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17 Cards in this Set
- Front
- Back
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Measure of location |
Summarising each distribution by finding a measure which describes the size of the values in the distribution - representative of the data set as a whole |
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Measure of spread |
For values that are distributed differently, need to consider how spread out the data is |
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Measures of location |
Mode - most occurring values in the data (m) Median - 50th percentile (M) Mean - sum of all values divided by number of values - average |
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Bimodal |
Where multiple values are most common at once - mode ceases to be useful as a ‘typical’ value |
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Advantages and disadvantages of the Mode |
Advantages: - most frequent value may be most useful measure eg. Majority opinion - very easy to evaluate - used with non numeric data - open ended distributions don’t affect finding it Disadvantages: - appropriate value might not exist eg all values different - if bimodal, no longer useful - could be extreme value in a skewed distribution and then is unsuitable - can not be used in further calculations - not involve all data points - small changes in values not reflected by small changes in mode - ^ descriptive way not analytical |
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Advantages and disadvantages- median |
Advantages: - useful to know value below which 50% of distribution lies - value of median not affecting by outlying values or open ended distributions Disadvantages: - doesn’t involve all data points - small changes in values not reflected proportionally by small changes in median - medians from separate distributions can’t combine - can not be used in further calculations |
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Advantages and disadvantages of the mean |
Advantages: - all values in data set used - possible to pool data from multiple sets to calculate overall mean - further used in statistical analysis - can be used for reflecting small changes in data set Disadvantages: - affected by outlying values - difficult to interpret for certain scenarios |
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Excel functions |
=MODE() : calculates mode =MEDIAN() : calculates median =AVERAGE() : calculates mean =QUARTILE() : calculates quartile |
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Weighted mean |
Back (Definition) |
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Measure of dispersion - Range |
Range = largest value - smallest value Easy to calculate and easy to understand But uses only 2 values and can be subject to distortion |
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Measure of dispersion |
Measures of the scatter, spread, variability or unpredictability of the data values relative to a measure of location |
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Measure of dispersion - Quartiles |
Quartile deviation - (Q3 - Q1)/2 |
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Standard deviation |
Find mean Find difference between every mean figure and actual figures (difference) Square these figures (d^2) Add them up Divide by number of values Square root this number for the standard deviation |
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What does a standard deviation figure tell us |
If standard deviation smaller, it means figures closer to the mean - less outliers or varied figures |
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Coefficient of variation |
Expresses standard deviation as a percentage of mean = (Standard deviation / mean ) x100% |
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Positive skew |
Mean > median > mode |
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Negatively skewed |
Mean < median < mode |
