Chapter 3 Flashcards
(22 cards)
Define: mean
Total of all values divided by number of values
Symbol: µ (population), X with overline (sample)
Define: median
The midpoint of a distribution; the number such that half of the values are above and half are below
Symbol: M
Mean vs median:
Mean is drawn toward outliers and skew; median is resistant
Define: mode
The value that occurs with highest frequency in a data set
Advantages and disadvantages of mode:
Pro: can be used in qualitative analysis
Con: may or may not exist, there may be more than one
Define: standard deviation
How closely values are clustered around the mean
For a symmetric distribution with one peak, the values of mean, median, and mode are:
Identical and at the centre of the distribution
For a right-skewed distribution, values of mean, median, and mode are:
Mean is largest, mode is smallest, and the value of the median is between them. Opposite for left-skewed.
Small SD means:
Values are spread over a relatively small range around the mean
Formulas for variance and SD for ungrouped data
*** slide 7
Variance and deviation are represented by:
Population - sigma
Sample - s
Define: population parameter or just parameter
A numerical measure (ex: mean, median, mode, variance, SD) calculated for a data set
Can SD be negative?
nope. only zero or positive.
Define: statistic
A summary measure calculated for a simple data set
Shortcut formulas for variance and SD for ungrouped data:
*** slide 7
Formulas for grouped data:
*** slide 10
Chebyshev’s theorem:
For any number k greater than 1, at least (1 - 1/k^2) of the data values lie within k standard deviations of the mean.
Empirical rule: For symmetric and bell-shaped distributions, __% of values lie within __ standard deviations of the mean.
68%, 1 SD
95%, 2 SD
99.7%, 3 SD
Quartiles:
Quartiles divide the dataset into 4 equal parts. Values below the first quartile are the lower quarter. The second quartile is the median. Values above the third quartile are the upper quarter.
Define: interquartile range
The difference between the first and third quartiles
Five-number summary:
Min, Q1, Q2, Q3, max
Box and whisker plot shit: