Exam 3: Displaying and Summarizing Quantitative Data

A particular student has a grade point average (GPA)of 2.5 in their first three courses.What is the minimum average they will need in their fourth and fifth courses so that their overall GPA on all five courses is at least 3.0?

Here are some scores from a recent Mathematics exam: 95.5,65.9,93.2,80.6,56.8,50,86.4,54.5,40.9,77.3,79.5,10,65.9,70.5,15,77.3,81.8,12,50,79.5,60.2.Which is a better summary of the scores,the mean or the median? Explain.

Shown below are the data and summary statistics for the reading scores of 29 fifth graders. 1.3 1.5 2.1 2.5 2.7 3.1 3.4 3.6 3.7 3.8 4.1 4.2 4.3 4.5 4.6 4.7 4.7 4.8 4.8 5.1 5.1 5.2 5.3 5.4 5.4 5.6 5.6 5.8 5.9 Count Mean Median StdDev Min Max Q1 Q3 29 4.2 4.6 1.3 1.3 5.9 3.50 5.25 Write a brief summary of the performance of the fifth graders.

A class of sixth graders takes a diagnostic reading test,and the scores are reported by reading grade level.The 5-number summaries for the 20 boys and 21 girls are shown: Boys: 4.7 5.9 6.4 7.6 7.8 Girls: 4.1 5.8 6.4 6.8 8.0 a)Which group had the highest score? b)Which group had the greatest range? c)Which group had the greatest interquartile range? d)Which group's scores appear to be more skewed? Explain. e)Which group generally did better on the test? Explain. f)If the mean reading level for boys was 6.6 and for girls was 6.4,what is the overall mean for the class?

Here are some summary statistics for the recent English exam: lowest $\text { score } = 36 \text {, }$ mean $\text { score } = 71 \text {, }$ $\text { median } = 85.2 \text {, }$ $\text { range } = 74 \text {, }$ $\mathrm { IQR } = 61 \text {, }$ $\mathrm { Q } 1 = 28 \text {, }$ standard deviation = 8.3.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

Here are the weights,in grams,of several snack crackers. 25.23 34.59 22.11 45.93 19.56 22.40 31.18 34.59 43.37 27.22 25.23 36.00 39.69 20.13 13.32 36.00 22.40 39.69 48.76 19.56 15.88

The test scores of 19 students are listed below.Find the interquartile range (IQR)by hand. 91 47 86 70 59 64 97 55 90 78 82 83 50 88 75 43 92 94 67

In a survey,26 voters were asked their ages.The results are shown below.Construct a histogram to represent the data (with 5 bins beginning with a lower bin limit of 19.5 and a bin width of 10).What is the approximate age at the centre? 43 56 28 63 67 66 52 48 37 51 40 60 62 66 45 21 35 49 32 53 61 53 69 31 48 59

Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $15,000 Mean salary = $\$ 35,000$ median = $25,000 Range = $60,000 IQR = $30,000 First quartile = $17,500 Standard deviation = $20,000 Do you think the distribution of salaries is symmetric,skewed to the left,or skewed to the right? Explain why.

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.Use 4 bins with a bin width of 10,and begin with a lower bin limit of -0.5.What is the approximate amount at the centre? 6 15 3 36 25 18 12 18 5 30 24 7 0 22 33 24 19 4 12 9

Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $\$ 15,000$ ,mean salary = $\$ 35,000,$ median = $25,000,range = $60,000, IQR = $30,000,first quartile = $\$ 17,500,$ standard deviation = $20,000. Between what two values are the middle 50% of the salaries found?

The weekly salaries (in dollars)of 24 randomly selected employees of a company are shown below. 310 320 450 460 470 500 520 540 580 600 650 700 710 840 870 900 1000 1200 1250 1300 1400 1720 2500 3700 Choose the boxplot that represents the given data. I II III IV V

Two sections of a class took the same quiz.Section A had 15 students who had a mean score of 80,and Section B had 20 students who had a mean score of 90.Overall,what was the approximate mean score for all of the students on the quiz?

Last year,nine employees of an electronics company retired.Their ages at retirement,in years,are listed below. 55 63 64 50 60 58 67 50 50 Round your answer to the nearest tenth.

The weekly salaries (in dollars)of 24 randomly selected employees of a company are shown below,and displayed on the following boxplot. 310 320 450 460 470 500 520 540 580 600 650 700 710 840 870 900 1000 1200 1250 1300 1400 1720 2500 3700 Find the IQR and the standard deviation.Which is the most appropriate measure of spread?

Which set has the largest standard deviation? Set 1 Set 2 80 110 120 130 180 10 40 50 60 110

Number of times each face of a fair six-sided die shows in 60 tosses.

The ages of the 21 members of a track and field team are listed below.Find the standard deviation. 15 18 18 19 22 23 24 24 24 25 25 26 26 27 28 28 30 32 33 40 42

The heights,in centimetres,of 18 randomly selected Grade 8 students are given below. 120 145 187 155 119 136 127 141 179 163 182 202 114 171 134 150 167 171

The normal annual precipitation (in millimetres)is given below for 21 different cities. 39.1 30.6 18.5 35.0 27.1 27.8 8.6 23.2 42.6 34.7 21.2 12.0 5.1 14.4 22.7 10.9 16.0 25.4 17.2 14.7 51.7