data analysis: graphs presentation and display of quantitative data

Question 1

what are the different ways in which we can represent/ summarise data

Answer 1

there are various ways in which we can represent data:

• summarising data in a table
• bar charts
• line graphs
• histograms
• scatter graphs

Question 2

how are data represented on a table

Answer 2

when tables appear in the results section of a report, they are not merely raw scores but converted to descriptive statistics

It is also standard practice to include a summary paragraph beneath the table explaining the results

Question 3

what are bar charts

Answer 3

bar charts are a type of graph which the frequency of each variable is represented by the height of the bars

Question 4

how is data presented in bar charts

Answer 4

data can be represented visually using a suitable graphical display so the difference in mean values can be seen

the frequency or amount of each category is plotted on the vertical y - axis - essentially the height of the bars

the bars are separated on a bar to denote that we are dealing with separate conditions

Question 5

when do we represent data using bar charts

Answer 5

bar charts are used when data is divided into categories otherwise known as discrete data

Question 6

what are scattergraphs

Answer 6

scattergraphs are a type of graph that represents the strength and direction of a relationship between co - variables in a correlational analysis

Question 7

what is the difference between scattergraphs and other graphs

Answer 7

unlike the other forms of graphs discussed, scattergraphs do not depict differences but associations between co - variables

either of the co - variables can occupy the x and y axis ( it does not matter) and each point on the graph corresponds to the x and y position of the co - variables

Question 8

what is the difference between histograms and bar charts

Answer 8

in histograms, the bar charts touch each other

this shows that the data is continuous rater than discrete like in bar charts

Question 9

how do we represent data on histograms

Answer 9

the x axis is made up of equal sized interval of a single category e.g.
percentage scores in a maths test is broken down into intervals: 0-9, 10-19, 20-29

Thee y-axis represents the frequency (number of people who scored a certain mark) within each interval

If there was a zero frequency for one of the intervals, the interval remains but without the bar

Question 10

what are line graphs

Answer 10

line graps represents continuous data and use points connected by lines to show how something changes in value e.g. over time

Question 11

how are the IV and DV plotted on line graphs

Answer 11

Typically, the IV is plotted on the x - axis and the DV on the y - axis

Question 12

what does the area underneath the graph represent

Answer 12

the are underneath the graph represents the total population of a sample

68.26% of the population will fall between one standard deviation

two deviations above and below the mean = 95.44% of the population

three standard deviations above and below the mean =99.73% of the population

Question 13

what is a normal distribution

Answer 13

If you measure certain variables, such as the height of all the people in your school/ college, the frequency of these measurements should form a bell - shaped curve

“A symmetrical spread of frequency data that forms bell - shaped pattern. The mean, median and mode are all located at the highest peak”

Question 14

why do the “tails” of the curve never touch the x - axis

Answer 14

as the tails never touch the horizontal x - axis, it will never reach zero.

This is because more extreme scores are always theoretically possible

Question 15

what is a skewed distribution

Answer 15

a skewed distribution does not have a balanced symmetrical pattern

The data is lean to one side or the other e.g.

• positively skewed
• negatively skewed

Question 16

what is a negatively skewed distribution

Answer 16

a negative skew is where most of the distribution is concentrated towards the right

an example of a negatively skewed data is:

a very easy test would produce a destruction where the bulk of the scores are concentrated on the right resulting in the long - tail of anomalous scores on the left

Question 17

where are the central tendencies situated on a negatively skewed distribution

Answer 17

the mean is pulled to the left ( due to the lower scores who are in the minority)

the mode is at the the highest peal

the medium is in the middle of these two

Question 18

what is a positively charged distribution

Answer 18

a positive skew is where most of the distribution is concentrated towards the left of the graph

this results in a long tail on thee right

an example of a positively charged distribution is:

imagine a very difficult test which most people got lower marks with only a handful of students at the higher end
This produces a positive skew

Question 19

where are the central tendencies situated on a positively skewed distribution

Answer 19

the mode: remains at the higher point

median: comes next
mean: dragged across to the right

this is because candidates that got a high score had the effect of pulling the mean to the right as calculating the mean includes all scores ( this is why the mode and medium remains fairly stable