U2 + U3 - Processing and representing data

Question 1

What can continuous data be represented by?

Answer 1

• Histograms
• Cumulative frequency curves
• Line graphs

Question 2

What can discrete data be represented by?

Answer 2

• Bar charts

- CF step polygons

Question 3

What can categorical data be represented by?

Answer 3

• Frequency tables (normal freq tables, relative freq tables, cf tables)
• Pie charts
• Bar charts

Question 4

What can ordinal data be represented by?

Answer 4

• Bar charts
• Pie charts
• Tables

Question 5

What do you need to ensure when drawing a pictogram? (4)

Answer 5

• Each picture is the same size
• The picture can be divided easily to show different frequencies
• The spacing between the pictures is the same in each row
• You write a key to show what each symbol represents

Question 6

2 properties of a bar chart

Answer 6

• Bars are equal width with equal spaces between them

- The height of the bar represents the frequency

Question 7

Differences (2) between histograms and bar charts

Answer 7

• The bars of a bar chart don’t touch, but in a histogram, the bars touch because the data is continuous
• You can draw on a frequency polygon using the midpoint of each class on a histogram

Question 8

Why are composite bar charts good?

Answer 8

The total frequencies and the frequencies of each component can be easily compared

Question 9

Compare a stem-and-leaf diagram with a bar chart

Answer 9

A stem and leaf diagram shows the shape of the data distribution in the same way as a bar chart, but you can still see the original data values

Question 10

How to compare
i) total frequencies
ii) proportions
in comparative pie charts

Answer 10

i) Compare the areas

ii) Compare the individual angles

Question 11

Why would you use comparative pie charts over normal pie charts?

Answer 11

When two sets of data have different total frequencies, drawing two pie charts the same size to represent them would be misleading.

Question 12

In a cumulative frequency graph, when would you use curved lines and when would you use straight step polygons?

Answer 12

Curved lines - continuous data

Straight lines - discrete data

Question 13

What is a choropleth map?

Answer 13

A map that is used to classify regions of a geographical area. Regions are shaded with an increasing depth of colour. A key shows what each shade represents.

Question 14

What is positive skew? What is negative skew?

Answer 14

POS - Most of the data values are at the lower end

NEG - Most of the data values are at the upper end

Question 15

Misleading things about graphs (7)

• scales that do not start at zero
• scales that do not increase uniformly
• thick lines on a graph
• axes without labels
• graphs and charts without keys
• colours on a graph
• 3D diagrams

Answer 15

• Scales that do not start at zero give a misleading impression of the heights of bars
• Scales that do not increase uniformly distort the shape of anything plotted on them
• Lines on a graph that are drawn too thick make it difficult to read information
• Axes without labels prevent you from knowing what the data represents
• Graphs and charts without keys may be impossible to interpret
• Colours may make some parts of a graph or chart stand out more than others
• 3D diagrams make comparisons difficult as data proportions appear distorted

Question 16

Advantages of bar charts and line graphs (2)

Answer 16

• They show trends and patterns in data

- You can read values from the scale as long as it is not too small

Question 17

Advantage and disadvantage of pie charts

Answer 17

ADV:
- They show proportions

DISADV:
- They don’t show accurate data values

Question 18

Advantage and disadvantage of tables

Answer 18

ADV:
- They give exact data values for different categories

DISADV:
- They don’t show trends and patterns as clearly

Question 19

In pie charts, what does
i) the area of each sector
ii) the area of the whole pie chart
represent?

Answer 19

i) the area of each sector is proportional to the total frequency it represents
ii) the area of the whole pie chart is proportional to the total frequency

Question 20

Median in discrete data

Median in continuous data

Answer 20

Discrete: (n+1)/2
Continuous: 1/2

Question 21

What is standard deviation?

Answer 21

A measure of how much all the values deviate from the mean value (how spread out they are)

Question 22

Using calculation, what indicates

i) positive skew
ii) negative skew

Answer 22

i) mean > median > mode

ii) mode > median > mean

Question 23

Advantages of mode (4)

Disadvantages of mode (2)

Answer 23

ADV:

• Easy to find
• Can be used with any type of data
• Unaffected by open-ended or extreme values
• Mode is always a data value

DISADV:

• May be no mode or sometimes more than one
• Cannot be used to calculate a measure of spread

Question 24

Advantages of median (4)

Disadvantage of median (1)

Answer 24

ADV:

• Easy to calculate
• Unaffected by extreme values
• Best to use when data is skewed
• Can be used to help calculate quartiles, interquartile range and skew

DISADV:
- May not be a data value

Question 25

Advantages of mean (2)

Disadvantages of mean (2)

Answer 25

ADV:

• Uses all the data
• Can be used to calculate standard deviation and skew

DISADV:

• Always affected by extreme values
• Can be distorted by open-ended classes

Question 26

What can you compare mode with?

Answer 26

Range for quantitative data

Question 27

What can you compare median with?

Answer 27

Range, interquartile range

Question 28

What can you compare mean with?

Answer 28

Range, standard deviation

Question 29

In a distribution:

Answer 29

• 50% of the data is less than the median, and 50% is greater
• 25% of the data is less than the lower quartile
• 25% of the data is greater than the upper quartile
• 50% of the data is between the lower and upper quartiles