HD1/L2.1 Excellence in skills development Exercise 1 Discrete Data Holiday Destinations USA, 12%

Australia, 8%

Europe, 12%

India, 16%

China, 16%

UK, 36%

Seventy five people were questioned in this survey.

1) a) What percentage of the people who were surveyed holiday outside the UK?

b) How many people holiday in the UK?

c) How many people travel to destinations outside the UK and Europe? 2) This table shows how many people attended a French conversation class in 2008-9.

Term 1

Key:

4 learners Term 2

Term 3

a) How many people does this symbol represent?

b) How many learners in term 2?

c) How many more learners attended in term 1 than in term 3?

d) What type of chart/graph is this?



HD1/L2.1 Excellence in skills development Exercise 2 Discrete Data 1) This comparative bar chart compares the body mass index of a group of men and

women. Body Mass Index Survey

500

1000

1500

2000

2500

3000

Normal Overweight Obese

MenWomen

No.

of P

eopl

e

a) What does each line on the vertical axis represent?

b) Of the people surveyed, approximately how many women are obese?

c) Are more men or more women overweight according to the survey?

men / women

d) Approximately how many people in total are overweight and obese?

e) According to the survey, most women are:

normal / overweight / obese

f) Approximately how many more men are overweight than obese?

g) Approximately how many people took part in the survey all together?



HD1/L2.1 Excellence in skills development Exercise 3 Discrete Data 1) This component bar chart shows the total number of properties in 5 towns. House Price Comparison


0

100

200

300

400

500

600

700

800

Northley Tomleigh Princeton Nickleby Rokehampton

Num

ber o

f Hou

ses

>£100,000 <£100,000

a) What does each line represent on the vertical axis?

b) How many properties are there in total in Rokehampton?

c) What does this colour represent?

d) How many properties cost less than (<) £100,000 in Tomleigh?

e) What is the total number of properties costing more than £100,000?

f) Which town has the least number of properties costing more than £100,000?

g) Which 2 towns have the most properties costing more than £100,000?


HD1/L2.1 Excellence in skills development Exercise 4 Continuous Data Weight Loss Chart

82 80

Wei

ght (

kg)

78 76 Pat Jane 74

72

70 68 1-Jan 8-Jan 15-Jan 22-Jan 29-Jan 5-Feb

Date 1) a) Pat was heavier than Jane on 1st January, by how much?

b) How much weight did Pat lose between 8 Jan and 29 Jan?

c) How much weight did Pat lose in total?

d) Who lost the most weight between 1 Jan and 15 Jan?

e) What was Jane’s weight on 5th February?

f) What does each line represent on the vertical axis?

g) Complete the table:

Weights of: Dates

1-Jan 8-Jan 15-Jan 22-Jan 29-Jan 5-Feb

Pat

Jane



HD1/L2.1 Excellence in skills development Exercise 5 Continuous Data Temperature February 2009

Sun 8Sat 7 Fri 6Thu 5Wed 4Tue 3Mon 2 Sun 1-2

-4

-6

6

4

Deg

rees

Cel

sius 2

0 Date

MinMax 1) a) What was the maximum temperature on Sun 1 February?

b) What does the horizontal axis show?

c) What was the minimum temperature on Sun 8 February?

d) What does each line represent on the vertical axis?

e) On which date was the temperature range the greatest? ____/____/_______

f) What were the highest and lowest minimum temperatures of the eight days?

highest ____________ lowest ____________

g) What was the difference between the lowest maximum temperature and the highest minimum temperature?


STATISTICS LEVEL 2

HD1/L2.2


Excellence in skills development 15 Exercise 6 Discrete Data 1) This set of data relates to the number of birds counted in 40 gardens. The chart

shows the six most common of these birds.

Robin Blackbird Starling Dunnock Collared Dove Woodpigeon 80 90 40 50 55 60

Goldfinch Chaffinch Greenfinch Great Tit Coal Tit Blue Tit

35 60 30 50 65 85

Robin Coal Tit0

No

of B

irds

ChaffinchWoodpigeon

a) Add the scale to the vertical axis.

b) Add the missing bird labels on the bar chart to show the 6 most common birds.

c) Add the bar for Woodpigeon to the chart.

d) Add a title to the horizontal axis.

e) Add a title to the chart.

f) Which birds are not featured in this bar chart?

STATISTICS LEVEL 2

HD1/L2.2


Excellence in skills development 15 Exercise 7 Discrete Data A protractor is necessary for this exercise. 1) This data shows the 6 most common birds from a garden bird survey. To represent

this information in a pie chart you need to turn the percentages into the degree of angle needed for representing each bird.

Bird Robin Blackbird Woodpigeon Coal Tit Blue Tit Chaffinch

Number 80 90 60 65 85 60

% 18% 20% 14% 15% 19% 14%

Angle _____o _____o _____o _____o _____o _____o

a) Calculate the angles from the percentages given making sure there is a total of 360 o. Complete the table above.

b) Use a protractor to draw a pie chart to represent this data.

c) Write a short paragraph to explain what your pie chart illustrates.

STATISTICS LEVEL 2

HD1/L2.2


Excellence in skills development 15 Exercise 8 Continuous Data This line graph below has been compiled using the following data.

UK Average Temperatures 2007 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Temperature oC 4 2 7 8 12 22 24 25 22 18 13 8 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1) Use the information given to complete the graph.

a) Add the scale to the y axis. b) Add the titles to the x and y axis.

c) Add the following data to the line graph.

UK Average Temperatures 2008 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Temperature oC 5 7 6 9 15 16 22 26 24 15 11 10

d) Add a key and an appropriate title to the line graph. 2) Use your line graph to answer the following questions.

a) Which month, in each year, had the lowest average temperature?

2007 ____________ 2008 ____________

b) What is the difference between the temperature for June 2007 and June 2008?

STATISTICS LEVEL 2

HD1/L2.2


Excellence in skills development 15 Exercise 9 Collect, Organise and Represent Data A protractor is necessary for this exercise. 1) Sally has started to make a tally chart of the shoes in her wardrobe:

Type of Shoe Tally Total Percentage High heel l l l l l l 7

Flat l l l l

Sandal l l l

Trainer l l

a) Complete the tally chart.

b) Calculate the percentage of each type of shoe and create a pie chart. Show all

workings out. Be careful to make sure that you label the chart clearly. 2) Mylene is comparing class sizes in local schools; this is the data that she has

accumulated:

School Year 1 Year 2 Year 3 Year 4 St Mary’s 5 6 8 12

Benedict Street 15 20 22 22

St Joseph’s 20 25 25 27

Draw a chart to show this data to best effect. The chart should be labelled clearly. 3) The table shows the value of £1 - £10 in Euros in December 2007 and 2008.

£1 £2 £3 £4 £5 £6 £7 £8 £9 £10 Dec-07 1.40 2.80 4.20 5.60 7.00 8.40 9.80 11.20 12.60 14.00

Dec-08 1.17 2.34 3.51 4.68 5.85 7.02 8.19 9.36 10.53 11.70

Use this information to draw a line graph to show the difference in value for these 2 months. Make sure that you label the graph clearly.


HD1/L2.3 Excellence in skills development Information Mean, Median and Mode There are three types of averages; mean, median and mode. The mean average is the most widely used average.

To find the:

MEAN add up all the values together, then divide by the total number of values.

MEDIAN put the numbers in numerical order, the median is the value of

the middle number. If there are two middle numbers, add both together and divide by two.

MODE look for the number that occurs the most often. Sometimes

there can be more than one mode and sometimes there isn’t a mode at all.

