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Chapter 2: Problem 3

The Cereal FACTS report provides information on nutrition content of cereals as well as who they are targeted for (adults, children, families). We have selected a random sample of 20 cereals from the data provided in this report. Shown below are the fiber contents (percentage of fiber per gram of cereal) for these cereals. \({ }^{17}\) $$\begin{array}{rlr} \hline & \text { Brand } & \text { Fiber \% } \\ \hline 1 & \text { Pebbles Fruity } & 0.0 \% \\ 2 & \text { Rice Krispies Treats } & 0.0 \% \\ 3 & \text { Pebbles Cocoa } & 0.0 \% \\ 4 & \text { Pebbles Marshmallow } & 0.0 \% \\ 5 & \text { Frosted Rice Krispies } & 0.0 \% \\ 6 & \text { Rice Krispies } & 3.0 \% \\ 7 & \text { Trix } & 3.1 \% \\ 8 & \text { Honey Comb } & 3.1 \% \\ 9 & \text { Rice Krispies Gluten Free } & 3.3 \% \\ 10 & \text { Frosted Flakes } & 3.3 \% \\ \hline \end{array}$$ $$\begin{array}{llr} \hline & \text { Brand } & \text { Fiber \% } \\ \hline 11 & \text { Cinnamon Toast Crunch } & 3.3 \% \\ 12 & \text { Reese's Puffs } & 3.4 \% \\ 13 & \text { Cheerios Honey Nut } & 7.1 \% \\ 14 & \text { Lucky Charms } & 7.4 \% \\ 15 & \text { Pebbles Boulders Chocolate PB } & 7.4 \% \\ 16 & \text { Corn Pops } & 9.4 \% \\ 17 & \text { Frosted Flakes Reduced Sugar } & 10.0 \% \\ 18 & \text { Clifford Crunch } & 10.0 \% \\ 19 & \text { Apple Jacks } & 10.7 \% \\ 20 & \text { Dora the Explorer } & 11.1 \% \\ \hline \end{array}$$ (a) Create a stem and leaf plot of the distribution of the fiber content of these cereals. (b) Create a dot plot of the fiber content of these cereals. (c) Create a histogram and a relative frequency histogram of the fiber content of these cereals. (d) What percent of cereals contain more than \(7 \%\) fiber?

Short Answer

Expert verified
35% of cereals contain more than 7% fiber.

Step by step solution

01

Organize Fiber Data

Identify and list the fiber percentages of all 20 cereals in ascending order: 0.0, 0.0, 0.0, 0.0, 0.0, 3.0, 3.1, 3.1, 3.3, 3.3, 3.3, 3.4, 7.1, 7.4, 7.4, 9.4, 10.0, 10.0, 10.7, and 11.1.
02

Create a Stem and Leaf Plot

Divide the numbers into stems and leaves. The stems will represent the tens and the leaves the decimal digits: Stems: 0, 3, 7, 9, 10, 11 Leaves: - 0: 0, 0, 0, 0, 0 - 3: 0, 1, 1, 3, 3, 3, 4 - 7: 1, 4, 4 - 9: 4 - 10: 0, 0, 7 - 11: 1.
03

Create a Dot Plot

Plot each fiber percentage on a number line, marking each fiber percentage with its occurrence: - Place dots above numbers on a line that corresponds to each fiber percentage: - 0: Five dots - 3.0, 3.1, 3.3: One, two, and three dots respectively - 3.4: One dot - 7.1: One dot - 7.4, 9.4, 10.0, 10.7, 11.1: Two, one, and one, one, one dot respectively.
04

Create a Histogram

Create bins that include ranges covering the fiber percentages. A possible bin width could be 2%: Bins: 0-2%, 2-4%, 4-6%, 6-8%, 8-10%, 10-12%. Count how many fiber percentages fall into each bin and draw the histogram accordingly.
05

Create a Relative Frequency Histogram

Convert the counts from the histogram to relative frequencies by dividing the count in each bin by the total number of cereals (20) and then, plot the relative frequency histogram using the same bins: - 0-2%: 25% (5/20) - 2-4%: 35% (7/20) - 6-8%: 15% (3/20) - 8-10%: 5% (1/20) - 10-12%: 20% (4/20).
06

Calculate the Percentage of Cereals with More Than 7% Fiber

Identify how many cereals have more than 7% fiber: 7.4, 7.4, 9.4, 10.0, 10.0, 10.7, 11.1. There are 7 such cereals.Calculate the percentage:\[ \text{Percentage} = \left( \frac{7}{20} \right) \times 100 = 35\% \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Stem and Leaf Plot
A stem and leaf plot is a simple way to display data and observe its distribution. It helps to see how often each number appears and how the numbers are spread out. In a stem and leaf plot, each number is split into a "stem",
Dot Plot
Dot plots are a straightforward method of visualizing small sets of numerical data. They are particularly effective in showing the distribution and frequency of data points. In a dot plot, each data value is represented by a dot above
Histogram
A histogram is a graphical depiction of data using bars of different heights. Each bar groups numbers into ranges, and it is similar to a bar graph; however, histograms group numbers into ranges (also called bins) and do not have s
Relative Frequency Histogram
A relative frequency histogram provides similar information as a standard histogram, but it focuses on how often a data point appears relative to the total number of points. This means each bar's height shows the proportion of data tha

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The Cereal FACTS report from Exercise 2.3 also provides information on sugar content of cereals. We have selected a random sample of 20 cereals from the data provided in this report. Shown below are the sugar contents (percentage of sugar per gram of cereal) for these cereals. $$\begin{array}{rlr} \hline & \text { Brand } & \text { Sugar \% } \\ \hline 1 & \text { Rice Krispies Gluten Free } & 3 \% \\ 2 & \text { Rice Krispies } & 12 \% \\ 3 & \text { Dora the Explorer } & 22 \% \\ 4 & \text { Frosted Flakes Red. Sugar } & 27 \% \\ 5 & \text { Clifford Crunch } & 27 \% \\ 6 & \text { Rice Krispies Treats } & 30 \% \\ 7 & \text { Pebbles Boulders Choc. PB } & 30 \% \\ 8 & \text { Cinnamon Toast Crunch } & 30 \% \\ 9 & \text { Trix } & 31 \% \\ 10 & \text { Honey Comb } & 31 \% \\ \hline \end{array}$$ $$\begin{array}{llr} \hline & \text { Brand } & \text { Sugar \% } \\ \hline 11 & \text { Corn Pops } & 31 \% \\ 12 & \text { Cheerios Honey Nut } & 32 \% \\ 13 & \text { Reese's Puffs } & 34 \% \\ 14 & \text { Pebbles Fruity } & 37 \% \\ 15 & \text { Pebbles Cocoa } & 37 \% \\ 16 & \text { Lucky Charms } & 37 \% \\ 17 & \text { Frosted Flakes } & 37 \% \\ 18 & \text { Pebbles Marshmallow } & 37 \% \\ 19 & \text { Frosted Rice Krispies } & 40 \% \\ 20 & \text { Apple Jacks } & 43 \% \\ \hline \end{array}$$ (a) Create a stem and leaf plot of the distribution of the sugar content of these cereals. (b) Create a dot plot of the sugar content of these cereals. (c) Create a histogram and a relative frequency histogram of the sugar content of these cereals. (d) What percent of cereals contain more than \(30 \%\) sugar?
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