Statistics A Basic statistical terms Notice the key vocabulary in these three short texts about statistics. A normal distribution of data means that most of the examples in a set of data are close to the average, while relatively few examples tend to one extreme or the other. Normally distributed data shown on a chart will typically show a bell curve. It will often be necessary to work out the extent to which individuals deviate1 from the norm2 and to calculate the figure that represents standard deviation . Six children are 7, 8, 8, 8, 11 and 12 years old. Their average age is 9 years old (the sum of their ages divided by six). The mode (the most frequent value) is 8. The median is 9.5 (the halfway point between the two extremes of the range). | Statisticians are often concerned with working out ! correlations4 - the extent to which, say, left-handedness correlates with intelligence. They must ensure that any data they collect is valid, i.e. that it is measuring what it claims to measure - all the subjects in the sample5 must be appropriately and accurately assessed as left- or right-handed, ■ for example. The figures must also be reliable, i.e. they would be consistent6 if the measurements were repeated. Usually, statisticians hope that their calculations will show/indicate a tendency, e.g. that left-handed people will be shown to be significantly7 more intelligent than right-handed people. ' differ 2 the average 3 average difference from the norm 4 connections, often as cause and effect 5 the subjects of the experiment or group representing the total population measured 6 the same 7 noticeably B A probability' problem Notice the vocabulary in this problem from a statistics textbook. Sue picks a card at random2 from an ordinary pack of 52 cards. If the card is a king, she stops. If not, she continues to pick cards at random, without replacing them, until either a king is picked or six cards have been picked. The random variable3, C, is the total number of cards picked. Construct a diagram to illustrate the possible outcomes4 of the experiment, and use it to calculate the probability distribution5 of C. ' likelihood of something happening 2 by chance 3 number or element of a situation that can change 4 results 5 assessment of probabilities for each possible value of C Other useful nouns for talking about statistics In a class of 8 women and 4 men, what proportion1 are male? Answer: one third In the same class what is the female to male ratio2? Answer: 2:1 The figures show a trend3 towards healthier eating habits. The study investigates the increase in the volume4 of traffic on the roads. 1 number compared with another number 2 relationship between two numbers showing how much bigger one is 3 change in a particular direction 4 amount, quantity We say 10 per cent (NOT the 10 per cent or 10 percentage) of students got an A for their exam but the percentage of students achieving an A has increased. 60 Academic Vocabulary in Use Exercises 26.1 Complete the sentences. 1 The six subjects who took the test scored 24, 22, 16, 16, 16, and 14 points out of 30. The .....................................was 16. The......................................score was 19 and the......................................score was 18. 2 The......................................of all donations to the charity in 2003 was $3,938. The smallest donation . was $10 and the largest was $130. Most were around the......................................point of $60. 3 Each questionnaire item asked respondents to choose one of a......................................of six options, with the two.....................................being Very dissatisfied indeed' and 'completely satisfied'. 26.2 Use the correct form of the words in the box to complete this text. distribute trend significant probable random correlation outcome vary Life insurance companies base their calculations on the laws of , that is they assess the likely , given the different such as age, sex, lifestyle and medical history of their clients.The premiums are therefore not chosen at but are carefully calculated.The ; of ages at which death occurs and causes of death are studied to see if they with other factors to be taken into account in setting the premiums; Naturally, the companies also monitor social .......... and react to any changes which might affect mortality rates. 26.3 Answer the questions. 1 There are 12 male students and 6 female students in the class. What is the ratio of males to females? And what proportion of the class is male? 2 If I am collecting data on course choices among second-year undergraduates and my sample is too small, what exactly do I need to do? 3 If my data show that students have a tendency to choose the type of clothing their friends choose, does it mean that they always, often or rarely choose similar clothes? 4 If I repeat the same experiment three times and the results are not consistent, is my method reliable? 5 If 20 out of 200 students fail an exam, what proportion, in percentage terms, failed? 6 If the average score in a test is 56, and Barbara scores 38, by how many points has she deviated from the norm? 7 If the volume of court cases increases, what changes: the type of case, the size of each case or the total number of cases? 8 What does standard deviation tell us? (a) What the standard of something is, (b) what the norm is, or (c) what the average difference from the norm is? 9 If a general survey of teenage eating habits asks questions about what teenagers eat for breakfast and lunch, is the survey likely to be valid? 10 Here is a graph showing how many students got scores within each 10-mark band in a biology test. Are the scores normally distributed? What is the shape of the graph called? What kinds of statistical data are likely to be discussed in your discipline? Find a relevant chart, graph or table and write about it using some terms from this unit. 30-39 40-49 50-S9 60-69 70-79 80-89 90-100 range of scores Academic Vocabulary in Use 61 h fi "A 1 Normal distribution (1) http://www.voutube.com/watch?v=ed-vkd46 m4&feature=relmfli Probably more than others Definitely more / than others / so s Same a 1 Me D Sei s others an * sue a Probably less than ol hers \ Definitely less \ than others 1 » 2 t D SD \^ 2% 14% 1 34% ' 34% ' 14% ' 2% SO = Standard Deviation Listen to the recording and answer questions. 1) What does the speaker want to show?........ 2) How is the mean denoted?.......................... 3) What is a random variable in the example? 4) How is the standard deviation denoted?..... 5) What does the number 62 denote?............. 6) What does the shaded area show?.............. 7) What does z represent?............................... 8) What does x denote?................................... 9) What do we need tables for?...................... 10) What does the function phi(z) denote,........ 11) Why should we round the phi(z) value?..... 12) How do you read the notation z = X-fi e 21 . The Greek Alphabet Letters Name Pron. Cap-ital Smáli A a alpha /'alfa/ B P beta /'bi:t»/ r Y gamma /'gams/ A 8 delta /'delta/ E G epsilon /'epsilon/ Z C zeta /'zi:ta/ H n eta /'i:ta/ © e theta /'©i:ta/ I iota /ai'auta/ K K kappa /'kaspa/ A A lambda /'laemda/ M mu /mju:/ Letters Name Pron. Capital Small N v nu /njui/ \ xi /ksai/ . 0 o omicron /'sumikran/ n Jt P' /pai/ p p rho /rou/ z sigma /'sigma/ T T tau /tau/ Y 0 upsilon /'jupsibn/ * 4» phi /fai/ X x chi /kai/ 4* psi /psai/ Si (0 omega /'aumiga/ Which Greek letters will you use to represent: a) angles in a triangle................................................ b) the first infinite ordinal...................................... c) the ratio of a circle's circumference to its diameter............................. d) the summation operator........................................... e) set membership......................................................... f) the golden ration 1.618... in mathematics, art and literature............. g) a general eigenvalue in linear algebra................................................... h) the population mea nor expected value in probability and statistics i) a risk management measure in mathematical finance........................ j) a finite difference or difference operator..............................................