Histograms

I've often wondered where one finds histograms in real life.  We find them in the textbooks but I've never really used them in real life so I needed to find something I could share with the students.

When it comes to creating histograms, this article is a great one for introducing histograms, types of histograms, example of taking data and turning it into a histogram, creating histograms using excel, and information on interpreting histograms.  There are five types of histograms students are likely to run across in real life.

The first is a normal distribution which is lower on both ends, rising to its maximum in the middle so both sides are roughly the same.  Then there is the binomial distribution has two equal peaks with a dip in the middle.  A histogram could be a right skewed distribution which has the peak on the x = 0 and it decreases from there while the left skewed distribution begins at its lowest point at x = 0, and increases to its peak on the right side.  A right skewed distribution is a positive distribution while the left skewed distribution is negatively distributed.  The final distribution is a random distribution which has a variety of peaks and valleys running through the whole graph.

Scholastic has a lesson designed to help students understand that a histogram is a type of bar graph showing frequency, connecting the definition of mean to histograms, and they learn how actuaries use the histograms.  The activity has students graph claims paid out from a number of Hurricanes and Tropical Storms.  Once the information is graphed students then interpret the information in order to answer certain questions.

Shoder has a nice lesson utilizing interactive activities to help students learn more about interpreting histograms, intervals, scales, and sample problems.  The lesson plan includes everything needed to complete the lesson along with full instructions.

I also found a lovely lesson using a histogram from the New York Times online edition as the basis of a "What do you notice?" and "What do you see?" activity.  The histogram looks at the meals sold by the Chipolte restaurants in terms of calories and dishes.

The distribution shows all the meals sold by the restaurant to the public.  The most of the dishes sold are in the 1000 calorie range with a full day of sodium included.  The dish is a meat burrito with cheese, salsa, guacamole, sour cream, along with rice and beans.  The article goes on to present two more histograms, one looking at the amount of sodium and the other grams of saturated fats.  At the end, it gives sample meals and the total calories.

The lesson begins by having students look at the histogram and write down their answers to "What do you notice?" and "What do you wonder?" but its done in pairs.  One student brainstorms to the first question while the other records their thoughts and then the students switch.  They repeat the process for the second question. They then share their thoughts before developing inquiring questions to investigate in deeper detail.

Let me know what you think, I'd love to hear.  Have a great day.