Top-Ten Review after First Quartile of Course

Top-Ten Review after First Quartile of Course

So far, we have discussed descriptive statistics and probability. Let’s divide the top-ten concepts into a pair of top-five concepts.

Considering statistics first, we examine a sample then compose five problems representing the five most fundamental statistical concepts.

2.2 2.9 2.6 2.4 2.9 2.1 2.4 2.6 2.7 2.3 Table 1: Sample

1) Calculate the mean, median, and mode.

2) Calculate the range, variance, and standard deviation.

3) Display the data as a frequency distribution in the form of a bar graph.

4) Display the data as a relative frequency distribution in the form of a histogram using 5 rectangles. Describe the distribution. Explain why the mean and median are not representative statistics for this sample.

5) Create a boxplot.

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Turning to probability, let’s consider the probability distribution.

x 4 8 −8

p(x) 0.5 0.125 0.375 Table 2: Probability Distribution

1) What is the probability of a positive outcome?

2) Represent the probability distribution as a spinner.

3) With three successive spins, what is the probability of not getting three negative outcomes in a row?

4) Calculate the expected value. If the distribution represents a game, is the game fair?

5) Calculate the variance and standard deviation.

Answers to Problems Representing Top Five Statistical Concepts 1) ¯ x = 2.51, median = 2.5, mode = 2.4, 2.6, 2.9

2)range = 0.8, s

≈ 0.07656, s ≈ 0.2767

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3)

4) 2.1 ≤ x ≤ 2.9, 0 ≤

≤ 0.4, class widths =

= 0.16

The distribution is bimodal (has two humps). The median occurs in the center, being the point that divides the lower 50% of data from the upper 50% of data. For this sample, the mean very nearly equals the median.

These measures of central tendency are not representative statistics because the sample has a dearth of data in the dead center. Instead, the sample has typical values just to the right and just to the left of the center.

5) 2 ≤ x ≤ 3; x-scale = 0.1; 5-number summary ={2.1, 2.3, 2.5, 2.7, 2.9} = {low number, lower quartile, median, upper quartile, high number}

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Answers to Problems Representing Top Five Probability Concepts 1) p = 0.625

2)

3) p = 1 − (0.375)

≈ 0.947 4) µ = 0, yes, game is fair 5) σ

= 40 and σ ≈ 6.3

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