What is Numerical Data?

Numerical Data Responses are numbers Example: How many siblings do you have? (Answers might be 3, 2, 0, 1, 1, 2) Most of these questions can be phrased as “How Many…. ?”

Numerical or Categorical Data? How many places have you lived? What is your favorite pizza topping? How many teeth have you lost? How many inches long is your foot? Who is your favorite singer? What kind of ice cream do you like? What score did you get on your math test? #1,3,4,7 are numerical. Students are sometimes confused because we talk about total numbers in categories (like 8 kids like pepperoni) when analyzing data, but they can focus on what is the survey question and what response would each person give? For example, we might ask “What’s your favorite pizza topping?” and the responses would be words like “mushroom” not numbers like “3”.

Make up a survey question of your own Share your question with a partner. They must decide whether it’s “Numerical” data or not. Ask a few partners to share out their questions for the group to consider. Especially if a group is debating about it. Let the class consider it and decide.

How to organize numerical data Line plots (3rd grade) 3 4 5 6 7 Stem and leaf plots (5th grade) 5 0 1 1 4 7 6 5 6 7 7 7 2 Histograms (new in 7th grade!)

What’s a histogram? Ask students to look at this graph and tell what they notice Bars are touching (unlike bar graph) Each column represents a range of scores Specific scores not shown (one person scored between 71-75, but we don’t know his exact score) Ranges are evenly distributed (5 points in each ‘bin’) Doesn’t say 80-85 and 85-90, because which column would 85 go in?

“That’s not fair!” What’s wrong here? This graph is not correct because 90-100 doesn’t show an equal interval (30 point range in the others). *Important – students can get turned around between the numeric responses to the survey and the number of people who answered that way. For example, they may be thinking they want different ranges so there’s 3 people in each interval, but this is not important.

Why is that bar missing? 0 people spent that amount of time on homework – notice we still leave space for that interval, though. Imagine a number line across the bottom – we wouldn’t just leave some numbers out.

Try to make your own histogram We asked a class to measure their hands in centimeters. Here are their answers: 20, 14, 15, 15, 18, 19, 21, 17 How would you organize these numbers in a histogram? Discuss: What decisions did you have to make? (ranges – only need between 14-21, how many numbers should go in each ‘bin’? How tall would the columns have to be?)

BONUS (teacher use) You can help change a line plot to a histogram by ‘boxing in’ the data. 5 6 7 8 9 10 11 12 13 14 This slide for teacher information only – if students struggle with overlapping intervals on histograms (like 0-5, and 5-10), you might start by converting a line plot since you wouldn’t box in the same number twice.