Making Sense of Data

Transcription

1 Tips for Revising Making Sense of Data Make sure you know what you will be tested on. The main topics are listed below. The examples show you what to do. Plan a revision timetable. Always revise actively by working through questions. Look at the examples when you need to. Tick each topic when you have revised it this will help you feel more positive! Try lots of past papers you can download them from the AQA website at When you get the Data Sheet, think about what questions might be asked. Practise them. Tips for the exam Don t panic! Easier said than done! but try to stay calm. It will help you think more clearly. Read each question carefully. Underline important information if it helps. If you have time left at the end, check your answers. If you decide to change an answer, cross out the old answer. The methods that you need are listed below. You will have a calculator in the exam, so most of the examples show how to use a calculator to solve the problems, rather than other methods. Fractions To write something as a fraction: think of it as ' out of ' top of fraction bottom simplify the fraction by dividing top & bottom by the same numbers (or using your calculator) To write amounts as a fraction, they must be in the same units eg. both in pence or both in s 1 out of 4 people replied to a survey. What fraction is this? Josh spends 5 on stationery including 75p on a pen. What fraction of the 5 is75p? Instead of 4 you could then again 1 a b c 4 75 a b c 5 5 To find a fraction of something: divide it by the bottom number (denominator) then multiply by the top number (numerator). A company invests 5 of its profits of 36. How much does it invest? On a calculator: The Nuffield Foundation - 1 -

2 Decimals s To change a decimal to a fraction: use the place value of the last digit hundredths a b c 1 To change a fraction to a decimal: divide the top by the bottom To put decimals in order of size: it is useful to add s so they have the same number of decimal places. Ratios To divide in a ratio: divide the quantity by the total number of parts. multiply (if necessary) to find the answer. Rounding If the next figure is 5 or more, round up If the next figure is less than 5, round down Put these decimals in order of size, starting with the smallest: 1.,.56, 1.8, 1.15,.9 Writing them all with dp: 1.,.56, 1.8, 1.15,.9 The correct order is:.56,.9, 1.8, 1.15, 1. s When 96 adults completed a questionnaire, the ratio of replies from men and women was in the ratio 1 : 3. How many replies were from women? Total number of parts One part Number of replies from women s On one day, a shop's takings were Express these takings: (a) to the nearest 1 (b) to the nearest 1 (c) to the nearest 1 (d) to the nearest 1 pence (a) to nearest 1 (b) to nearest 1 (c) to nearest 1 (d) to nearest 1 pence Approximations To find an approximate value of a calculation: round all numbers to 1 significant figure, then do the calculation. s Jackie paid 1.95 for 36 postcards. Using approximations, estimate the average (mean) cost per postcard. Average (mean) cost Round 195p to p and 36 to 4 5 pence each 4 The Nuffield Foundation - -

3 Percentages To write a % as a fraction or decimal, divide by 1 s 64% % a b c 1 To write a decimal or fraction as a % multiply by % (i.e. 5 of 1) 5 1 4% or a b c 5 1 4% To write one quantity as a percentage of another: Snow fell on 4 of the 31 days in March. Express this as a percentage. write as a fraction then multiply by 1 to change to a percentage. N.B. They must be in the same units % (nearest %) or 4 a b c % To write an increase/decrease as a % increase % increase original amount 1 decrease % decrease original amount 1 The number of employees at a factory increased from 175 to 185. What was the % increase? Increase % increase % (1dp) The average donation to a charity fell from 11.5 to 9. per person. What was the % reduction? Reduction (i.e..3) % reduction % To work out a % of something: Find 35% of divide by 1 to find 1% then multiply by the % you need The cost of a new car is 7499, but its value falls by 5% in a year. What is the reduction in value? (nearest ) To find the final amount: add an increase or subtract a decrease (reduction) Read the question carefully - it may want just the increase (or decrease) or the final amount. A population of 48 birds is expected to rise by 7 1 %. What is the expected population after the rise? Increase 7.5% of Expected population The Nuffield Foundation - 3 -

