4: Exploration of Single Variables Flashcards
What is the mean?
The sum of observations divded by the number of obeservations.
Coventions
Sample size - n
Observations of variable y - y1, y2, y3, . . . , yn
Sample mean - y¯
What is the median?
Splits the sample size into two parts with equal numbers of observations, ordered from highest to lowest. Sample size n is odd - single obsevation occurs in the middle. Sample size n is even - two observations in the middle, median is the midpoint.
What is the mode?
The value the occurs most frequently.
What is the range?
The difference between the largest and smallest observation.
What is deviation?
The deviation d of an observation yi from the sample mean y¯ is the difference between them. d = yi - y¯. The deviation is positive when it falls above the mean. The deivation is negative when it falls below the mean.
What is the problem for deviation?
Σd = Σ(yi − y¯) is always zero. The negative differences cancel out the postive ones. The negative number is always squared so it is positive. So it becomes Σ(yi − y¯)
^2.
What is standard deviation?
The standard deviation s is the positive square root of the variance s^2. As the units of measurements are squared - makes variance difficult to interpret.
What are the properties of standard deviation?
Standard deviation is equal to or greater than 0. Standard deviation is equal to 0 when all observations have the same value. The greater the variability around the mean, the larger the value of standard deviation.
What is the pth percentile?
Is the point such that p% of observations fall below or at the point and (100 - p) % fall above it.
What are the quartiles?
The 25th percentile is the lower quartile. The 75th percentile is the upper quartile. The difference between the quartiles is the interquartile range.