Examples Find the mean of the following: 6 3 4 8 2 There are 5 numbers. (6 + 3 + 4 + 8 + 2) = 23 23 ÷ 5 = 4.6 Mean = 4.6 Find the median of the following: 6 3 4 8 2 Put in order: 2 3 4 6 8 The middle number is 4. Median = 4 Find the median of the following: 5 6 9 3 4 7 Put in order: 3 4 5 6 7 9 The middle numbers are 5 and 6. Add together and divide by 2. Median = 5.5 Find the mode of the following: 1 2 2 2 3 3 4 5 6 Mode = 2 There are more 2s than any other number. Find the mode of the following: 1 2 2 2 3 3 4 4 4 5 6 There are equal numbers of 2 and 4. Mode = 2 and 4



HD1/L2.3 Excellence in skills development Exercise 10 Mean, Median and Mode 1) The chart below shows the results from a survey conducted on six people regarding

their rates of pay. Rates of Pay


0 1 2 3 4 5 6 7 8 9

10

Evie Ryan Naseen Jess Millie Harry

Wag

e (£

) per

hou

r

a) Calculate the mean rate of pay.

b) List the people who get more than the mean rate of pay.

c) What was the median rate of pay? 2) Last Thursday evening there were 9 classes running in the college. Listed below are

the attendance figures.

Evening Class No of Learners Accounting NVQ 14 Customer Service 9 English Language 10 Food Safety in Catering 6 Health & Safety in the Workplace 12 Mathematics GCSE 9 Plumbing 13 Science 11 Sign Language 15

a) What was the mean number of learners who attended a

class last Thursday evening?

b) What was the modal number of learners?

STATISTICS LEVEL 2

HD1/L2.3


15Excellence in skills development

Exercise 11 Mean, Median and Mode A calculator can be used for this exercise. 1) The table below shows the scores of the bksb snooker team in the last eight games

played.

Player Scores of the last eight games played Bob 21 64 60 82 64 39 58 12 Di 35 92 147 85 35 106 147 89 Stelios 25 60 42 44 96 48 45 96 Liam 15 109 62 70 76 0 76 88 Claire 103 76 94 0 109 147 76 147 James 93 45 48 93 76 104 0 85 Linda 33 92 62 76 33 17 82 61 Russ 76 147 44 63 103 90 32 109 Samara 72 12 86 15 0 71 63 73

From the table calculate:

a) The mean average of each players score.

Mean Scores Bob Di Stelios Liam Claire James Linda Russ Samara

b) The median average of each players score.

Median Scores Bob Di Stelios Liam Claire James Linda Russ Samara

c) The modal average of each players score.

Mode Scores Bob Di Stelios Liam Claire James Linda Russ Samara

2) The bksb snooker team are playing a short match this weekend and only 4 players

need to go.

a) Which 4 players do you think should play?

b) Why did you choose these four players?

15 STATISTICS LEVEL 2 HD1/L2.4 Excellence in skills development Information Range The range tells you how much of a spread there is within sets of data. It is the difference between the highest and lowest values. To find the RANGE, take the lowest value from the highest value. Examples Find the range of the following: £4.97 £7.59 £8.07 £3.82 £9.34 Highest value = £9.34 Lowest value = £3.82

9.34 − 3.82 (Highest − Lowest) Range = £5.52

Total Amount of Silver Coins in Peoples' Pockets 350 Find the range from this bar chart:

300 Highest value = 325 pence

Am

ount

in P

ence

250

Lowest value = 75 pence

200 325 − 75 (Highest − Lowest)

150 Range = 250 100 50

0 Claire Names

Bob James RussLiam Exercise 12 1) This graph shows the temperatures over the course of a week. What was the

temperature range over the seven days?


-6

-5

-4

-3

-2

-1

0 1 2

Sun Mon Tues Wed Thurs Fri Sat Days

Tem

pera

ture

°C


HD1/L2.3 HD1/L2.4 Excellence in skills development Exercise 13 Mean, Median, Mode and Range

Temperature chart for a fortnight in January

1) From the temperature chart above, work out the:

a) modal temperature __________

b) range of temperatures __________ 2) Decide which type of average, you think would be the most appropriate to use in

each situation. (You are not required to do any actual calculations.)

a) Phil is trying to decide if he is being reasonably paid. He asks a few friends who are doing similar jobs how much they get.

Mean/Median/Mode

b) A few learners are having problems with a particular question. They decide to compare answers.

Mean/Median/Mode

c) Ten learners are asked how long they spend doing homework. A typical value is needed.

Mean/Median/Mode


Functional Skills Mathematics - Yolamynvqresources.yolasite.com/resources/LR 15 Mathematics L2...

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