4 Averages & Range Mode the most common item. Median the middle value in an ordered list. s The ages of a group of friends are given below: Putting the ages in order: If there are middle values, add them and divide by. Mode 18 years Median years sum of the items Mean number of items Range highest value lowest value Mean years Range years Spreadsheet formulas To multiply use * To divide use / Sum means total Average gives the mean. You can also find the median and mode. Tally Charts Tally charts are used to collect and organise data. To draw a tally chart: List the categories in the first column of a table. Draw a tally l for each item. (Cross off each item as you put it in the table to help you keep track.) Draw every 5 th tally through the previous four this will help you to count them later. Count the number for each category (i.e. the frequency). Find the total to make sure you have all the items. s To add A3 and B3 A3+B3 To subtract A3 from B3 B3 A3 To multiply A3 and B3 A3*B3 To divide A3 by B3 A3/B3 To add a column from A1 to A1 SUM(A1:A1) To find the mean of a column of values from A1 to A1 AVERAGE(A1:A1) To find the median of a column of values from A1 to A1 MEDIAN(A1:A1) To find the mode of a column of values from A1 to A1 MODE(A1:A1) The colours of the cars sold in a week by a dealer were: Black Red Silver Red Silver Blue Black Red Silver White Red Blue Silver Red Blue Red Black Blue White Silver Draw a tally chart. The finished tally chart looks like this: Colour of Car Tally Frequency Black l l l 3 Blue l l l l 4 Silver l l l l 5 Red l l l l l 6 White l l Total The Nuffield Foundation - 4 -

5 Pictograms To draw a pictogram: Choose a symbol to use (use one that's easy to draw) The number of houses planned for an estate are: Type of House Number Terraced 8 Semi-detached 5 Detached 3 Bungalow Decide how many items the symbol should represent (1,, 5, 1,, 5, 1 etc). Include a key to show this. Draw symbols to show the number in each category (making sure they are lined up neatly. Remember to give the pictogram a title to say what it is about. Pie Charts To draw a pie chart: Find the total number of items. Divide 36 by the total this gives the angle for each item. Multiply by the number in each category to find the angles. Check the angles add to 36. (If rounding makes the sum 359 or 361, adjust the angle of the biggest sector to make the total 36.) Draw the pie chart. Remember to include the title and labels (or a key). The pictogram below shows this information. Terraced Semi-detached Detached Bungalow Houses planned for an estate Survey about the way factory employees travel to work: Total 144 So angle for each person Walk Transport to Work Cycle Key: Transport Number of Angle to work workers Car Bus Train Walk Cycle Total 144 (check) 36 Car houses Note If the data is given in %, the angle for each % is So multiply the % for each category by 3.6 to find the angles. Train Bus The Nuffield Foundation - 5 -

6 Bar Charts To draw a bar chart: Horizontal axis Decide how to fit a bar for each category into the available space. Reasons given by college students for absences: Reason Male Female Illness Appointment Holiday Interview 75 6 Vertical axis Decide on a scale to reach the highest number. Use an easy scale like 1,, 5, 1,, 5, 1,,... Draw the bars the right height and label them. If there is more than one set of data, include a key. Number of absences Reasons given for absences by college students Male Female Include a title to say what the chart shows. Graphs Data pairs are often plotted on a graph to see whether or not there is any relationship. To draw a scatter graph: Decide on a scale for each axis that will cover the lowest and highest values. Choose easy scales like 1,, 5, 1,, 5, 1,, 5, 1, Plot points to show the data pairs. Include a title to say what the chart shows. NB Do not join the points unless they lie on a straight line. The graph shows that the more time the student spends on a computer, the less time he tends to spend watching TV. Each division Illness Appointment Holiday Interview Reason Student's activities on weekday evenings: Time watching TV (mins) Day Time on computer (minutes) Time watching TV (minutes) Mon 5 35 Tues Wed 95 3 Thurs Fri Each division 5 5 Student's weekday evening activities Each division Time on computer (mins) The Nuffield Foundation - 6 -

7 Line Graphs These are often used to show how something changes with time. To draw a line graph: If one of the variables is time, put it on the horizontal axis. Year % households with mobile phones Decide on a scale for the vertical axis that will reach the highest value. Choose an easy scale like 1,, 5, 1,, 5, 1,, 5, 1, 8 Households with mobile phones Plot and join the points with straight lines. Include a title to say what the chart shows. You may be asked to interpret the graph. This graph shows the % of households with mobile phones has risen between and 5 The steepest increase was between 1 and. Proportionality A set of data is directly proportional to another when: steps of fixed size in one dataset give steps of fixed size in the other the graph is a straight line through the origin, O The gradient gives the constant of proportionality, k. The equation relating x and y is y kx Misleading Graphs & Charts The size of the icons sometimes makes pictograms misleading. Bar charts and graphs can be misleading when the vertical axis does not start at zero. Percentage 6 4 Each division Year y steps of x 4 6 y y kx 4 6 x steps of 5 1 Gradient k.5 4 Equation is y.5x Average number of cups of coffee sold per week: In this pictogram, the second cup is twice as tall, but looks 5 cups 5 cups much too large because its area is four times as big. The Nuffield Foundation - 7 -