In our experiment our findings were:
- You can expect to receive 17 M&M’s in a “Fun Size” bag of M&M’s.
- You can also expect that to vary by 1 M&M.
- The lowest amount of M&M’s you can expect to receive in a “Fun Size” bag is 15 M&M’s.
- The highest amount of M&M’s you can expect to receive in a “Fun Size” bag is 19 M&M’s.
- “Fun Size” packages containing 18 M&M’s occurred the most.
- The shape of our graphs of data goes downhill to the left meaning there were more packages with high numbers of M&M’s rather than packages with low numbers of M&M’s.
• 12/11- Tyler bought 150 “Fun Size” packages of M&M’s. Tyler, Victoria, and Jackie did systematic random sampling and found measure of central tendencies, measures of dispersion, sample size, and population.
• 12/12- In class Jackie wrote out entire procedure as well as starting the report.
• 12/13- In class Courtney found Q1, Q3, and z-score and worked on the report. Out of class Courtney found objectives.
• 12/15- Tyler made all graphs on computer. Victoria did Empirical Rule and Chebychev’s Theorem. Courtney wrote summary of statistics, explained the data graphically, and explained the distribution. Jackie came up with deceptive statistic and typed the report.
• 12/18- Everyone helped do finishing touches on the report by making revisions and making sure math is correct.
• 12/28-1/2- Tyler and Jackie made Prezi.
The Average Amount of M&M's in a "Fun Size" Package
By Jackie Baker, Victoria Grace, Tyler Gross, and Courtney Caugh
Time Log
Deceptive Statistic
Sampling List
Amount of M&M's per "Fun Size" Bag
Data Information
Bag # Amount M&M’s
10 18
20 17
30 15
40 16
50 18
60 18
70 17
80 19
90 17
100 18
110 16
120 18
130 18
140 17
150 17
The histogram is deceptive because the minor grid lines and spacing makes it seem as it there were a lot more bags with 17 &18 M&M's rather than any other number.
Sampling Technique
Box and Whisker Plot
Systematic Sample
- Variable: The amount of M&M's in a " Fun Size" bag
- Population: 150 "Fun Size" bags
- We first figured out the sample size of the population
- Gave every bag a number using a random number generator
- Used a random number generator to pick a number to determine the starting bag (the first bag of M&M’s to be counted)
- Then counted out every 10th bag after that to decide which bags would be a part of the sample.
Measures of Central Tendency
Objective
Distribution
The objective of our project was find out the average amount of M&M's you can expect to receive from a "Fun Size" bag of M&M's.
The data distribution is skewed to the left and contains no outliers so the Empirical rule doesn't apply. However according to Chebychev's Theorum 75% of the data must lie within 2 standard deviations of the mean our data proves this to be true considering 93% of our data was within 2 standard deviations of the mean.
Percentiles
16 M&M's: (3/15)x100= 20th percentile
18 M&M's: (14/15)x100= 94th percentile
Z- Score
Histogram
16-18 M&M's: (16-17)÷1.03 = -.9709 = .1660
(18-17)÷1.03 = .9709 = .8340
• .8340-.1660 = .7180x100 = 71.8%
71.8% of “Fun Size” M&M bags will contain between 16 and 18 M&M’s.
Summary
Empirical Rule
Measures of Dispersion
Our distribution is not normal because...
- 73% of our data was 1 standard deviation away from the mean instead of 69%
- 93% was 2 standard deviations instead of 95%
- However 100% was 3 standard deviations away
Frequency
ChebyChev's Theorem
- Variance: (14.93323/(15-1))= 1.06 M&M’s^2
- Standard Deviation:(sqrt14.93323/(15-1))= 1.03 M&M's
- 5 Number Summary: 15 17 17 18 19
Q1 Q2 Q3
ChebyChev's Theorem was proven correct because at least 75% of our data was 2 standard deviations away (actually 93%) and at least 88.9% of our data was within3 standard deviations of the mean (actually 100%.)
Amount of M&M's in a "Fun Size Package