Statistics 1 Lee University
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| Descriptive statistics | methods of organizing, summarizing, and presenting data in an informative way.
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| Inferential statistics | A decision, estimate, prediction, or generalization about a population, based on a sample.
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| Population | A collection of all possible individuals, objects, or measurements of interest
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| Sample | A portion or part of the entire population
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| Qualitative variable | Nonumeric characteristic
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| Quantitative variable | Numeric characteristic
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| Discrete variables | Can only assume certain values. (whole numbers)
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| Continuous variables | Can assume any value. (including decimals or fractions)
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| Nominal data | Data that can be classified into categories, but cannot be arranged in any order. Example- Eye color, gender, religion.
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| Interval data | Numerical data with no natural zero point. Example- Temperature
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| Ordinal data | Qualitative data that can be placed in order. Example- During a taste test of 4 soft drinks, Mellow Yellow was ranked number 1, Sprite number 2, Seven-up number 3, and Orange Crush number 4
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| Ratio data | Quantitative data with zero as a starting point. Differences in data are meaningful. Example- Income of a profession.
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| Four levels of Measurment in data | Nominal, ordinal, interval and ratio data.
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| Class interval | Lower limit of one class minus the lower limit of another class.
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| Class frequency | The number of observations in each class.
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| Class midpoint | A point that divides the class into two different parts. The average of the class.
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| Bar chart | A graph in which the classes are reported on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are proportional to the heights of the bars.
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| Pie chart | A chart that shows the proportion or percent that each class represents of the total number of frequencies.
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| Determine the class interval or width | i ( is greater than or equal to) (H – L)/k where i is the class interval, H is the highest observed value, L is the lowest observed value, and k Is the number of classes. Round up to convenient number.
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| Determine number of classes | A useful recipe to determine the number of classes (k) is the “2 to the k rule.” such that 2(to the power of)k > n.
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| Steps in creating a frequency table | Decide number of classes, determine class interval or width, Set up individual class limits, tally data into classes, count number of data points in each class
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| Relative class frequency | The percent of total that each class represents. Presented in decimal form.
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| Determine relative class frequency | Class frequency divided by total number of observations.
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| Histogram | A graph in which the classes are marked on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are represented by the heights of the bars and the bars are drawn adjacent to each other.
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| Frequency polygon | Shows the shape of a distribution and is similar to a histogram.
It consists of line segments connecting the points formed by the intersections of the class midpoints and the class frequencies.
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| Cumulative Frequency Distribution |
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| Parameter | Measurable characteristic of population
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| Statistic | Measurable characteristic of sample
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| Sample mean | Sum of all variables in the sample / Number of values in the sample
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| Sample mean | X bar
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| n | Number of observations or values in a sample
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| i | Class interval
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| k | Number of classes
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| H | Highest observed value
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| L | Lowest observed value
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| Weighted mean | An average computed by giving different weights to some of the individual values. If all the weights are equal, then the weighted mean is the same as the arithmetic mean
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| Determine weighted mean | (w1x1+w2x2+w3x3)/w1+w2+w3
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| Median | The midpoint of the values after they have been ordered from the smallest to the largest, or the largest to the smallest. Middle number if n is odd. Average of two middle numbers if n is even.
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| Mode | The data point that appears the most.
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| Measures of Dispersion | Range, Mean Deviation, Varience and Standard Deviation
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| Range | Highest minus Lowest value.
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| Determine Mean Deviation | Take each data point, subtract mean and find absolute value for each. Add all these new values and divide by the number of data points. E(x-xbar)/n
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| Variance | The arithmetic mean of the squared deviations from the mean.
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| Standard Deviation | The square root of the variance.
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| Determine population variance | Take each data point, subtract the mean and square it. Add all of these numbers and divide by the number of data points. E(x-xbar)^2/n
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| Determine population standard deviation | Take each data point, subtract the mean and square it. Add all of these numbers and divide by the number of data points. Find the square root. Square root of E(x-xbar)^2/n
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| Population variance | Variance of every data point.
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| High standard deviation and variance | Spread out data
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| Low standard deviation and variance | Condensed data
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| Determine sample variance | Take each data point, subtract the mean and square it. Add all of these numbers and divide by one less than number of data points. E(x-xbar)^2/n-1
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| Determine sample standard deviation | Take each data point, subtract the mean and square it. Add all of these numbers and divide by one less than the number of data points. Find the square root. Square root of E(x-xbar)^2/n-1
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| Chebyshev’s Theorem | 1-(1/k^2) k is number of standard deviations. Shows what percent of population or sample lies within a number of standard deviations.
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| Empirical rule | 68% of observations lie within plus or minus 1 standard deviation. 95% of observations lie within plus or minus 2 standard deviations. 99.7% of observations lie within plus or minus 3standard deviations. (for symmetrical bell shaped freq distribution)
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| Red sea rule 1 | Realize that God means for you to be where you are
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| Red sea rule 2 | Be more concerned for God’s glory than for your relief
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| Red sea rule 3 | Acknowledge your enemy, but keep your eyes on the Lord
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| Red sea rule 4 | Pray. Invitation, insurance, illumination
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| Locate percentile | (n+1)P/100 P is desired percentile
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| First quartile | 25% of data. To find, do .25*(n-1)
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| Third quartile | 75% of data. To find, do .75*(n-1)
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| Contingency Tables | A table used to show a relationship between two qualitative variables.
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| Positively Skewed | Median is less than mean. Peak is left of median.
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| Negatively Skewed | Mean is less than mean. Peak is right of median.
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| Pearson's Coeffecient of Skewness | Three times the mean minus the median all divded by the standard deviation. 3(xbar-Median)/s
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| Software Coeffecient of Skewness | n/(n-1)(n-2)Σ(x-xbar)/s^3
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| Coeffecients of Skewness | Range from -3 to 3. Negative number, negative skewness. Positive number, postive skewness. 0 means frequency table is symetrical.
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