Friday 24 November 2017

Statistics

In statistics you may encounter theoretical type questions where it is expected that you can recognise different types of data, these are categorical which can be nominal or ordinal and numerical which can be discrete or continuous. It is also necessary to be able to judge the reliability of the data and whether there may be bias, or what situations may cause a bias.

Questions may be asked on data handling; this involves representing data graphically and/or describing the data numerically using measures of central tendency (mean, median and mode) and the range as a measure of variability.

Sample question 1

There are 22 players on the Irish rugby squad for a game. Their heights (in centimetres) are given below.

180, 188, 185, 180, 183, 177, 180, 183, 198, 191, 191

185, 185, 180, 185, 196, 180, 188, 180, 183, 191, 193

(a) What is the height of the tallest player?

198 cm

(b) How many of the players are over 184 cm in height?

12

(c) What percentage of the players are below 181 cm in height? Give your answer correct to the nearest whole number.

7 x 100 = 31.8181 ... = 32%

22 x 1

The arm spans (in centimetres) of the same players in the same order are given below.

180, 184, 188, 178, 182, 176, 180, 185, 201, 190, 189

185, 186, 182, 182, 196, 181, 189, 178, 184, 190, 193

(d)Find the median arm span.

176, 178, 178, 180, 180, 181, 182, 182, 182, 184, 184, 185, 185, 186, 188, 189, 189, 190, 190, 193, 196, 201

184 + 185 = 184.5cm

2

(e)Complete the table below to show the height and arm span of the tallest and shortest player in the squad.

(f)Write the ratio of height to arm span for (i) the tallest

player and (ii) the shortest player in part (e).

Tallest: 198: 201 Shortest: 177: 176

(g)Write each ratio in (f) above as a decimal. Give your

answer correct to two decimal places.

Tallest: 0.99 Shortest: 1.01

(h)The coach is 170 cm tall. What would you expect his arm span to be? Give a reason for your answer.

Answer: 170 cm

Reason: The ratio is almost 1:1

Sample question 2

Tom's third year Physical Education class did a fitness test. The number of sit-ups that each student did in one minute is recorded below:

59 48 27 53 36 29 52 46 45 37 49 51

33 45 38 52 40 51 37 44 47 45 60 41

(a) Represent the data above on a stem-and-leaf diagram.

(b) How many students are in the class?

24

(c) What is the range of sit-ups for the class?

60 - 27 = 33

(d) What is the mode of the data?

45

(e) Find the mean of the data correct to one decimal place.

(f) Tom did 48 sit-ups in the test. How does this compare to the rest of the class?

Tom was above average when compared with the rest of the class, 15 students did less sit-ups and 8 did more.

Irish Independent

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