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Use the slingshot to pop as many balloons as you can to let the fish drop back into the sea. Each round is a set of ten balloons. When all ten balloons have passed or been popped you will get a score. Drag the x to the column which matches your score. As you complete each round you will build a line plot using your scores as data.

Grade 2 » Measurement & Data

CCSS.MATH.CONTENT.2.MD.D.9

*Represent and interpret data:* Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

Balloon Pop Statistics: Mean, Median, Mode, and Range

Measurement and Data

Third Grade through Sixth Grade (can be used even in high school or university introductory courses in data analysis)

Students will understand and calculate measures of central tendency (mean, median, and mode) and variability (range) using a line plot to summarize and describe a quantitative distribution.

CCSS.MATH.CONTENT.6.SP.A.1; CCSS.MATH.CONTENT.6.SP.A.2; CCSS.MATH.CONTENT.6.SP.A.3; CCSS.MATH.CONTENT.6.SP.B.4; CCSS.MATH.CONTENT.6.SP.B.5;

- Computers or tablets for each child directed to http://toytheater.com/balloon-pop/
- A teacher’s computer or tablet that can be projected on a wall or board
- Chalk board or whiteboard
- Paper and pencils for students

Begin by instructing the students to play one round of Balloon Pop and then stop. Ask them to share with you the number of balloons they popped. Ask them if they think that their score really represents how good they are at the game. If they played again, would they knock down as many balloons?

X | ||||||||||

X | X | X | ||||||||

X | X | X | X | X | ||||||

X | X | X | X | X | X | |||||

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

The mode gives us the most common score in our data. Looking at our line plots, all we have to do is look for the tallest column of X’s to find our mode. Let’s say in your 15 trials playing the game, you got the above distribution of scores. This means that there are the most X’s above the 5 balloons point in the line plot because you tended to knock down 5 balloons the most frequently. Therefore, the mode is 5 balloons.

Ask students to calculate their own mode in their own line plots by looking for the column with the most X’s. Ask around the class to see who had the highest mode. Did anyone get a mode of 10? If they did, ask them how many 10s they got.

The median is the center data point around which half of the other scores fall below and half of the other scores fall above. To calculate the median, you need to count the number of Xs in the table. (Ensure that your students have an odd number of Xs to simplify this.). Take the total number of Xs and add 1, then divide by 2.

In the example above, the answer is the 8th X. Find where the 8th x is in the line plot starting from the top or the bottom. That means we’d see that the first x falls under three, then four X’s under five (that’s a total of 5 x’s so far), then there are 3 more X’s under 6 which is where the 8th case is. That means that the median score is 6, or, to interpret this more meaningfully, we could say that half of the time we popped six or more balloons and half the time we popped six or fewer balloons.

Ask the students to calculate their own median from their own line plots. Assuming everyone did 15 rounds, they will all be looking for the 8th score in the series.

This one is a bit more work to calculate but Balloon Pop simplifies it for us by calculating the total score for all of our trials. All we need to do is take that total score and then divide by the number of trials. In our case, our mean is calculated as so: 96/15=6.4. To interpret this value, we would say that on average we popped 6.4 balloons.

Ask your students to calculate their mean scores by taking their total score divided by the number of rounds they played. Ask them to share their scores. Who got the highest number of popped balloons on average?

The range is the simplest measure of variability and is easy to calculate. All you do is take the lowest score in the distribution and subtract it from the highest. In our example, the lowest score we got was 3 and the highest we got was 9. This means that our range is 9-3=6. To interpret this value, we would say that we have a 6 balloon range of scores.

Ask students to share their ranges. Who has the smallest range? Who has the largest? Allow students to notice that a bigger range doesn’t mean higher average scores and a lower range doesn’t mean lower scores. One could have a range of zero if they always knock down 10 balloons and also if they always miss all the balloons.

Have the students do another round of 15 games (this will also help them to refocus their attention and give their brains a break!) and then have them calculate the mode, the median, the mean, and the range for their new scores.

Ask students to reflect on other contexts in which measures of central tendency and variability might be useful. This could also extend into a homework assignment asking students to find examples of measures of central tendency in the media and write an assignment about how they are used.

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