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Analyzing Sugar Content in Cereals: A Statistical Study

Explore the sugar content in different cereals, calculate percentages, teaspoons, and pounds of sugar, and analyze data using box plots and the Empirical Rule. Determine outliers and find the standard deviation.

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Analyzing Sugar Content in Cereals: A Statistical Study

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  1. Topic 5 Review Part 1: Concept Test Review

  2. thespian : theater :: musician : • instrument • cd • symphony • movie

  3. Cereal K/A Grams Sugar (in 1 oz) Golden Crisp Apple Jacks Cocoa Pebbles Cap’n Crunch Alpha Bits Kellogg’s Raisin Bran Double Dip Crunch Life, Cinnamon Frosted Mini-Wheats Just Right Fruit & Fiber Date Corn Chex Rice Chex Cheerios Puffed Rice K K K K K A A K A A A A A A A 15 14 13 12 11 9 8 8 7 7 5 3 2 1 0 Amount of Sugar in Cereals

  4. Cereal K/A Grams Sugar (in 1 oz) Golden Crisp Apple Jacks Cocoa Pebbles Cap’n Crunch Alpha Bits Kellogg’s Raisin Bran Double Dip Crunch Life, Cinnamon Frosted Mini-Wheats Just Right Fruit & Fiber Date Corn Chex Rice Chex Cheerios Puffed Rice K K K K K A A K A A A A A A A 15 14 13 12 11 9 8 8 7 7 5 3 2 1 0 One ounce is approximately 28.4 grams. What percentage of the weight of a box of Golden Crisp is sugar? • 52.8% • 28.4% • 100 % • 68% • 18.9%

  5. Cereal K/A Grams Sugar (in 1 oz) Golden Crisp Apple Jacks Cocoa Pebbles Cap’n Crunch Alpha Bits Kellogg’s Raisin Bran Double Dip Crunch Life, Cinnamon Frosted Mini-Wheats Just Right Fruit & Fiber Date Corn Chex Rice Chex Cheerios Puffed Rice K K K K K A A K A A A A A A A 15 14 13 12 11 9 8 8 7 7 5 3 2 1 0 A teaspoon of sugar weighs about 4 grams. How many teaspoons of sugar are in a 1-ounce serving of Golden Crisp? • 1 • 2.35 • 15 • 3.75

  6. Cereal K/A Grams Sugar (in 1 oz) Golden Crisp Apple Jacks Cocoa Pebbles Cap’n Crunch Alpha Bits Kellogg’s Raisin Bran Double Dip Crunch Life, Cinnamon Frosted Mini-Wheats Just Right Fruit & Fiber Date Corn Chex Rice Chex Cheerios Puffed Rice K K K K K A A K A A A A A A A 15 14 13 12 11 9 8 8 7 7 5 3 2 1 0 We divided the list into “kid” and “adult” cereals as indicated by a K or an A. If the cereal box had a cartoon character, a child’s toy, or a picture of children on the front, we classified it as a kid’s cereal (K). Otherwise, the cereal was classified as an adult cereal (A).

  7. Cereal K/A Grams Sugar (in 1 oz) Golden Crisp Apple Jacks Cocoa Pebbles Cap’n Crunch Alpha Bits Kellogg’s Raisin Bran Double Dip Crunch Life, Cinnamon Frosted Mini-Wheats Just Right Fruit & Fiber Date Corn Chex Rice Chex Cheerios Puffed Rice K K K K K A A K A A A A A A A 15 14 13 12 11 9 8 8 7 7 5 3 2 1 0 If you eat a 1-ounce serving of Cocoa Pebbles every morning for a year, how many grams of sugar would you eat? • 5755 • 4745 • 13 • 365

  8. Cereal K/A Grams Sugar (in 1 oz) Golden Crisp Apple Jacks Cocoa Pebbles Cap’n Crunch Alpha Bits Kellogg’s Raisin Bran Double Dip Crunch Life, Cinnamon Frosted Mini-Wheats Just Right Fruit & Fiber Date Corn Chex Rice Chex Cheerios Puffed Rice K K K K K A A K A A A A A A A 15 14 13 12 11 9 8 8 7 7 5 3 2 1 0 How many pounds of sugar is this? (one pound is about 454 grams.) • 10.36 • 14.56 • 14 • 10.45

