This week: Data and averages Name and describe key data collection vocabulary, including data types Name and describe types of sample Explain characteristics of a good hypothesis Calculate the mean, median, mode and range Calculate averages from sets of data, frequency tables and bar charts

crayons ate dad (2 words) Anagrams adat arc poem pithy shoes a pyramid art (2 words) true oil crayons ate dad (2 words) I tint aqua vet scout union tequila vita secret ID maples cussen continuous data sample compare quantitative hypothesis census primary data outlier secondary data qualitative discrete

Answers adat arc poem pithy shoes data compare hypothesis a pyramid art true oil primary data outlier crayons ate dad secondary data I tint aqua vet scout union quantitative continuous tequila vita secret ID qualitative discrete maples cussen sample census

Discrete vs continuous Count it or measure it? Examples?

How many cows are there in that field? Discrete Continuous

How fast can your car go? Discrete Continuous

How much water is there in this bottle? Discrete Continuous

How many CDs do you own? Discrete Continuous

What is your shoe size? Discrete Continuous

How much does a whale weigh? Discrete Continuous

How much does a Mars Bar cost? Discrete Continuous

What is the temperature of this fire? Discrete Continuous

How long does the bus to Birchington take? Discrete Continuous

How many goals have you scored this year? Discrete Continuous

Discrete Qualitative Continuous What is the breed of that dog? Discrete Qualitative Continuous

Hypothesis A good hypothesis is a statement, NOT a question A good hypothesis can be tested Is this a good or a bad example of a hypothesis? If bad, how could you change it to make a good hypothesis? In tubes of Smarties there are always the same number of each colour.

Are these good or a bad hypotheses Are these good or a bad hypotheses? What needs to change to improve the bad hypotheses? Do you always get the same number of crisps in a packet? Goldfish can read books. Can you survive a bite from a shark? Exams are getting easier. January is warmer than February. Adele is more popular than Madonna. The music from the 1980s is the best. The most popular subject at school is maths.

Choosing a sample Usually, the population is too large to survey all of its members. A small, but carefully chosen sample can be used to represent the population. The sample must reflect the characteristics of the population from which it is drawn.

There are two questions to be asked about a sample: How big does the sample need to be? How is a sample taken so that it represents the population accurately? Sample size can vary but usually the larger the sample, the more reliable the results. A new canteen is going to open at the college. The canteen manager wants to find out what students would like on the menu. He decides to ask the students. What population should he use? Describe how to choose the sample. Give one advantage and one disadvantage of him using a census. An estate agent wants to get information about house prices in the city where she works. What is the population she will use? Why would she not use a census of the house prices? She decides to use a sample. She also decides to use the prices of all houses on her list of houses for sale. Give a reason why this might be a poor sample.

Discuss whether this will form a satisfactory sample for the poll. A market research company is going to do a national opinion poll. They want to find out what people think about the European Union. The company is going to do a telephone poll. First they will pick 10 towns at random. Then they will pick 10 telephone numbers from the telephone book for each town. They will ring these 100 telephone numbers. The people who answer will form the sample. Discuss whether this will form a satisfactory sample for the poll.

The mean is calculated by adding up all the values and dividing by how many there are.

HOMEWORK How can we find the mean, median, mode and range from the frequency table? Score 1 2 3 4 5 6 Tally What is wrong with just adding all the frequencies and dividing by six ?

How can we find the mean, median, mode and range from our bar chart? HOMEWORK How can we find the mean, median, mode and range from our bar chart? Can we find the mean and median without writing anything down?

This bar chart represents the scores that were obtained when a number of people entered a penalty-taking competition. Each person was allowed six penalty kicks. How many people entered the competition? How can you tell? How can you calculate the mean, median and modal number of penalties scored? What proportion of the people scored one penalty? What is that as a percentage? What proportion scored three penalties? Six penalties? Can you think of another type of statistical diagram that can be used to show proportions?

Heights of 10 students: 175cm; 154cm; 198cm; 145cm; 134cm; 156cm; 156cm; 167cm; 145cm; 156cm Calculate the mean, median, mode and range of this set of data.

ABC Motoring Here are the number of tests taken before successfully passing a driving test by 40 students of “ABC Motoring” Number of tests taken Number of People 1 9 2 11 3 7 4 6 5 2, 4, 1, 2, 1, 3, 7, 1, 1, 2, 2, 3, 5, 3, 2, 3, 4, 1, 1, 2, 5, 1, 2, 3, 2, 6, 1, 2, 7, 5, 1, 2, 3, 6, 4, 4, 4, 3, 2, 4 It is difficult to analyse the data in this form, so group the results into a frequency table.

