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IB DP Maths: AI SL復習筆記4.1.7 Interpreting Data

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月19日下午3:00

The?mode?is useful for?qualitative data
- It is not as useful for quantitative data as there is not always a unique mode
The?mean includes all values
- It is affected by outliers
- A smaller/larger mean is preferable depending on the scenario
  - A smaller mean time for completing a puzzle is better
  - A bigger mean score on a test is better
The?median is not affected by outliers
- It does not use all the values
The range gives the full spread?of the all of the data
- It is affected by outliers
The?interquartile range gives the spread of the middle 50%?about the median and is not affected by outliers
- It does not use all the values
- A bigger IQR means the data is more spread out about the median
- A smaller IQR means the data is more centred about the median
The?standard deviation?and?variance?use all the values to give a measure of the?average spread?of the data about the mean
- They are affected by outliers
- A bigger standard deviation means the data is more spread out about the mean
- A smaller standard deviation means the data is more centred about the mean

Box plots
- Can be used with ungrouped?univariate?data
- Shows the range, interquartile range and quartiles clearly
- Very useful for comparing data patterns quickly
Cumulative frequency graphs
- Can be used with continuous grouped univariate data
- Shows the running total of the frequencies that fall below the upper bound of each class
Histograms
- Can be used with continuous grouped univariate data
- Used with equal class intervals
- Shows the frequencies of the group
Scatter diagrams
- Can be used with ungrouped?bivariate?data
- Shows the graphical relationship between the variables

Compare a?measure of central tendency
- If the data?contains outliers - use the median
- If the data is?roughly symmetrical – use the mean
Compare a?measure of dispersion
- If the data?contains outliers - use the interquartile range
- If the data is?roughly symmetrical – use the standard deviation
Consider whether it is better to have a smaller or bigger average
- This will depend on the context
  - A smaller average time for completing a puzzle is better
  - A bigger average score on a test is better
Consider whether it is better to have a smaller or bigger spread
- Usually a smaller spread means it is more consistent
Always relate the?comparisons to the context?and consider reasons
- Consider the?sampling technique?and the?data collection?method