Math 227 Test 1 (Ch2 and 3) Name

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1 Math 227 Test 1 (Ch2 and 3) Name 1) In a survey, 20 people were asked how many magazines they had purchased during the previous year. The results are shown below. Construct a histogram to represent the data. using 4 classes ) Find the range for the given sample data. 2) Jorge has his own business as a painter. The amounts he made in the last five months are shown below. $2426 $2463 $1451 $2154 $1119 A) $1012 B) $1307 C) $975 D) $1344 2) Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data. 3) Christine is currently taking college astronomy. The instructor often gives quizzes. On the past 3) seven quizzes, Christine got the following scores: A) 19.7 B) 12,367 C) 10,032.1 D) 39 Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. 4) The heights in feet of people who work in an office are as follows A) 0.5 B) 0.1 C) 1.2 D) 0.2 4) A-1

2 Solve the problem. 5) If the standard deviation of a set of data is zero, what can you conclude about the set of values? A) The sum of the values is zero. B) The sum of the deviations from the mean is zero. C) All values are identical. D) All values are equal to zero. 5) 6) Without calculating the standard deviation, compare the standard deviation for the following three data sets. (Note: All data sets have a mean of 30.) Which do you expect to have the largest standard deviation and which do you expect to have the smallest standard deviation? Explain your answers in terms of the formula s = Set A: Set B: Set C: (x - x) 2 n ) Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth. 7) The heights in feet of people who work in an office are as follows A) 0.2 B) 0.5 C) 0.1 D) 1.2 7) Use the empirical rule to solve the problem. 8) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmhg and a standard deviation of 12 mmhg. What percentage of 18-year-old women have a systolic blood pressure between 96 mmhg and 144 mmhg? A) 99.7% B) 95% C) 99.99% D) 68% 8) Solve the problem. Round results to the nearest hundredth. 9) The mean of a set of data is 4.11 and its standard deviation is Find the z score for a value of A) 2.23 B) 2.53 C) 2.01 D) ) A-2

3 Find the number of standard deviations from the mean. Round your answer to two decimal places. 10) In one town, the number of pounds of sugar consumed per person per year has a mean of 8 pounds and a standard deviation of 1.7 pounds. Tyler consumed 11 pounds of sugar last year. How many standard deviations from the mean is that? A) 1.00 standard deviations above the mean B) 1.76 standard deviations below the mean C) 1.76 standard deviations above the mean D) 1.00 standard deviations below the mean 10) Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual. Consider a score to be unusual if its z-score is less than or greater than Round the z-score to the nearest tenth if necessary. 11) A test score of 48.4 on a test having a mean of 66 and a standard deviation of ) A) -17.6; unusual B) -1.6; unusual C) 1.6; not unusual D) -1.6; not unusual Determine which score corresponds to the higher relative position. 12) Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? A) Both scores have the same relative position. B) A score of 92 C) A score of ) 13) Which score has a higher relative position, a score of 60 on a test for which x = 53 and s = 10, or a score of on a test for which x = 206 and s = 49? A) A score of 60 B) Both scores have the same relative position. C) A score of ) A-3

4 Find the percentile for the data value. 14) In a data set with a range of 55.4 to and 400 observations, there are 276 observations with values less than 86. Find the percentile for 86. A) 32 B) C) 69 D) ) 15) Describe any similarities or differences in the two distributions represented by the following boxplots. Assume the two boxplots have the same scale. 15) Construct a modified boxplot for the data. Identify any outliers. 16) The weights (in ounces) of 27 tomatoes are listed below ) A-4

5 17) Human body temperatures have a mean of F and a standard deviation of Sallyʹs temperature can be described by z = What is her temperature? Round your answer to the nearest hundredth. A) F B) F C) F D) F 17) Find the percentile for the data value. 18) Data set: ; data value: 52 A) 43 B) 57 C) 50 D) 20 18) 19) Which of the following statements regarding percentiles is true? (More than one statement may be true). 19) A : In any data set, P90 is greater than P80 B: In any data set, P 10 + P90 is equal to 2 Q2 C: In a set of 20 test scores, the percentile of the second highest score is 95 A) B B) C C) A D) All of the above 20) Responses to a survey question about eye color are coded as 1 (for brown), 2 (for blue), 3 (for green), 4 (for hazel), and 5 (for any other color). Does it make sense to find the mean, median, or mode of the coded eye colors? 20) A-5

6 Answer Key Testname: MATH 227 TEST 1 1) The approximate amount at the center is 16 magazines. 2) D 3) A 4) D 5) C 6) Set C would have the largest standard deviation, since its values as a group are farther from 30 than in Sets A and B. Set A has the smallest standard deviation, namely 0, since all values are the same, and thereby equal the mean. 7) A 8) B 9) A 10) C 11) D 12) B 13) B 14) C 15) Answers will vary. 16) Outliers: 1.7 oz, 4.2 oz 17) C 18) A 19) C 20) It does not make sense to find the mean or median since the coded results do not measure or count anything. The numerical codes are just labels for different eye colors. It does make sense to find the mode, which will represent the most commonly occurring eye color. A-6

MATH 227 CP 3 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

MATH 227 CP 3 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the mean for the given sample data. Unless indicated otherwise, round your answer to