Finding the Mean Number of tests taken Number of People 1 9 2 11 3 7 4 When finding the mean of a set of data, we add together all the pieces of data Number of tests taken Number of People 1 9 2 11 3 7 4 6 5 This tells us that there were nine 1’s in our list. So we would do: 1+1+1+1+1+1+1+1+1 = 9 (It is simpler to use 1x9!!) We can do this for every row.

Number of tests x Frequency Finding the Mean Number of tests taken Number of People 1 9 2 11 3 7 4 6 5 Number of tests x Frequency 1 x 9 = 9 2 x 11 = 22 3 x 7 = 21 4 x 6 = 24 5 x 3 = 15 6 x 2 = 12 7 x 2 = 14 We now need to add these together So we have now added all the values up. What do we do now? We divide by how many values there were. So we divide by the total number of people. 40 107 107 ÷ 40 = 2.7 (1dp) Students who learn to drive with ABC motoring, pass after 2.7 tests.

Bob’s Driving School Now let’s look at another Driving school from the same town. Here are the number of tests taken by 40 students at “Bob’s Driving School” 3, 2, 4, 1, 3, 2, 3, 1, 2, 1, 2, 4, 4, 4, 5, 2, 3, 4, 3, 4, 4, 5, 5, 2, 3, 2, 4, 5, 3, 3, 4, 3, 2, 2, 2, 2, 4, 3, 3, 3 Grouping the data will help us to analyse it more efficiently…

Number of tests x Frequency Bob’s Driving School Number of tests taken Number of People 1 3 2 11 12 4 10 5 Number of tests x Frequency 1 x 3 = 3 2 x 11 = 22 3 x 12 = 36 4 x 10 = 40 5 x 4 = 20 40 121 121 ÷ 40 = 3.0 (1dp) Which of the two driving schools would you choose? Write two sentences to say why. Students who learn to drive with Bob’s Driving School, pass after 3.0 tests.

Mean = 2.7 Range = 6 Mean = 3.0 Range = 4

Mean from a Frequency Table The number of goals scored by Premier League teams over a weekend was recorded in a table. Calculate the mean, median, mode and range. Frequency Goals 2 1 4 2 8 3 3 4 2 5 1

Averages from Frequency Tables The frequency table shows the weights of eggs bought in a shop weight 58g 59g 60g 61g 62g 63g frequency 3 7 11 9 8 2 Mode = most common weight = 60g Position of median = = 20.5 , so the median = 60g Mean = = 60.45g

Sam and his partner recorded the number of times they could hit a ping pong ball between them without it going off the table. Their results are in the table below. Consecutive hits (h) Frequency Midpoint Midpoint x Frequency 0 < h ≤ 20 3   20 < h ≤ 40 17 40 < h ≤ 60 25 60 < h ≤ 80 56 80 < h ≤ 100 8 100 < h ≤ 120 Total What is different about this table? What difference does this make to what you know or do not know about the data? What can you say about the mode, mean, median or range?

The amounts spent by 50 customers at a shop are shown in the table. HOMEWORK The amounts spent by 50 customers at a shop are shown in the table. (a) Work out the probability that a customer chosen at random spent more than £20. (b) Explain why it is not possible to work out the probability that a customer chosen at random spent exactly £8. (c) Use midpoints to calculate an estimate of the mean amount spent at the shop. (a) 19/50 or 0.38 or 38%, (b) the original data is not known, or we do not know if any of the 18 spent exactly £8, (c) £16.60 (not £16.6)

Company A Salary (£) Frequency 0 < £ ≤ 10 000 2   0 < £ ≤ 10 000 2 10 000 < £ ≤ 20 000 10 20 000 < £ ≤ 30 000 19 30 000 < £ ≤ 40 000 16 40 000 < £ ≤ 50 000 3

Company B Salary (£) Frequency 10 000 < £ ≤ 20 000 6   10 000 < £ ≤ 20 000 6 20 000 < £ ≤ 30 000 17 30 000 < £ ≤ 40 000 27 Which company will you choose to work for? Give reasons for your answer. You must show your working.

Comparing two sets of data Two classes, A and B, did the same test. For class A the mean score was 31 and the range was 28. Here are the scores for class B: Scores Frequency 0 < s < 10 2 10 < s < 20 4 20 < s < 30 9 30 < s < 40 12 40 < s < 50 3 Clues: modal class & class containing the median score – any use? estimate of mean? can you find the range?

A Mean Set A set of five numbers has: A mode of 12 A median of 11 A mean of 10 What could the numbers be?

Find the 5 numbers from the following list that have: a mode of 15 a median of 14 a mean of 12 a range of 10 21 5 11 14 11 15 11 15