Most of our day was dedicated to our Data Analysis Project. The assignment was designed to compare and contrast experimental and theoretical probability. The instructions were to use MnM's or Skittles, or some such colorful candy. This is our last official Grade seven Math task. Finishing it off with a bag of crappy candy wasn't going to cut it. We went with Lindt truffle balls instead.

From our studies ...

Purpose: to first determine the theoretical probability for each color in a bowl of Lindt Balls and then run an experiment to compare the experimental probability of pulling out each colour to its theoretical probability.

Method

1. Sort a bag of Lindt Balls into individual colours
2. Count and record how many colours in each category
3. Place balls in bowl and mix well.
4. Set aside for later
5. Add up all the balls to find total number of balls

Calculations

Total number of balls = 4 + 4 + 9 + 12 + 17 + 12 + 11 = 8 + 20 + 12 + 17 + 12 = 20 + 20 + 29 = 69

Medium, Mode, and Mean of Numbers * Medium
4, 4, 9, 12,12, 17
9 + 12 = 21/2 = 10.5 = 11
2

Mode
4 and 12 (bimodal)

Mean
69/7 = 9.86 = 10

Conclusions on Theoretical Probability

Looking at the Table 1.1, we can see that orange Lindt balls are most common, at 25 percent of the total. Black and purple/pink are least common, both at 6 percent of the total. There are 2 modes. Black and purple/pink each represent a mode of 6 percent of the total. Blue and green balls represent a mode of 17 percent. Our data was bimodal. I was most likely to get around 10 of each colour as represented by the mean. Median was 11.

Section Two: Experimental Probability

Method

1. Obtain the bowl of Lindt balls made in section one

2. To avoid bias, put on a blindfold

3. Randomly pull out one chocolate

4. Remove blindfold

5. Record the ball colour in the tally table below

6. Replace the chocolate back in the bowl

7. Remix Chocolates

8. Repeat steps 2-8 fifty times.

(lll) = 5 tallies

Section Three: Findings

I compared my experimental and theoretical probabilIties. Theoretically, orange should have been the most common Lindt Ball chosen at random, at 25 percent. However, experimentally, I found that blue, at 20 percent, was the most common colour chosen. Black and purple/pink should have been the least common colours chosen. Purple/pink was indeed chosen at the lowest frequency, 10 percent, but surprisingly green was also the least commonly chosen, also at 10 percent. Theoretically, green should have been chosen at around 17 percent. Yellow had the same experimental and theoretical probability at 16 percent.

The experimental and theoretical probability for red was close at 14 percent and 13 percent, respectively. Black had a experimental probability, 12 percent, twice its theoretical probability of 6 percent. Orange’s experimental probability, 18 percent , was lower then its theoretical probability by 7 percent. Perhaps if I had run the experiment a hundred times, I would have found that experimental and theoretical probabilities would have come closer to merging. For comparison, I have added a pie chart for the theoretical probabilities.