  9. Cereal K/A Grams Sugar (in 1 oz) Golden Crisp Apple Jacks Cocoa Pebbles Cap’n Crunch Alpha Bits Kellogg’s Raisin Bran Double Dip Crunch Life, Cinnamon Frosted Mini-Wheats Just Right Fruit & Fiber Date Corn Chex Rice Chex Cheerios Puffed Rice K K K K K A A K A A A A A A A 15 14 13 12 11 9 8 8 7 7 5 3 2 1 0 Give the 5-number summary, the range, and the inter-quartile range for the number of grams of sugar in all 15 types of cereal. • 0, 3, 7, 12, 15, 15, 9 • 3, 4, 8, 12, 15, 16, 8 • 0, 3, 8, 12, 15, 15, 9 • 1, 2, 3, 4, 5, 4, 2

  10. Construct a box-and-whisker plot of the cereal data

  11. Cereal K/A Grams Sugar (in 1 oz) Golden Crisp Apple Jacks Cocoa Pebbles Cap’n Crunch Alpha Bits Kellogg’s Raisin Bran Double Dip Crunch Life, Cinnamon Frosted Mini-Wheats Just Right Fruit & Fiber Date Corn Chex Rice Chex Cheerios Puffed Rice K K K K K A A K A A A A A A A 15 14 13 12 11 9 8 8 7 7 5 3 2 1 0 Are any of the cereals outliers? • Yes • No

  12. Cereal K/A Grams Sugar (in 1 oz) Golden Crisp Apple Jacks Cocoa Pebbles Cap’n Crunch Alpha Bits Kellogg’s Raisin Bran Double Dip Crunch Life, Cinnamon Frosted Mini-Wheats Just Right Fruit & Fiber Date Corn Chex Rice Chex Cheerios Puffed Rice K K K K K A A K A A A A A A A 15 14 13 12 11 9 8 8 7 7 5 3 2 1 0 Looking at the dotplot of this data, does the Empirical Rule apply? • Yes • No

  13. Please fill in the blanks for the empirical rule: with ______________ distributions, about __% of the observations fall within one standard deviation of the mean, about__% of the observations fall within two standard deviations of the mean, and about __% fall within three standard deviations of the mean. • Mound-shaped, 48, 69, 100 • Skewed Right, 68, 95, 99.7 • Symmetric, 68, 98, 99.8 • Mound-shaped, 68, 95, 99.7

  14. Cereal K/A Grams Sugar (in 1 oz) Golden Crisp Apple Jacks Cocoa Pebbles Cap’n Crunch Alpha Bits Kellogg’s Raisin Bran Double Dip Crunch Life, Cinnamon Frosted Mini-Wheats Just Right Fruit & Fiber Date Corn Chex Rice Chex Cheerios Puffed Rice K K K K K A A K A A A A A A A 15 14 13 12 11 9 8 8 7 7 5 3 2 1 0 Find the standard deviation of the cereals by hand or with a calculator. • 4.78 • 7.67 • 4.61 • 15 • 8

  15. A set of 10 math scores has a mean of 50 and a standard deviation of 8.  A set of 12 English scores has a mean of 55 and a standard deviation of 2. Use the empirical rule to find the following:Approximately how many of the 10 math exam scores are between 42 and 58?(Note: assume both exam scores have a mound-shaped distribution.) • 4 • 5 • 6 • 7 • 8 • 9

  16. A set of 10 math scores has a mean of 50 and a standard deviation of 8.  A set of 12 English scores has a mean of 55 and a standard deviation of 2. Use the empirical rule to find the following:Approximately how many of the 12 English exam scores are between 61 and 49? • 8 • 9 • 10 • 11 • 12

  17. A set of 10 math scores has a mean of 50 and a standard deviation of 8.  A set of 12 English scores has a mean of 55 and a standard deviation of 2. Use the empirical rule to find the following:What is the z-score of an Math exam that is 24 points below the mean? • 3 • -3 • 68% • -2 • 99.7% • 95%

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