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This article provides an introduction to basic statistics and the normal distribution. It covers topics such as data collection, surveys, interviews, frequency distribution, measures of central tendency and dispersion, and the use of charts, tables, and graphs. The article also discusses statistical methods, statistical terminology, and the use of statistical computer packages.
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Basic of Statistics & Normal Distribution
What Is Statistics? • Collection of Data • Survey • Interviews • Summarization and Presentation of Data • Frequency Distribution • Measures of Central Tendency and Dispersion • Charts, Tables,Graphs
Statistical Methods Statistical Methods Descriptive Inferential Statistics Statistics
Key Terms • 1. Population (Universe) • All Items of Interest • 2. Sample • Portion of Population • 3. Parameter • Summary Measure about Population • 4. Statistic • Summary Measure about Sample • P in Population & Parameter • S in Sample & Statistic
StatisticalComputer Packages • 1. Typical Software • SAS • SPSS • MINITAB • Excel • 2. Need Statistical Understanding • Assumptions • Limitations
Standard Notation Measure Sample Population Mean ` m X Stand. Dev. S s 2 2 Variance S s Size n N
Mean • Measure of Central Tendency • Most Common Measure • Acts as ‘Balance Point’ • Affected by Extreme Values (‘Outliers’) • Formula (Sample Mean) n å X i X + X + L + X 1 2 n i = 1 X = = n n
Advantages of the Mean • Most widely used • Every item taken into account • Determined algebraically and amenable to algebraic operations • Can be calculated on any set of numerical data (interval and ratio scale) -Always exists • Unique • Relatively reliable
Disadvantages of the Mean • Affected by outliers • Cannot use in open-ended classes of a frequency distribution
n + 1 Positioning g Point = 2 Median • Measure of Central Tendency • Middle Value In Ordered Sequence • If Odd n, Middle Value of Sequence • If Even n, Average of 2 Middle Values • Not Affected by Extreme Values • Position of Median in Sequence
Advantages of the Median • Unique • Unaffected by outliers and skewness • Easily understood • Can be computed for open-ended classes of a frequency distribution • Always exists on ungrouped data • Can be computed on ratio, interval and ordinal scales
Disadvantages of Median • Requires an ordered array • No arithmetic properties
Mode • Measure of Central Tendency • Value That Occurs Most Often • Not Affected by Extreme Values • May Be No Mode or Several Modes • May Be Used for Numerical & Categorical Data
Advantages of Mode • Easily understood • Not affected by outliers • Useful with qualitative problems • May indicate a bimodal distribution
Disadvantages of Mode • May not exist • Not unique • No arithmetic properties • Least accurate
Relationship among Mean, Median, &Mode • If a distribution is symmetrical, the mean, median and mode coincide • If a distribution is non symmetrical, and skewed to the left or to the right, the three measures differ. A negatively skewed distribution (“skewed to the left”) A positively skewed distribution (“skewed to the right”) Mode Mean Mean Mode Median Median
Range = X - X l arg est smallest Range • Measure of Dispersion • Difference Between Largest & Smallest Observations
“VARIATION” The Root Of All Process EVIL
What is the standard deviation? • The SD says how far away numbers on a list are from their average. • Most entries on the list will be somewhere around one SD away from the average. Very few will be more than two or three SD’s away.
Variance & Standard Deviation • Measures of Dispersion • Most Common Measures • Consider How Data Are Distributed • Show Variation About Mean (`X or m)
What is the standard deviation • Same means different standard deviations SD S D
Sample Standard Deviation Formula(Computational Version) s =
S CV = × 100% X Coefficient of Variation • 1. Measure of Relative Dispersion • 2. Always a % • 3. Shows Variation Relative to Mean • 4. Used to Compare 2 or More Groups • 5. Formula (Sample)
Coefficient of Variation • 1. Measure of relative dispersion • 2. Always a % • 3. Shows variation relative to mean • 4. Used to compare 2 or more groups • 5. Formula: • 6. Population Sample s CV (100) CV (100) _ x
_ x _ x _ x Summary of Variation Measures Measure Equation Description x - x Total Spread Range largest smallest Q - Q Spread of Middle 50% Interquartile Range 3 1 Dispersion about 2 Standard Deviation x Sample Mean (Sample) n 1 Dispersion about Standard Deviation 2 x Population Mean (Population) N 2 Squared Dispersion Variance ( x ) about Sample Mean (Sample) n 1 Relative Variation Coeff. of Variation s / (100)
