Parameter
a numerical measurement describing some characteristic of a
population
Statistic
a numerical measurement describing some characteristic of a
sample
Discrete data
results when the number of possible values is either a finite number or a
countable
number (That is, the number of possible values is 0, 1, 2, and so on.)
ex. counting eggs in the hen house
Continuous (numerical) data
results from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps
ex. amount of milk from a cow (not an exact number of gallons)
Nominal level of measurement
characterized by data that consists of names, labels, or categories only
The data cannot be arranged in an ordering scheme such as low to high)
Ordinal level of measurement
they can be arranged in some order, but differences between the values cannot be determined or are meaningless
Interval level of measurement
the difference between any two data values is meaningful (however there is no natural zero where there is none of the quantity present)
Ratio level of measurement
there is a natural zero or starting point where none of the quantity is present (differences and ratios are both important)
Class boundaries
numbers used to separate classes, but without the gaps created by class limits
Class midpoints
midpoints of the classes
Class width
the difference between two consecutive upper class limits or two consecutive lower class boundaries (not the upper of one class to the lower of the next class)
Relative frequency distribution
the frequency of one class divided by the total amount of frequencies
Cumulative frequency distribution
the sum of the frequencies of a given class and all previous classes (the cumulative frequency of the last class equals the sample size)
Relative frequency histogram
the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies
Pie chart
graph depicting qualitative data as slices of a pie
Stem-and-leaf plot
represents data by separating each value into two parts:
1. the stem - leftmost digit
2. the leaf - rightmost digit
Dot plot
a graph which each data value is plotted as a point along a scale of values (dots of equal values are stacked)
Mean
average
Median
middle value (remember to arrange in numerical order)
if there are 2 middle numbers, find the average of them
Mode
often denoted by M and is the value that occurs most frequently
bimodal - 2 modes
multimodal - 3 or more and not listed
Midrange
value midway between the highest and lowest values
(add the highest and lowest values and then divide by 2)
Range
the difference in a set of data between the highest and lowest value
Variance
the measure of variation equal to the square of the standard deviation of a set of values
Standard Deviation
measure of variation of values about the mean in a set of sample values
Empirical Rule
�About 68% of all scores fall within 1 standard deviation of the mean.
�About 95% of all scores fall within 2 standard deviations of the mean.
�About 99.7% of all score fall within 3 standard deviations of the mean.
z-score (or standard score)
the number of standard deviations that a given x is above or below the mean
- positive z-score is that far above the mean and negative is that far below the mean
z = (x-M)/o