Displaying Quantitative Data Ch. 4 Displaying Quantitative Data

Discuss with your group: “What do you think will be different in charts that display quantitative data compared to categorical data?” Warm-Up

Histograms look a lot like bar charts but are used for quantitative variables! Make sure to pay attention to the differences while watching this video: https://www.youtube.com/watch?v=JsEwJ D1mYpU Histograms

For histograms, slice up the entire span of values covered by the variable into equal-width sections called bins Replacing the counts with % is called relative frequency histogram

“I feel the pressure, under more scrutiny, and what I do “I feel the pressure, under more scrutiny, and what I do? Act more stupidly. bought more jewelry, more Louis V, my momma couldn't get through to me.” - ???

Money made from Kanye’s albums in the U. S

You can also create histograms with graphing calculators! (p. 54)

Grades Frequency 60s 2 70s 4 80s 7 90s 5 100 1

Stem-and-Leaf Display Stem-and-Leaf plots contain all the information found in histograms but displayed differently Stem-and-Leaf Display

What if the data are not numbers with a tens and ones digits. i. e. 1 KEY: 1|5 = 1.5

What about big numbers such as 210,350,300,290,440? KEY: 2|1 = 210 , 2|10 = 210

We can use stem and leaf plots to compare data collected from two groups. How? Comparing Two Groups

A dotplot is a simple display that places a dot along an axis for each case in the data Dotplots

Split into halves like usual and record data for each person’s shoe size (in cm) in your group. Create ??? that represents this data. (Make sure everyone keeps this data, we will be using it in the future!) Class activity

What are the advantages of each of these graphs: histogram, stem and leaf plot, and dotplot?

What is the Center?

After drawing a histogram for our data, we want to describe the distribution Three things to look at: shape, center, and spread Shape, Center, & Spread

Shape

Humps on a graph are called modes, graphs can be unimodal, bimodal, or multimodal If all data on a graph are the same height, than it is uniform

Graphs can be symmetric If not, more data values lie on one side of the middle Tails are the thinner ends of a distribution If one tail stretches out further than the other, the graph is said to be skewed towards the long tail

Outliers are data values that stand off from the body of the distribution They can affect the measurements of data significantly, so it is always important to identify them Cont.

Finding the center of a graph may not always be simple, depending on the shape What is the easiest graph shape for locating a center? Center

Describing spread involves looking if the data is tightly clustered around the center or spread out Spread will be expanded on in later chapters Spread

Comparing Distributions A lot of times, comparing two or more distributions can be very interesting (i.e. salaries of jobs in the medical field vs. engineering) Look at the center, shape, and spread of each distribution to compare Comparing Distributions

When data is collected in a specific order (i. e When data is collected in a specific order (i.e. years), there may be patterns Use timeplots to observe any noticeable patterns/behavior Timeplots

We can make a skewed distribution more symmetric by re-expressing the data There are many ways of re-expression such as taking the square root or logarithm of each data value Improving Symmetry

Cont.

https://www.youtube.com/watch?v=Lrgp KjiQbQw