summarising numerical data

Question 1

what is the difference between discrete and continuous data?

Answer 1

discrete = data takes on whole unit values only - i.e) number of children, number of episodes of angina

continuous= data can take on any value i.e) blood pressure/weight

Question 2

what are the two things that can go wrong when we ‘summarize’ data?

Answer 2

• we present aspects of the data that lead to the wrong conclusion
• we leave out important aspects of the data, leading to the reader drawing the wrong conclusion

Question 3

when is a numerical representation useful? When is it not useful?

Answer 3

When you need exact information = useful

when you want people to appreciate a pattern/significant = awful

Question 4

When should we ‘summarise’ data?

Answer 4

when there are too many individual measurements to effectively display on a graph/visual

Question 5

what is a ‘quantile’?

Answer 5

a figure that cuts off a specified percentage of the data values -

ex) the 25th percentile or below, the 50th percentile or below etc.

Question 6

what is the ‘median’?

Answer 6

the half way point of the data values -

half of the values lie at or below the median , it is the 50th percentile

Question 7

how does the median differ from the mean?

Answer 7

the mean = the average

Question 8

Will an outlier effect the median or the mean?

Answer 8

an outlier will effect the mean, but not the median

Question 9

why is the range not a good idea of variability?

Answer 9

b/c it is based on only two pieces of data - the biggest and smallest value which are likely to be atypical cases or even errors!

Question 10

what is the interquartile range?

Answer 10

divide the values into ‘quartiles’ and then give the 25%- 75% range as an indication apart from outliers

Question 11

what is the difference between a quartile and quantile?

Answer 11

quartile = values that cut data into four equal groups

quintiles = cut data into 5 equal groups

Question 12

how can quantiles help with understanding?

Answer 12

ex) if you get a test score back of 58% you’ll be pretty bummed until you learn that you’re in the 90th percentile for the class- in other words, you did 9/10ths better than the class!

Question 13

how how to interpret/visualise the median and interquartile range

Question 14

What does a boxplot show?

Answer 14

Question 15

how does a boxplot show quartiles?

Answer 15

it builds a box around the 25th and 75th percentiles

Question 16

what is the outlier detection rule based on?

Answer 16

the interquartile range

see how far away the observation is from the central 50% of values (from 25% - 75%)

Question 17

interpret this boxplot on graph

Answer 17

note increasing risk with age - the box plot is necessary to interpret the data correctly