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### 35 Cards in this Set

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 Class frequency The number of observations in the data set that fall into a particular class. Class relative frequency The class frequency divided by the total number of observations in the data set: that is, *the book puts the formula here but I can't do it like the book can, so here is my best attempt: class relative frequency=class frequency/n Class percentage the class relative frequency multiplied by 100; that is, class percentage=(class relative frequency) x 100 Bar Graph The categories (classes) of the qualitative variable are represented by bars, where the height of each bar is either the class frequency, class relative frequency, or class percentage. Pie Chart The categories (classes) of the qualitative variable are represented by slices of a pie (circle). The size of each slice is proportional to the class relative frequency. Pareto Diagram A bar graph with the categories (classes) of the qualitative variable (i.e., the bars) arranged by height in descending order from left to right. Dot Plot -The dot plot condenses the data by grouping all values that are the same. -The numerical value of each quantitative measurement in the data set is represented by a dot on a horizontal scale. When data values repeat, the dots are placed above one another vertically. Stem-and-Leaf Display -The stem-and-leaf display condenses the data by gourping all data with the same stem. -The stem is the portion of the measurement to the left of the decimal point, while the leaf is the portion to the right of the decimal point. -The numerical value of the quantitative variable is partitioned into a "stem" and a "leaf." The possible stems are listed in order in a column. The leaf for each quatitative measurement in the data set is placed in the corresponding stem row. Leaves for observations with the same stem value are listed in increasing order horizontally. Histogram -The histogram condenses data by grouping data values into the same class. -The horizontal axis of the figure is divided into class intervals. The vertical axis gives the number (or frequency) of the reading that fall into each interval. -The possible numerical values of the quantitative variable are partitioned into class intervals, each of which has the same width. These intervals form the scale of the horizontal axis. The frequency or relative frequency of observations in each class interval is determined. A vertical bar is placed over each class interval, with the height of the bar equal to either the class frequency or class relative frequency. How do I represent the formulas with a sigma and other wacky symbols in them? =? I don't yet know. Central Tendency of a set of measurements the tendency of the data to cluster, or center, about certain numerical values. Variability of a set of measurements The spread of the data Mean (or arithmetic mean or average) The mean of a set of quantitative data is the sum of the mesurements, divided by the number of measurements contained in the data set. Mean of a sample -represented by x-bar (an lowercase x with a bar over it) -the formula for representing the mean of a sample is too complicated for me to currently put it here. What are the symbols for the Sample Mean and the Population Mean? -Sample Mean: x-bar -Population Mean: lowercase mu -the x-bar is a lowercase x with a bar over it and the mu is the greek lowercase mu. Median The median of a quantitative data set is the middle number when the measurements are arranged in ascending (or descending) order. How to calculate a Sample Median M (italic M) Arrange the n measurements from the smallest to the largest. 1. If n is odd, M is the middle number 2. If n is even, M is the mean of the middle two numbers. Skewness A data set is said to be skewed if one tail of the distribution has more extreme observations than the other tail. Mode The mode is the measurement that occurs most frequently in the data set. Modal Class The measurement class containing the largest relative frequency. The measures of central tendency are the mean, median, and mode. The numerical descriptive measures are The central tendency and the variability The measure of the variability is also known as the spread The range The range of a quantitative data set is equal to the largest measurement minus the smallest measurement. The sample variance The sample variance for a sample of n measurements is equal to the sum of the squared distances from the mean, divided by (n-1). The symbol s-squared (*can't make that symbol here) is used to represent the sample variance. The sample standard deviation The sample standard deviation, s, is defined as the positive square root of the sample variance, s-squared, or, mathematically (as best as I can put it here): s = square-root of s-squared. Symbol for sample variance s-squared Symbol for Sample standard deviation s symbol for population variance sigma-squared (just imagine it) symbol for population standard deviation sigma Measures of relative standing Descriptive measures of the relationship of a measurement to the rest of the data. pth percentile (p is italic) For any set of n measurements (arranged in ascending or descending order), the pth percentile is a number such that p% of the measurements fall below that number and (100-p)% fall above it. Formula for the sample z-score for a measurement x z = (x minus x-bar) divided by s --Where z is the z-score, x is the measurement, x-bar is the sample mean, and s is the sample standard deviation Formula for the population z-score for a measurement x z = (x minus mu) divided by sigma --Where z is the z-score, x is the measurement, mu is the population mean, and sigma is the population standard deviation. Interpretation of z-Scores for Mound-Shaped Distributions of Data 1. Approcimately 68% of the measurements will have a z-score between -1 and 1. 2. Approximately 95% of the measurements will have a z-score between -2 and 2. 3. Approximately 99.7% (almost all) of the measurements will have a z-score between -3 and 3.