Histogram A frequency plot that shows the number of times a response or range of responses occurred in a data set.

It can only be used to show continuous data What is a histogram? A histogram is like a bar chart, but there are some important differences. It can only be used to show continuous data The bars on a histogram touch. The bars found on a bar graph do not touch. It can only be used to show numerical data The data is always grouped.

Histogram: Pros and Cons Advantages: Visually strong Good for determining the shape of the data Disadvantages: Cannot read exact values because data is grouped into categories More difficult to compare two data sets

How do you make a histogram? Create a frequency table Count how many occurrences in the data Be sure to create equal intervals Label the x and y axis Choose a scale to label X and Y axis do not need to have the same scale Draw a bar for each interval. The height of the bar is the frequency for that interval. Bars must touch but not overlap.

Let’s try! A study collected the number of hours children watch TV. The collected the following number of hours: 8, 7, 5, 4, 9, 6, 3, 1, 7, 5, 4, 2, 3, 5, 2, 4, 3, 5, 7, 3, 6, 5, 3, 7, 2, 9, 6, 7, 8, 5, 4, 7, 3, 9, 4, 7, 3, 1, 2, 8, 5, 3, 7, 9, 5 1 6 2 7 3 8 4 9 5

Create the frequency table Number of hours of TV III 6 II 1 IIII IIII 7 IIII 2 8 IIII IIII 3 9 IIII I 4 IIII III 5 Frequency Number of hours of TV 14 1-3 16 4-6 15 7-9

Label x and y axis (Choose your scale!) Draw the bars

How To Compare Distributions Analyzing Histograms and Dot Plots

Analyzing Histograms When you compare two or more data sets, focus on the following four features: Center Spread Shape Unusual Features

Analyzing Histograms and Dot Plots Center (It is the MEDIAN)! EXAMPLE 5 6 7 8 9 10 11 12 13 14 15

To Find the Center: List out the numbers in order, smallest to largest, then find the median. 6,6,6,7,8,8,8,9,10,10,10,10,10,11,12 Center 5 6 7 8 9 10 11 12 13 14 15

Your Turn!

Analyzing Histograms and Dot Plots Spread (RANGE) Highest – Lowest = Range Less Spread 4 EXAMPLES More Spread 8

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Analyzing Histograms and Dot Plots Shape The shape of a distribution is described by symmetry, amount of skew, number of peaks, etc. Skewed Left EXAMPLES Symmetric, Unimodal Skewed Right

3 Overall Shapes: Normal/Symmetrical: Skewed left: Skewed right: The shape is symmetrical around the middle. Skewed left: Most of the data is to the right, with a long tail to the left. Skewed right: Most of the data is to the left, with a long tail to the right.

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Analyzing Histograms Unusual Features Unusual features refer to gaps: areas of the distribution where there are no observations and Outliers: a data point that stands out from the rest. (1.5 times the IQR) EXAMPLES Gap Outlier

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Graphical Displays for Data Homework Classwork/HOMEWORK Graphical Displays for Data Homework