Elementary Statistics Test 1

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