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Statistics

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the study of how to collect, organize, analyze, and interpret numerical information from data.

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Individuals

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the people or objects included in the study.

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Variable

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a characteristic of the individual to be measured or observed.

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Quantitative Variable

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has a value or numerical measurement for which operations such as addition or averaging make sense.

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Qualitative Variable

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describes an individual by placing the individual into a category or group, such as male or female.

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Population Data

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the data are from every individual of interest. Data from a specific population are fixed and complete.

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Sample Data

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the data are from only some of the individuals of interest. Data from samples vary from sample to sample and are NOT complete.

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Parameter

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a numerical measure that describes an aspect of a population.

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Statistic

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a numerical measure that describes an aspect of a sample.

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Nominal Level

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The nominal level of measurement applies to data that consists of names, labels, or categories. There are no implied criteria by which the data can be ordered from smallest to largest. We can put the data into categories.

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Ordinal Level

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The ordinal level of measurement applies to data that can be arranged in order. However, differences between data values either cannot be determined or are meaningless. We can order the data from smallest to largest or "worst" to "best". Each data value can be compared with another data value.

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Interval Level

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The interval level of measurement applies to data that can be arranged in order. In addition, differences between data values are meaningful. We can order the data and also take the differences between data values. At this level, it makes sense to compare the differences between data values. For instance, we can say that one data value is 5 more than or 12 less than another data value.

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Ratio Level

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The ratio level of measurement applies to data that can be arranged in order. In addition, both differences between data values and ratios of data values are meaningful. Data at the ratio level have a true zero. We can order the data, take differences, and also find the ratio between data values. For instance, it makes sense to sat that one data value is twice as large as another.

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Descriptive Statistics

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Descriptive statistics involves methods or organizing, picturing, and summarizing information from samples or populations.

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Inferential Statistics

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Inferential statistics involves methods of using information from a sample to draw conclusions regarding the population.

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Simple Random Sample

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A simple random sample of "n" measurements from a population is a subset of the population selected in a manner that every sample of size "n" from the population has an equal chance of being selected. Every sample of the given size must also have an equal chance of being selected.

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Random-Number Table

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Make one yourself by writing the digits 0-9 on separate cards and mixing the cards in a "hat". Draw a card, record the digit, return the card, mix up the cards, and draw again.

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Draw a Random Sample

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1. Number all members of the population sequentially. 2. Use a table, calculator, or computer to select random numbers from the numbers assigned to the population members. 3. Create the sample by using population members with numbers corresponding to those randomly selected.

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Simulation

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A simulation is a numerical facsimile or representation of a real-world phenomenon.

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Sampling With Replacement

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although a number has been selected for the sample, it is not removed from the population

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Stratified Sampling

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Groups or classes inside a population that share a common characteristic are called strata.

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Systematic Sampling

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It is assumed that the elements of the population are arranged in some natural sequential order

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Cluster Sampling

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Divide the pop. into sections and then randomly select certain sections and use all of the people in that section.

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Convenience Sampling

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Create a sample by using data from population members that are readily available - not very reliable.

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Census

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Measurements of the entire population

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Sampling

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Measurement of part of an existing population

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Simulation

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a numerical facsimile of real-world phenomena

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Observational Study

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no change/ intervention

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Experiment

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impose a treatment and measure the results

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Surveys

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Research method in which information is obtained by asking many individuals a fixed set of questions

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Frequency

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No. of observations in a given class

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Frequency Distribution

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Graphical or tabular portrayal of the frequency of all classes in the data set.

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Class Width

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Range/number of classes increase the value computed to the next highest whole number

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Range

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Largest # - smallest #

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Lower Limit

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is the lowest data value that can fit in a class

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Upper Limit

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is the highest data value that can fit in a class

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Mid-point

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is equal to the (lower class limit + the upper class limit)/2

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Class Boundaries

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To find upper class boundaries add 0.5 unit to the upper class limits. To find lower class boundaries subtract 0.5 unit from the lower class limits.

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Relative Frequency

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Class frequency/Total of all frequencies •f/n

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Frequency

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To determine frequency tally the data into classes.

