presentation of quantitative data

Question 1

what are the different ways you can present quantitative data?

Answer 1

• scattergram
• bar chart
• histogram

Question 2

explain how one can summarise data in a table

Answer 2

• it is important to note that when tables appear in the results section of a report they are not merely raw score but they have been converted to descriptive statistics
• it is standard practice to include a summary paragraph beneath a table explaining the numbers and drawing conclusions

Question 3

how can quantitative data be summarised in bar charts?

Answer 3

• data can be represented visually using a suitable graphical display so the difference in mean values can easily be seen
• the most suitable graph is a bar chart
• bar charts are used when data is divided into categories, otherwise known as discrete data
• bars are separated on a bar chart to denote that we are dealing with separate conditions
• the frequency or amount of each category is plotted on the vertical y-axis

Question 4

how are histograms used?

Answer 4

• in a histogram the bars touch each other, which shows that the x-axis is continuous rather than discrete
• the x-axis is made up of equal-sized intervals of a single category, for instance, percentage scores in a maths test broken down in intervals such as 0-9, 10-19, 20-29….
• the y-axis represents the frequency within each interval
• if there was a zero frequency for one of the intervals, the interval remains but without a bar

Question 5

explain the use of scattergrams

Answer 5

• scattergrams do not depict differences but associations between co-variables
• either of the co-variables occupy the x-axis and the other the y-axis (it doesn’t matter which) and each point on the graph corresponds to the x and y positions of the co-variables.

Question 6

what are the different types of distributions?

Answer 6

• normal distribution
• skewed distributions

Question 7

explain what skewed distributions are

Answer 7

• a spread of frequency data that is not symmetrical, where the data clusters to one end

Question 8

explain normal distribution

Answer 8

• a symmetrical spread of frequency data that forms a bell-shaped pattern
• the mean, the median and mode are all located at the highest peak
• most people are located in the middle area of the curve with very few at the extreme ends
• the mean, median and mode all occupy the same midpoint of the curve.
• the ‘tail’ of the curve, which extends outwards never touch the horizontal x-axis (and therefore never reach 0) as more extreme scores are always theoretically possible

Question 9

what is a positive skew

Answer 9

• a type of frequency distribution in which the long tail is on the positive (right) side of the peak and most of the distribution is concentrated on the left
• it results in a long tail on the right
• various measures of central tendency are affected by this situation- the mode remains at the highest point of the peak (which we would expect) , the median comes next, but the mean is dragged across towards the tail

Question 10

what is the opposite of a positive skew?
Explain this

Answer 10

• negative skew
• A type of frequency distribution in which the long tail is on the negative (left) side of the peak and most of the distribution is concentrated on the right
• a very easy test would produce a distribution where the bulk of the scores are concentrated on the right, resulting in the long tail of anomalous scores on the left
• the mean is pulled to the left this time 9due to the lower scores who are in the minority), with the mode dissecting the highest peak and the median in the middle.