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Assignment No 3 Chapter 3_Graphical Methods for Describing Data The following questions are in a True / False format. The answers to these questions will frequently depend on remembering facts, understanding of the concepts, and knowing the statistical vocabulary. Before answering these questions, be sure to read them carefully! T F

1. An outlier is an unusually small or large data value.

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2. The quantity number of observations often gives a rough estimate of the appropriate number of intervals in a histogram.

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3. A curve with tails that decline more rapidly than the tails of a normal curve is called a heavy-tailed distribution.

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4. The density of a class can be calculated by multiplying the relative frequency of the class times the class width.

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5. A pie chart is most useful for numeric data.

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6. For stem and leaf plots with single-digit leaves, commas must be used to separate the leaves.

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7. One advantage of histograms is that they may be used for large data sets.

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8. If the upper tail of a distribution stretches out farther than the lower tail, the distribution is negatively skewed.

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9. In a scatter plot, both the horizontal and vertical axes must be set at zero.

1.

Soft Drink Preference Coke 20%

30%

Pepsi Sprite Dr. Pepper

15%

Other 25%

10%

(a) How many out of the 300 students indicated a preference for Dr. Pepper?  45 students indicated a preference for Dr Pepper (300 x 0.15) (b) Write a few sentences summarizing the soft drink preference for this sample of students.  The 300 randomly selected students at a particular high school are surveyed with what are their preferences on soft drinks. Coke with being the majority of the student’s preference gathered the votes of 30% of the students or 90 students. Gathering 25% or 75 students have the preference of Pepsi as their soft drinks. 20% or 60 students prefer other soft drinks than what is given. 15% or 45 students prefer Dr. Pepper. And the least preference with 10% or 30 students’ vote goes to Sprite.

(c) Using the information in the pie chart above, sketch a relative frequency bar chart for these data.

Soft Drinks Preference 30% 25% 20% 15%

30% 25% 20%

10%

15% 10%

5% 0% Coke

Pepsi

Others

Dr. Pepper

Sprite

2. A statewide survey released by the University of Iowa Injury Prevention Research Center was designed to assess compliance with Iowa seatbelt law. The table at right

shows the results for 5 Iowa cities. % Age 2 – 5 properly restrained 84 79 58 92 59

City Belle Plaine Cedar Rapids Guttenberg Iowa City Manchester

% Age 6-10 properly restrained 93 94 68 99 82

(a) Display these data in a comparative bar chart so that the different ages can be compared for the different cities.

child restraint compliance % Age 2-5 properly restrained 94

93

% Age 6-10 properly restrained 99 82

92 84 79

68 59

58

% Age 6-10 properly restrained % Age 2-5 properly restrained Belle Plaine Cedar Rapids

Guttenberg

Iowa City

Manchester

(b) Write a brief description of the differences and similarities in the patterns you observe in your bar chart for part (a). 

The compliance of the cities with the restraint that age ranges 6-10 are higher than the compliance of the cities with the restraint that age ranges 2-5 in each city. Iowa City has the most percentage compliance with 92% in age range 2-5 and 99% on age ranges to 6-10 while the Guttenberg has the least percentage of compliance with 58% age ranges to 2-5 and 68% on age ranges 6-10.

3. The stem plot below displays the weights (in ounces) of a random sample of tomatoes grown on a local farm Weights of Tomatoes (oz) 2L|4 2H| 3L|2 3H|89 stem: ones 4L|13 leaf: tenths 4H|5589 5L|11122334 5H|668999 6L|223344 6H|5556

(a) Briefly describe the distribution of tomato weights. 

The distribution of tomatoes is skewed to the left (negatively skewed) with most of the tomatoes weigh in lower category of 5 (18 tomatoes) and the rest goes to the higher category of 5 and up to higher of 6.

(b) What is the weight of the heaviest tomato in the sample? 

The heaviest tomato is 6.6 oz (from category 6 higher)

4. An experiment was performed to determine which brand of comparably priced light bulbs, A or B, lasts longer on average. Ten bulbs of each brand were tested, and their lifetimes recorded in hours. The data are shown below: Bulb A: 88, 97, 110, 122, 128, 129, 135, 141, 150, 165 Bulb B: 23, 55, 93, 106, 111, 115, 123, 128, 153, 171

(a) Display these data using a comparative (back-to-back)

stemplot.

Bulb A (hrs) 17 16 15 14 13 12 11 10 7 9 8 8 7 6 5 4 3 2 1 0

5 0 1 5 982 0

Bulb B (hrs) 1 3 38 15 6 3

3

(b) What are the differences and similarities in the lifetime distributions for the two samples?  The distribution of the lifetime for the two bulbs are almost the same. But the distribution for Bulb A is closer than the distribution of Bulb B which is more scattered. Bulb A has generally higher values of number of hours of bulb than Bulb B that has only 171 as the highest.

(c) If your preference for brand A or B must be determined from the information in parts (a) and (b), which brand would you buy? Explain your choice using appropriate statistical terminology.  I would prefer buying Bulb A because the distribution of hours is closer and are not scattered or has lower variability than Bulb B. Bulb A gives more assurance with the quality of their bulb....