Drill Construct a Histogram to represent the data of test score averages in 20 cities using 5 Bars. Test Averages {62, 68, 72, 58, 83, 91, 70, 82, 68, 56, 88, 55, 99, 76, 80, 54, 68, 72, 93, 81}

One Possible Solution 543210 50-60 60-70 70-80 80-90 90-100

AP Statistics Day 3 Objective: students will be able to construct a box plot by hand and also to construct stem plot to represent a group of data.

Stemplots Each data point is represented by a single number (leaf) associated with a more significant number (stem) Rounding can help the shape of the distribution become more noticeable.

Stemplots (Stem and Leaf) The Stem or left side of the plot contains all the digits in each given value except for the rightmost digit. The Leaf or the right side of the plot contains the last digit in each number which is matched up with its corresponding “stem”.

Example of Data {23, 26, 28, 28, 31, 34, 38, 39, 41, 47, 56, 60, 61} Stem Leaf 2 3 6 8 8 3 1 4 8 9 4 1 7 5 6 0 1

Back To Back Stemplots 9th Grade Scores {16, 21, 24, 26, 26, 31, 35, 36, 41, 44, 44, 44, 49} 10th Grade Scores {8, 18, 22, 26, 29, 29, 33, 36, 40, 42, 47, 47, 49, 50, 50}

Back-to-Back Stemplots 9th Grade Stem 10th Grade 8 6 1 6 6 4 1 2 2 6 9 9 6 5 1 3 3 6 9 4 4 4 1 4 0 2 7 7 9 5 0 0

Split Stem Plots Is when you make a stem plot where each stem appears twice and the leaves from 0 – 4 correspond to the first stem and the leaves 5 – 9 correspond to the second stem. 2 0 0 2 3 4 5 5 8 9 3 1 1 3 4 4 5 5 6 8 9 9 4 0 0 0 3 7 7 8 8 8

Shape of the Distribution Shape: What shape does the data take? Symmetric or Not? Are there Outliers? Are there any Gaps in the data? Is the Distribution Skewed? WHY!!!!

Describing Shape Uniform Bell Symmetric Skew Bimodal

Uniform 1 13489 2 3 4 5 6 7 8 9 10

Bell and Symmetric 1 2 13 3 135 4 1357 5 135579 6 1355779 7 8 9 10

Skewed 1 2 1357 3 1355779 4 135579 5 6 7 13 8 9 10

“Skewness” We always say a graph is skewed towards the “tail” of the data. Skewed to the right Skewed to the left

Bimodal (Two modes) 1 2 1357 3 1355779 4 135579 5 6 13 7 8 9 10

Box Plots Are created by finding the 5 Number Summary and Plotting those 5 points on a number line, then creating the boxplot.

5 Number Summary Smallest Value (lower extreme) Lower Quartile (Q1) Median Upper Quartile (Q3) Largest Value (upper extreme)

Median To find the median of a set of data with “n” values simply use the formula and that will tell you where the middle term is once the pieces of data are in numerical order. Quartiles * The quartiles are found by finding the median of the data set on the right side of the median and the median of the data set on the left side of the median.