Week 1: Organising & Representing Data

Question 1

List the four classifications of data

Answer 1

Quantitative -

Qualitative -

Discrete -

Continuous -

Question 2

When is a bar chart used? (i.e. what kind of data)

Answer 2

A bar chart is used to show frequencies of discrete or categorical data, for example colours of cars produced in a batch. Traditionally, there are gaps between the bars and the width of the bar does not show anything.

Question 3

On a simple histogram, the area of the bar illustrates the ….

Answer 3

frequency density

Question 4

Define Cumulative Frequency.

Answer 4

The word cumulative means “growing by successive additions” or a running total.

We can use cumulative frequency to plot graphs which will allow us to find measures of central tendency in another way.

Question 5

what are Stem and leaf diagrams used for?

Answer 5

A stem and leaf diagram is one way of grouping data into classes and showing the shape of the data.

Question 6

Define Measures of location.

Answer 6

Also known as measures of central location

Used to find the centre (or average) of a set of data

Question 7

Define median. what sort of data is it best for?

Answer 7

middle value when data is put in numerical order .

best for skewed data or data with “outliers”

Question 8

Define mode. what sort of data is it best for?

Answer 8

value which occurs the most.
It is the only measure used for a nominal or “named” scales
It can be calculated easily
Examples are:
What colour is your hair?
Where do you live?

Question 9

Define mean. what sort of data is it best for?

Answer 9

sum of all observations divided by the number of observations. best for when data distribution is continuous and symmetrical such as when your data is normally distributed. It is very accurate.

Question 10

what is ‘discrete data’

Answer 10

definite values

Question 11

what is Grouped data ?

Answer 11

Grouped data uses small ranges of values rather than definite values. We can show grouped data in a frequency distribution table.

Question 12

Each of the 25 students on a computer course recorded the number of minutes x, to the nearest minute, spent surfing the internet during a given day. The results are summarised below.
x = 1075
(a) Find mean number of minutes spent surfing the internet for these data.

Two other students surfed the internet on the same day for 35 and 51 minutes respectively. (b) Without further calculation, explain the effect on the mean of including these two students

Answer 12

43 mins

43-35 =8
8 below mean

51-43= 8
8 above mean
so no effect

Question 13

Define. Range

Answer 13

Difference between the lowest and highest values in a data set

Question 14

Define. Outlier

Answer 14

Unusually high or low values in a data set

Question 15

Define. Standard deviation

Answer 15

The amount by which every value within a data set varies from the mean

Question 16

Define. Mean

Answer 16

Sum of all observations divided by the total number of observations

Question 17

Define. Bar chart

Answer 17

Sum of all observations divided by the total number of observations

Mean

A chart with bars whose lengths are proportional to quantities

Question 18

Define. Histogram

Answer 18

a bar graph showing the frequency depending on class width (no gaps)

Question 19

Define. Class width

Answer 19

upper boundary - lower boundary

Question 20

Define. Median

Answer 20

Middle value when the data is put in order

Question 21

Define. Mode

Answer 21

Value that occurs most often

Question 22

Define. Inter-quartile range

Answer 22

The extent to which the central 50% of values within the data set are dispersed