MTH 160 Unit 1 Notes

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School
Washtenaw Community College **We aren't endorsed by this school
Course
MTH 160
Subject
Statistics
Date
Sep 4, 2023
Pages
2
Uploaded by ShadowPrince77 on coursehero.com
Basic Statistics - Chapter 1 - Types of Samples and Types of Data A population is the entire collection of individuals about which information is sought. Parameters are numbers that describe the population. A sample is a subset of a population, containing the individuals that are actually observed. Statistics are numbers that describe a sample. A simple random sample is chosen by a method in which each collection of items is equally likely. For cluster sampling , the population is divided into groups, and a random sample of groups is drawn. For stratified sampling , the population is divided into groups, and a random sample of individuals is drawn from each group. A sample of convenience is a sample that is not drawn by a well-defined random method. Qualitative data refers to categories or features (labels). Quantitative data refers to counts or measures (numbers). Nominal data refers to items that have NO natural order. Ordinal data refers to items that can be ordered. Continuous data can take on any value in an interval (measures). Discrete data can be listed (counts). Basic Statistics - Chapter 3 - Numerical Summaries of Data STAT EDIT lets you enter data, and STAT CALC lets you calculate two screens of 1-Var Stats, where Sample Mean. The symbol µ (mu) represents the Population Mean in many formulas. S x = Sample Std. Deviation σ x = Population Std. Deviation Variance = ( Std.Deviation) 2 Coefficient of Variation = σ/µ Five Number Summary min, Q 1 , median, Q 3 , max (and the median is same as Q 2 ) Empirical Rule: For data sets that are approximately symmetric : 68% of the data values are between µ σ and µ + σ , 95% of the data values are between µ − 2 σ and µ + 2 σ , and almost all of the data values are between µ − 3 σ and µ + 3 σ . Chebyshev's Inequality: For any data set (even very skewed, with one tail), 75% or more of the of the data values are between µ − 2 σ and µ + 2 σ , and 89% or more of the data values are between µ − 3 σ and µ + 3 σ . z = (x-µ) / σ = how many standard deviations that value is from its population mean. x = µ + (z*σ) = value based on a given z-score Inner Quartile Range (IQR) = Q 3 - Q 1 Lower Outlier Boundary = Q 1 - 1.5 * IQR Upper Outlier Boundary = Q 3 + 1.5 * IQR
Basic Statistics - Chapter 2 - Graphical Summaries of Data Here are some things to remember about HISTOGRAMS: Approximately symmetric means that the right side and the left side are almost identical Skewed to the right , is also called positively skewed, which means the long tail is on the right side Skewed to the left , is also called negatively skewed, which means the long tail is on the left side Frequency histograms are based on counts and Relative Frequency histograms are based on percent Finally, classes must not overlap, must be of equal width, and there should be NO missing classes Here are some things to remember about STEM-&-LEAF PLOTS: The STEM is the first part of the number, and NO values are skipped, when setting up your stems The LEAVES are the rightmost part of the number, which is only the last digit Finally, the leaves are ordered from smallest to biggest values, as you move away from the stems Here are some things to remember about FREQUENCIES and RELATIVE FREQUENCIES: The frequency of a category is the number of times it occurs in the data set A frequency distribution is a table that presents the frequency for each category The relative frequency of a category is the frequency of the category divided by the sum of all the frequencies. (decimal or percent) - Pie Charts are based on relative frequency Basic Statistics - Chapter 4 - Summarizing Bivariate Data Scatterplots Press 2nd, Y= ( STAT PLOT ) and press 1 for first plot and select On and scatterplot icon (first icon). Press ZOOM and 9: ZoomStat. Press STAT and CALC. Select 4: LinReg (ax+b) -or- 8: LinReg (a+bx) and press ENTER . Linear Equations Two uses for the equation for the regression line include: Determine how much y differs , when given the difference in two values of x. The slope = b in the example screen above, and ∆x is the difference in x, so the difference in y is ∆y = b * ∆x . Predict the value of y, when given a value for x. Replace x with the given value and solve for y. Use either 4:LinReg for y = ax + b or 8:LinReg for y = a + bx, on your calculator. Two values that are used with the regression line include: r 2 = Coefficient of Determination , which is the % of variation explained by the regression line r = Correlation Coefficient , which describes the strength of the linear relationship (-1 ≤ r ≥ +1), and the direction of the line (negative is downward and positive is upward). Remember, correlation DOES NOT equal causation , as in example of ice cream sales and shark attacks! Another Reminder: If r and r 2 DO NOT appear when you use the LinReg app, then go to 2 nd and 0 to get the Catalog list. Scroll down to DiagnosticOn, hit enter twice, and Done should appear on your screen.
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