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Symmetrical Distribution Shape

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Mound shaped

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Uniform or Rectangular Distribution Shape

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Straight, flat line

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Skewed Left Distribution Shape

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Tail trails off to the left

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Skewed Right Distribution Shape

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Tail trails off to the right.

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Bimodal Distribution Shape

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Two peaks

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Outliers

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are data values that are very different from other measurements in the data set

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Bar Graphs

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Comparative qualitative or quantitative data -must have a title -beginning and total length of bars be shown -can be horizontal or vertical -should be of uniform width and spacing

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Pareto Chart

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Bar graph where the bar height represents the frequency of an event and bars are arranged in descending order from left to right. -must have a title

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Circle Graph/Pie Chart

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a.k.a. Sector graph useful for qualitative data -must have a title -5-6 Wedges (no more than 10) -avoid 3-D wedges -label wedges

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Trend Data

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Time plots/time series (linear graph) -useful quantitative data

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Stem-and-Leaf Plots/Displays

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exploratory data analysis -alternative to frequency distribution for small data sets -organizes and groups the data while retaining the specific data values

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Mode

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the mode of a data set is the value that occurs most frequently

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Median

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is the central value of an ordered distribution. 1. Order the data from smallest to largest. 2. For an odd number of data values in the distribution, Median=Middle data value 3. For an even number of data values in the distribution, Median=Sum of middle two values/2

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Mean

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Average found by: Sum of all the numbers/# of numbers ?x/N

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Trimmed Mean

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a measure of center that is more resistant than the mean but still sensitive to specific data values 1. Order data from smallest to largest 2. Delete the bottom and top 5% of data 3. Compute the mean of the remaining 90%

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Weighted Mean (Average)

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?xw/?w x is the data value and w is the weight assigned to that data value. The sum (?) is taken over all the data values.

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Range

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the difference btwn the largest and smallest values of a data distribution i.e. high value - low value=range

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Variance

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measures variability in terms of squared deviations from the mean defining formula S²=[?(x-x?)²]/n-1 or computation formula S²=[n(?x²)-(?x?)²]/n(n-1) Con- measured in squared units of data

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Standard Deviation

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Square root of variance measure variation from mean in same units of measurement as raw data defining formula S=?[?(x-x?)²]/n-1 or computation formula S=?[n(?x²)-(?x?)²]/n(n-1) Con- value of (s) depends on the units of measurement

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Coefficient of Variation

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Measure of relative variation =C.V.=(s/x?) X 100

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Chebyshev's Theorem

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1-1/k² k is constant ;1 k=2 at least 75% of the data fall in the interval from µ-2? to µ+2? k=3 at least 88.9% of the data fall in the interval from µ-3? to µ+3? k=4 at least 93.8% of the data fall in the interval from µ-4? to µ+4?

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Percentile

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Data must be rank ordered (from smallest to largest value)

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Quartile

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percentiles that divide the data into fourths. Low value=0-25% Q1=25-50% Q2=50% Q3=50-75% High value=75-100%

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IQR

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Interquartile Range IQR=Q3-Q1

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Correlation

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the measure of a relationship between two variables or sets of data (doesn't mean that one causes the other)

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Correlation Coefficient

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describes (r) the direction and strength of the relationship between two sets of variables (x and y) -1?r?1

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Positive Linear

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if values x and y are both "high" or both "low"

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Negative Linear

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if values x are "low", and values of y are "high" or values of x are "high", and values of y are "low"

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Probability

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is a numerical measure between 0 and 1 that describes the likelihood that an event will occur. P(A), read "P of A" denotes probability of A If P(A)=1, the event A is certain to occur If P(A)=0, the event A is certain not to occur

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Law of large numbers

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as the sample size increases and increases, the relative frequencies of outcomes get closer and closer to the theoretical (or actual) probability value.

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Statistical Experiment (Observation)

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can be thought of as any random activity that results in a definite outcome.

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Event

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is a collection of one or more outcomes of a statistical experiment.

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Simple Event

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is one particular outcome of a statistical experiment.

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Sample Space

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the set of all simple events constitutes the sample space of an experiment.

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Complement of an event

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is the event that A does not occur.

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