Question
In: Statistics and Probability
1. Find the mean, standard deviation, and five number summaries in each type of M&M (plain...
1. Find the mean, standard deviation, and five number summaries
in each type of M&M (plain and peanut) for the total number of
M&Ms in each bag.
2. Find the mean, standard deviation, and five number summaries for
the weights of Skittles in each bag.
3. Find the mean, standard deviation, and five number summaries for
the weights of Plain M&Ms in each bag.
4. Use the information found in Step 1 to draw side by side
boxplots, comparing the total number of M&Ms in each bag of
plain and peanut M&Ms. Discuss the shape of each.
5. Use the information found in Steps 2 & 3 to draw side by
side boxplots, comparing the weights of M&Ms in each bag of
Plain and the weights in each bag of Skittles. Discuss the shape of
each.
6. Write a summary paragraph about your data. Make at least 4
different observations about your data and/or boxplots using your
statistical knowledge.
Plain M&M: 15,14,15,15,14,16,15,14,15,16,16,14,15,14,15,15,14,17,17,15,15,17,14,16,14,16,17,13,16,16, 15, 17,6,14,16,15,13,15,17,15,17,14,15,14,16,14
Peanut Butter: 8,6,8,7,8,8,8,7,3,7,10,7,7,6,8,7,8,7,7,7,8,8,8,7,9,7,8,8,7,8,8,8,6,7,8,8,8,7,6,7,7,8,8,8,14,8,8,7,6
Skittles: 15,14,15,14,14,15,15,14,15,15,14,15,15,15,14,15,20,15,15,15,14,14,15,15,15,16,12,15,15,14, 14,15,14,15,14,14,14,13,16
Solutions
Expert Solution
1)
Plain M&M:
mean and standard deviation
| data | data-mean | (data - mean)2 |
| 15 | 0.0435 | 0.00189225 |
| 14 | -0.9565 | 0.91489225 |
| 15 | 0.0435 | 0.00189225 |
| 15 | 0.0435 | 0.00189225 |
| 14 | -0.9565 | 0.91489225 |
| 16 | 1.0435 | 1.08889225 |
| 15 | 0.0435 | 0.00189225 |
| 14 | -0.9565 | 0.91489225 |
| 15 | 0.0435 | 0.00189225 |
| 16 | 1.0435 | 1.08889225 |
| 16 | 1.0435 | 1.08889225 |
| 14 | -0.9565 | 0.91489225 |
| 15 | 0.0435 | 0.00189225 |
| 14 | -0.9565 | 0.91489225 |
| 15 | 0.0435 | 0.00189225 |
| 15 | 0.0435 | 0.00189225 |
| 14 | -0.9565 | 0.91489225 |
| 17 | 2.0435 | 4.17589225 |
| 17 | 2.0435 | 4.17589225 |
| 15 | 0.0435 | 0.00189225 |
| 15 | 0.0435 | 0.00189225 |
| 17 | 2.0435 | 4.17589225 |
| 14 | -0.9565 | 0.91489225 |
| 16 | 1.0435 | 1.08889225 |
| 14 | -0.9565 | 0.91489225 |
| 16 | 1.0435 | 1.08889225 |
| 17 | 2.0435 | 4.17589225 |
| 13 | -1.9565 | 3.82789225 |
| 16 | 1.0435 | 1.08889225 |
| 16 | 1.0435 | 1.08889225 |
| 15 | 0.0435 | 0.00189225 |
| 17 | 2.0435 | 4.17589225 |
| 6 | -8.9565 | 80.21889225 |
| 14 | -0.9565 | 0.91489225 |
| 16 | 1.0435 | 1.08889225 |
