Chapter 15 - Data processing, presentation and interpretation

Question 1

Variable, random variable

Answer 1

• denoted by capital letters e.g. X
• if its value varies, it is a variable
• if its value varies at random, it is a random variable e.g. value in a dice throw

Question 2

Frequency

Answer 2

• number of times a particular value occurs in a data set

Question 3

Categorical (qualitative) data

Answer 3

• come in classes e.g. types of bird
• can be described without using numbers
• displayed using pictograms, barcharts, dot plots and pie charts

Question 4

Numerical (quantitative) data

Answer 4

• defined in some way by numbers e.g. time taken to run a race

Question 5

Ranked data

Answer 5

• given by their position within a group e.g. placing 1st, 2nd or 3rd in a race
• displayed using box-and-whisker plot, cumulative frequency curve
• can deduce median (often called an average/measure of central tendency), quartiles, semi-quartile range (half the IQR, measures how far above/below a large/small value lies),

Question 6

Discrete variables

Answer 6

• can take certain values but not those in between e.g. shoe size
• displayed using a tally, vertical line chart, stem-and-leaf diagram, grouped frequency table
• can deduce mode, mean, midrange, median, standard deviation, range, IQR

Question 7

Continuous variables

Answer 7

• if measured accurately, can take any appropriate value; cannot list all the possible values
• displayed using frequency charts, histograms, cumulative frequency charts

Question 8

Distribution, unimodal and bimodal distributions, positive and negative skew

Answer 8

• pattern in which the values of a variable occur is called its distribution
• displayed in a diagram with the variable on the horizontal and frequency/probability on the vertical
• one peak = unimodal; two peaks = bimodal
• peak to the left = positive skew; peak to the right = negative skew

Question 9

Grouped data

Answer 9

• easy to allocate data to groups when variable can take many values e.g. age groups

Question 10

Bivariate and multivariate data

Answer 10

• two variables are assigned to each item in bivariate data e.g. age and mileage of second hand cars
• displayed using scatter diagrams, where linear association (relationship) going upwards = +ve correlation i.e. +ve gradient regression line (line of best fit) and r; linear association going downwards = -ve correlation i.e. -ve gradient regression line and r
  –> dependent variable (y-axis) affected by independent variable (x-axis)
  –> random variable (can take any value in a set) affected by controlled variable (only takes a set of predetermined values)
• more than two variables are involved in multivariate data; stored on spreadsheets

Question 11

Standard deviation

Answer 11

Mean absolute deviation takes the mean of how far each value is from the mean, by using the magnitudes (ignoring -ve sign)
Standard deviation takes the mean (divide by n-1) of the squares of how far each value if from the mean, so must be square rooted in the end
Variance is the standard deviation without square rooting
Outliers are more than two standard deviations from the mean, or most extreme 5% of data values with a normal distribution