Functional Skills Mathematics

Transcription

1 Functional Skills Mathematics Level 2 Learning Resource Statistics HD1/L2.1-4

2 Excellence in skills development 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 - Range HD1/L2.4 Page 16 Mean, Median, Mode and Range HD1/L2.3 Page 17 HD1/L2.4 West Nottinghamshire College 2

3 HD1/L2.1 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; % 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; % green. First work out the number of degrees for each sector, then use a protractor to draw the angles: Green, % 50 50% of 360 = 360 = º 35 35% of 360 = 360 = º Blue, 50% 126º % of 360 = 360 = Brown, 35% West Nottinghamshire College 3

4 HD1/L2.1 Exercise 1 Holiday Destinations USA, 12% Discrete Data UK, 36% Australia, 8% Seventy five people were questioned in this survey. India, 16% China, 16% Europe, 12% 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 Term 1 Term 2 Key: 4 learners 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? West Nottinghamshire College 4

5 HD1/L2.1 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 2500 No. of People Men Women 500 Normal Overweight Obese 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? West Nottinghamshire College 5

6 HD1/L2.1 Exercise 3 Discrete Data 1) This component bar chart shows the total number of properties in 5 towns. House Price Comparison Number of Houses > 100,000 < 100, Northley Tomleigh Princeton Nickleby Rokehampton 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? West Nottinghamshire College 6

7 HD1/L2.1 Exercise 4 82 Weight Loss Chart Continuous Data 80 Weight (kg) Pat Jane Jan 8-Jan -Jan 22-Jan 29-Jan 5-Feb Date 1) a) Pat was heavier than Jane on 1 st 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 Jan? e) What was Jane s weight on 5 th February? f) What does each line represent on the vertical axis? g) Complete the table: Weights of: Dates 1-Jan 8-Jan -Jan 22-Jan 29-Jan 5-Feb Pat Jane West Nottinghamshire College 7

8 HD1/L2.1 Exercise 5 Continuous Data Temperature February Degrees Celsius Sun 1 Mon 2 Tue 3 Wed 4 Thu 5 Fri 6 Sat 7 Sun Date Max Min 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? West Nottinghamshire College 8

9 Excellence in skills development HD1/L2.2 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 Goldfinch Chaffinch Greenfinch Great Tit Coal Tit Blue Tit No of Birds 0 Robin Woodpigeon Coal Tit Chaffinch 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? West Nottinghamshire College 9

10 Excellence in skills development HD1/L2.2 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 % 18% 20% 14% % 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. West Nottinghamshire College 10

11 Excellence in skills development HD1/L2.2 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 o C 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 o C 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? b) What is the difference between the temperature for June 2007 and June 2008? West Nottinghamshire College 11

12 Excellence in skills development HD1/L2.2 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 llll ll 7 Flat llll Sandal lll Trainer ll 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 Benedict Street St Joseph s 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 Dec Dec 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. West Nottinghamshire College 12

13 HD1/L2.3 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 MEDIAN MODE add up all the values together, then divide by the total number of values. 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. 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: There are 5 numbers. ( ) = = 4.6 Mean = 4.6 Find the median of the following: Put in order: The middle number is 4. Median = 4 Find the median of the following: Put in order: The middle numbers are 5 and 6. Add together and divide by 2. Median = 5.5 Find the mode of the following: Mode = 2 There are more 2s than any other number. Find the mode of the following: There are equal numbers of 2 and 4. Mode = 2 and 4 West Nottinghamshire College 13

14 HD1/L2.3 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 Wage ( ) per hour Evie Ryan Naseen Jess Millie Harry 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 a) What was the mean number of learners who attended a class last Thursday evening? b) What was the modal number of learners? West Nottinghamshire College 14

15 HD1/L2.3 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 Di Stelios Liam Claire James Linda Russ Samara 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? West Nottinghamshire College

16 HD1/L2.4 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: Highest value = 9.34 Lowest value = (Highest Lowest) Range = 5.52 Find the range from this bar chart: Highest value = 325 pence Lowest value = 75 pence (Highest Lowest) Range = 250 Amount in Pence Total Amount of Silver Coins in Peoples' Pockets 50 0 Liam Russ Claire Names Bob James Exercise 12 1) This graph shows the temperatures over the course of a week. What was the temperature range over the seven days? 2 1 Temperature C Sun Mon Tues Wed Thurs Fri Sat Days West Nottinghamshire College 16

17 HD1/L2.3 HD1/L2.4 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 West Nottinghamshire College 17