| 15 | 0.0435 | 0.00189225 |
| 13 | -1.9565 | 3.82789225 |
| 15 | 0.0435 | 0.00189225 |
| 17 | 2.0435 | 4.17589225 |
| 15 | 0.0435 | 0.00189225 |
| 17 | 2.0435 | 4.17589225 |
| 14 | -0.9565 | 0.91489225 |
| 15 | 0.0435 | 0.00189225 |
| 14 | -0.9565 | 0.91489225 |
| 16 | 1.0435 | 1.08889225 |
| 14 | -0.9565 | 0.91489225 |
five number summary
| Position | XXX (Asc. Order) |
| 1 | 6 |
| 2 | 13 |
| 3 | 13 |
| 4 | 14 |
| 5 | 14 |
| 6 | 14 |
| 7 | 14 |
| 8 | 14 |
| 9 | 14 |
| 10 | 14 |
| 11 | 14 |
| 12 | 14 |
| 13 | 14 |
| 14 | 14 |
| 15 | 14 |
| 16 | 15 |
| 17 | 15 |
| 18 | 15 |
| 19 | 15 |
| 20 | 15 |
| 21 | 15 |
| 22 | 15 |
| 23 | 15 |
| 24 | 15 |
| 25 | 15 |
| 26 | 15 |
| 27 | 15 |
| 28 | 15 |
| 29 | 15 |
| 30 | 15 |
| 31 | 16 |
| 32 | 16 |
| 33 | 16 |
| 34 | 16 |
| 35 | 16 |
| 36 | 16 |
| 37 | 16 |
| 38 | 16 |
| 39 | 16 |
| 40 | 17 |
| 41 | 17 |
| 42 | 17 |
| 43 | 17 |
| 44 | 17 |
| 45 | 17 |
| 46 | 17 |
Peanut Butter:
mean and standard deviation
| data | data-mean | (data - mean)2 |
| 8 | 0.4694 | 0.22033636 |
| 6 | -1.5306 | 2.34273636 |
| 8 | 0.4694 | 0.22033636 |
| 7 | -0.5306 | 0.28153636 |
| 8 | 0.4694 | 0.22033636 |
| 8 | 0.4694 | 0.22033636 |
| 8 | 0.4694 | 0.22033636 |
| 7 | -0.5306 | 0.28153636 |
| 3 | -4.5306 | 20.52633636 |
| 7 | -0.5306 | 0.28153636 |
| 10 | 2.4694 | 6.09793636 |
| 7 | -0.5306 | 0.28153636 |
| 7 | -0.5306 | 0.28153636 |
| 6 | -1.5306 | 2.34273636 |
| 8 | 0.4694 | 0.22033636 |
| 7 | -0.5306 | 0.28153636 |
| 8 | 0.4694 | 0.22033636 |
| 7 | -0.5306 | 0.28153636 |
| 7 | -0.5306 | 0.28153636 |
| 7 | -0.5306 | 0.28153636 |
| 8 | 0.4694 | 0.22033636 |
| 8 | 0.4694 | 0.22033636 |
| 8 | 0.4694 | 0.22033636 |
| 7 | -0.5306 | 0.28153636 |
| 9 | 1.4694 | 2.15913636 |
| 7 | -0.5306 | 0.28153636 |
| 8 | 0.4694 | 0.22033636 |
| 8 | 0.4694 | 0.22033636 |
| 7 | -0.5306 | 0.28153636 |
| 8 | 0.4694 | 0.22033636 |
| 8 | 0.4694 | 0.22033636 |
| 8 | 0.4694 | 0.22033636 |
| 6 | -1.5306 | 2.34273636 |
| 7 | -0.5306 | 0.28153636 |
| 8 | 0.4694 | 0.22033636 |
| 8 | 0.4694 | 0.22033636 |
| 8 | 0.4694 | 0.22033636 |
| 7 | -0.5306 | 0.28153636 |
| 6 | -1.5306 | 2.34273636 |
| 7 | -0.5306 | 0.28153636 |
| 7 | -0.5306 | 0.28153636 |
| 8 | 0.4694 | 0.22033636 |
| 8 | 0.4694 | 0.22033636 |
| 8 | 0.4694 | 0.22033636 |
| 14 | 6.4694 | 41.85313636 |
| 8 | 0.4694 | 0.22033636 |
| 8 | 0.4694 | 0.22033636 |
| 7 | -0.5306 | 0.28153636 |
| 6 | -1.5306 | 2.34273636 |
five point summary
we are allowed to solve one qustion only
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