STAT Chapter 2 What To Know

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(a) Be able to understand and read a frequency distribution table, a bar chart, and a pie chart.

(b) Given raw data, be able to calculate angles in pie charts, heights of bars in bar charts, and any of the entries in a frequency distribution table.

How to create a stem and leaf display, how to read a stem an leaf display, what a "stem" is and what a "leaf" is.

(b) Be able to create and read a dot plot.

(c) Be able to read a all 3 types of histograms; given a small sample or population, be able to calculate the height of a bar; know visually what skewed right, skewed left, symmetric, and uniform histograms look like.

The definitions and interpretation of all the one variable statistics covered starting on page 16; be able to calculate all of them with the TI-83/84; definition, interpretation, and calculation of percentiles, know what a distribution graph is, their various shapes, and the relationship between the median and mean for symmetric, skewed left, and skewed right distribution graphs.

Definition, calculation, and application of a z-scores, the statement of the empirical rule, application of the empirical rule including exploiting the symmetry of the distribution curve to obtain the answer as was done in (c) and (d) above.

Some values of 1 - 1/k2 in Chebyshev's Theorem (population assumed, but holds for samples as well)

k 1 - 1/k2 Interpretation

1 0 No useful information

1.5 .56 At least 56% of the data between µ - 1.5σ and µ + 1.5σ (z scores from -1.5 to 1.5) 2 .75 At least 75% of the data between µ - 2σ and µ + 2σ (z scores from -2 to 2)

2.5 .84 At least 84% of the data between µ - 2.5σ and µ + 2.5σ (z scores from -2.5 to 2.5)

3 .89 At least 89% of the data between µ - 3σ and µ + 3σ (z scores from -3 to 3)

General Method for Solving Chebyshev Problems:

1. You are given a population or sample of unknown shape, or if known, is not bell shaped and symmetrical. (population assumed below, for a sample replace µ with x and σ with s)

2. You are asked for the minimum fraction (or percentage) of data that is in some interval (L, U) that is centered at the mean µ (or x).

_______|_____________|_____________|________ L µ U µ - kσ µ + kσ

3. The value k to use in the formula 1- 1/k2 is just the number of standard deviations U is above the mean; this is just the z-score of U, so that

Uk

µ σ −= [also note that L k µ σ − = , the number of standard deviations L is below the mean ]

4. If you are given the population size (N), or sample size (n) , and are asked the minimum number of data values in (L, U), just multiply 1 -1/k2 by N or n.