ASSIGNMENT # 2

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  1. The Degree of Reading Power (DRP) test is used to measure the reading ability of children. Below are the DRP scores of 44 third-grade students, measured during research on ways to improve reading performance:

4026391442182543462719

4719263534154440383146

5225353533293441492852

4735482233415127145445

a)Make a stemplot of the data. Describe the shape of the distribution of the data.

b)Make a simple frequency histogram of these same data using the classes 10 and under 15, 15 and under 20, … etc. Describe the shape of the distribution of the data.

c)In general , what is the main difference between a stemplot and an histogram.

d)Report the sample mean, sample standard deviation and the 5-number summary.

e)Obtain the boxplot and comment on the plot.

  1. The stemplot below shows of the percent of residents aged 25 to 34 in each of the 50 states of the USE ( the stems are whole percents and the leaves are tenths of a percent):

10 / 9
11 / 0
12 / 1 / 3 / 4 / 4 / 6 / 7 / 7 / 8 / 8 / 9
13 / 0 / 0 / 1 / 2 / 4 / 5 / 5 / 5 / 6 / 6 / 7 / 8 / 9 / 9 / 9 / 9
14 / 1 / 1 / 2 / 2 / 2 / 3 / 4 / 4 / 4 / 4 / 5 / 7 / 8 / 9
15 / 2 / 4 / 4 / 7 / 8 / 9 / 9 / 9

a)Find the five-number summery of this distribution.

b)Using the 1.5x IQR criterion to identify all the outliers of the data set.

c)How much does the median change if you omit all the outliers.

d)Calculate the sample mean, sample variance and the sample standard deviation of the data set.

  1. The median of any normal distribution is the same as its mean. We can use normal calculations to find the quartiles and related descriptive measures for normal distributions.

a)What is the area under the standard normal curve to the left of the first quartile? Use this to find the value of the first quartile for a standard normal distribution. Find the third quartile similarly.

b)Your work in (a) gives the z-scores for the quartiles of any normal distribution. Scores on the Wechsler Intelligence Scale for Children (WISC) are normally distributed with mean 100 and standard deviation 15. What are the quartiles of WISC scores?

c)What is the value of the IQR for the standard normal distribution?

d)What percent of the observation in the standard normal distribution are suspected outliers according to the 1.5xIQR criterion?

  1. How does the fuel consumption of a car change as its speed increases? Here are data for British Ford Escort. Speed is measured in kilometres per hour; and fuel consumption is measured in liters of gasoline used per 100 kilometers traveled.

Speed / Fuel used / Speed / Fuel used
10 / 21 / 90 / 7.57
20 / 13 / 100 / 8.27
30 / 10 / 110 / 9.03
40 / 8 / 120 / 9.87
50 / 7 / 130 / 10.79
60 / 5.9 / 140 / 11.77
70 / 6.3 / 150 / 12.83
80 / 6.95

a)Make a scatterplot.

b)Describe the form of the relationship. In what way is it not linear? Explain why the form of the relationship makes sense.

c)It does not make sense to describe the variable as either positively associated or negatively associated. Why not?

d)Is the relationship reasonably strong or quite weak? Explain your answer.

  1. Use data from Exercise 2.11 (page 122).

a)Make a scatterplot. Use different symbols or colors for women and men. Do you think the correlation will be about the same for men and women or quite different for the two groups? Why?

b)Find “r” for women alone and also for men alone.

c)Calculate the mean body mass for the women and for the men. Does the fact that the men are heavier that the women on the average influence the correlations? If so, in what way?

d)Lean body mass measured in kilograms. How would the correlations change if measured body mass in pounds? (There are about 2.2 pounds in a kilogram).

  1. Suppose that the test scores for a college entrance exam are normally distributed with a mean of 450 and a standard deviation of 100:

a)What percent of those who take the exam score between 350 and 550?

b)A student who scores above 400 is automatically admitted. What percent score above 400?

c)The upper 5% receive scholarships. What score must they make on the exam to get a scholarship?

  1. Data corresponding to the life span of a particular electronic component and the heat it is exposed to are given below:

Heat (C) / 50 / 100 / 150 / 200 / 250 / 300
Life span (hours) / 875 / 884 / 762 / 424 / 365 / 128

a)Make a scatterplot of these data and find the least-squares regression line of life span on heat.

b)Compute the intercept and the slope of the regression line.

c)Find the residuals.