WARM - UP What percent of students are Females in a freshman class? Freshman Sophomore Junior Senior Male 127 53 50 57 Female 71 47 43 42 287 203 198 100 93 99 490 What percent of students are Females in a freshman class? What percent of the Freshman class students are females? What percent of males represent the senior class? What percent of the senior class are males? 14.5% 35.9% 19.9% 57.6%

WARM – UP Eye Color Blue Brown Hazel 3 or below 14.0% 61.0% 25.0% 4+ 13.5% 60.8% 25.7% Blue Brown Hazel 3 or below 129 561 230 4+ 73 330 139 GPA 920 542 Determine if an association exists between ones eye color and ones GPA at a large school. Justify your answer by examining the conditional distribution of eye color among the two levels of GPA. Since the Distribution of eye color is relatively the same for each GPA level, eye color had little to do with your GPA. (No Association = Independent variables)

Displaying Quantitative Distributions Chapter 4 Displaying Quantitative Distributions I. Histograms: A bar graph representing quantitative values and frequency.

II. Dotplots: A dotplot places a dot along an axis for each case in the data instead of a bar. The dotplot to the right shows Kentucky Derby winning times, plotting each race as its own dot. You might see a dotplot displayed horizontally or vertically.

Describing Distributions When describing a distribution, comment on: Center, Unusual features, Shape, and Spread. When describing a distribution, comment on: Center, Unusual features, Shape, and Spread. You are expected to…. CUSS

CENTER: The center is a numerical value that attempts to summarize the approximate ‘typical value’ of the distribution. “Average” UNUSUAL: You should always mention any stragglers, or outliers, that stand off away from the body of the distribution. If any gaps are present in the distribution, we might have data from more than one group.

SHAPE: 1. A histogram with one main peak is dubbed unimodal; histograms with two peaks are bimodal. 2. A distribution with NO mode is called Uniform and is roughly flat.

SHAPE (continued): 3. A distribution is symmetric if the right and left sides (tails) are mirror images of each other. Skewed to the Right Appr. Symmetric Skewed to the Left

SPREAD: RANGE = Highest - Lowest The spread is a numerical summary of how tightly the values are clustered around the center.

Displaying Quantitative Distributions with a Histogram Ex.) Thirty seeds were planted in each of 8 containers with an experimental fertilizer. After 2 weeks the number of germinated seeds was then recorded. 12, 15, 12, 22, 10, 14, 16, 20 Center - ≈ 14 Unusual - Nothing Shape - ≈ Skewed Right Spread - ≈ 12 data 15 graph 4 3 2 1 0 Frequency 0 3 6 9 12 15 18 21 24 Number of germinating seeds

Describe the following Distribution. Shape – Skew Right Center - ≈ 18 Spread - ≈ 38 15 10 5 Shape – ≈ Symmetric Unusual- Outlier@110 Center - ≈ 82 Spread - ≈ 38 No. of Customer Service Phone Calls 0 10

COMPARE the following Distribution. 15 10 5 No. of Customer Service Phone Calls B 0 10 Shape: A – Skew Right B – Appr. Normal Center: B has a LARGER center than A Spread: A and B have about the SAME Spread

HW: Page 65: 5-10 Center ≈ 10 Unusual - NOTHING Shape ≈ Bimodal Main Peak = Skewed Right Spread ≈ 35

HW: Page 65: 5-10 Shape ≈ Unimodal = Skewed Right Center ≈ 3 Spread ≈ 8

HW: Page 65: 5-10 Shape ≈ Bimodal Shape ≈ Skewed Right Center ≈ 12 Spread ≈ 24 Shape ≈ Symmetric Center ≈ 46 Spread ≈ 26

HW: Page 65: 5-10