Topic 2 - Numerical Measures Flashcards
1
Q
What are the 3 measures of central tendency
A
- Arithemtic Mean
- Median
- Mode
2
Q
What are the 4 measures of variability
A
- Range
- Interquartile Range
- Variance
- Standard Deviation
3
Q
What is a benefit of the median
A
- Not affected by extreme values
4
Q
What is the pro and con of the mode
A
- Pro: Not affected by extreme values
- Con: There may be no mode or several modes
5
Q
What information do measures of variability provide
A
- Information on the spread or variability of the data values
6
Q
What is a disadvantage of the range
A
- Ignores the way in which data is distributed
7
Q
What is a benefit of the interquartile range
A
- Can eliminate some outlier problems
8
Q
What is the variance
A
- Average of squared deviations of values from the mean
9
Q
What is the difference in calculation between population and sample variance and standard deviation
A
- Population: divide by N
- Sample: divide by n-1
10
Q
Why do we divide by n-1 for sample variance
A
- So that the sample variance is an unbiased estimator of the population variance
11
Q
What is an unbiased estimator
A
- The average of the sample variances for all possible samples to equal the population variance
12
Q
How can we infer the standard deviation graphically
A
- Wide base = Large standard deviation
- Shallow base = Small standard deviation
13
Q
What is the empirical rule
A
- If the curve is bell shaped
- mu +- 1s.d contains 68% of values in pop or sample
- mu +- 2s.d contains 95% of values in pop or sample
- mu +- 3.d contains 99.7 values in pop or sample
14
Q
What is the z-score
A
- Shows the position of an observation relative to the mean of the distribution
- Indicates the number of s.d a value is from the mean
- z > 0 value greater than mean
- z < 0 value less than mean
- z = 0 equal to mean
15
Q
How is the z-score calculated
A
- If the data set is the entire population and the population mean and s.d are known
- z = x - mu / s.d
