Stats - Quiz 1

Which of the following are qualitative (categorical) variables? Amount of rain each day A person's blood type Amount of time a student spends on homework each week Amount of gasoline purchased Arrival status of a train (early, on time, late, canceled)

-A person's blood type -Arrival status of a train (early, on time, late, canceled)

Which of the following are quantitative variables? Amount of time a student spends on homework each week Arrival status of a train (early, on time, late, canceled) Amount of rain each day Amount of gasoline purchased A person's blood type

-Amount of time a student spends on homework each week -Amount of rain each day -Amount of gasoline purchased

The data below give the ages of a random sample of 15 students. Calculate the percentile rank of 43 and 26. Round solutions to one decimal place, if necessary. 26, 26, 49, 22, 30, 19, 26, 49, 43, 26, 20, 23, 48, 44, 23

19,20,22,23,23,26,26,26,26,30,43,44,48,49,49 Percentile Rank of 43 = 70% (5+0.5(4))/15

The data below give the speeds, as measured by radar, of a random sample of 8 vehicles traveling on I-95. Calculate the first, second, and third quartiles of the data. Also determine the interquartile range. 63, 90, 100, 90, 64, 68, 72, 68

63, 64, 68, 68, 72, 90, 90, 100 Q1 = 66 (64+68/2) Q2 = 70 (68+72/2) Q3 = 90 (90+90/2) IQR = 24 (Q3-Q1)

The average square footage of a U.S. single-family home is 2250 square feet with a standard deviation of 100 square feet. Consider a random sample of 1000 homes. Use Chebyshev's Rule to address the following questions. Round solutions to the nearest whole number, if necessary. At least how many of the sample homes have square footage between 1550 and 2950 square feet?

Chebyshev Rule (1 - 1/k^2) * 100 1550 and 2950 7 standard deviations to get to mean (1 - 1/7^2) * 100 * 1000 = 980 homes

Consider two completely different data sets: price per gallon of gas in Fort Pierce and SAT scores of students at a certain high school. The price per gallon of gas data set has a mean of $2.98 and a standard deviation of $1. The high school SAT scores data set has a mean of 1002 and a standard deviation of 156. Calculate the Coefficient of Variation for both data sets. Round solutions to one decimal place, if necessary.

Coefficient of Variation for the price per gallon of gas data set: 33.6% (1/2.98) Coefficient of Variation for high school SAT scores data set: 15.6% (156/1002) Which data set has greater variability? Price per gallon of gas Thus, we see that when comparing two data sets, the data set with the larger standard deviation does not necessarily have greater variabilty.

The ages of 8 statistics students are given below. Determine the 5 number summary and select the correct boxplot for these data. 17, 21, 24, 27, 29, 32, 35, 35

Min = 17 Q1 = 22.5 Q2 = 28 Q3 = 33.5 Max = 35

The data below show the miles driven on a single day by a random sample of 12 students. Calculate the 40th and 52nd percentiles of the data. 13, 30, 32, 41, 61, 63, 70, 72, 81, 81, 86, 107

P40 = 62 0.40*(12+1) = 5.2 61 + 63/2 = 62 P52 = 66.5 0.52*(12+1) = 6.76 63+70/2 = 66.5

30 students were asked about their favorite sport. Soc, Foot, Bask, Hock, Foot, Hock, Base, Base, Bask, Hock, Foot, Soc, Hock, Soc, Base, Foot, Foot, Soc, Base, Foot, Soc, Hock, Bask, Bask, Hock, Hock, Soc, Hock, Hock, Hock

The data in the table above are qualitative Complete the frequency distribution for the data. (class / frequency) Football / 6 Basketball / 4 Soccer / 6 Baseball / 4 Hockey / 10 Complete the relative frequency distribution for the data. Football / 0.2 Basketball / 0.133 Soccer / 0.2 Baseball / 0.133 Hockey / 0.333

The following data are the ACT scores of all students in a history class. 3, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 13, 15, 18, 21, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 27, 30, 31, 33, 36

The data in the table above are quantitative (discrete) Complete the frequency distribution for the data. (ACT Score / Frequency) 1-6 / 2 7-12 / 9 13-18 / 3 19-24 / 4 25-30 / 9 31-36 / 3 Complete the relative frequency distribution for the data. (ACT Score / Relative Frequency) 1-6 / 0.07 7-12 / 0.3 13-18 / 0.1 19-24 / 0.13 25-30 / 0.3 31-36 / 0.1 Complete the cumulative frequency distribution for the data. 1-6 / 2 7-12 / 11 13-18 / 14 19-24 / 18 25-30 / 27 31-36 / 30

Data were collected for 325 sea turtles on the Treasure Coast. The weight of the turtles (in pounds) is summarized in the table below. Weight (lbs) / Frequency 60 - 64 / 31 65 - 69 / 37 70 - 74 / 94 75 - 79 / 73 80 - 84 / 39 85 - 89 / 16 90 - 94 / 35

What is the class boundary between the fourth and fifth classes? Class boundary = 79.5 What is the lower limit of the fifth class? Lower Class Limit = 80 What is the midpoint of the first class? Midpoint = 62 What is the upper limit of the second class? Upper Class Limit = 69

The following table gives the round-trip commute times for a selection of employees at a large company. Complete the stem-and-leaf plot below use the tens place as the stem and the ones place as the leaf. Describe the shape of the distribution.

a) Data were collected for 1 quantitative b) Do these data constitute a population or sample? sample c) c) Complete the stem-and-leaf plot below. 5 - 0, 0, 1, 3, 4, 4, 5, 5, 8 6 - 0, 1, 2, 6, 7, 7, 9 7- 1, 2, 4, 5, 9 8 - 0, 9, 9 9 - 4 d) In regard to shape, the data are right skewed

A data set of the ages of a sample of 325 Galapagos tortoises has a minimum value of 1 years and a maximum value of 110 years. Suppose we want to group these data into five classes of equal width. Assuming we take the lower limit of the first class as 1 year, determine the class limits, boundaries, and midpoints for a grouped quantitative data table. Hint: To determine the class width, subtract the minimum age (1) from the maximum age (110), divide by the number of classes (5), and round the solution to the next highest whole number.

class width = 22 (110/5) (Class Limits / Lower Boundary / Upper Boundary / Class Midpoint) 1 - 22 / 0.5 / 22.5 / 11.5 23 - 44 / 22.5 / 44.5 / 33.5 45 - 66 / 44.5 / 66.5 / 55.5 67 - 88 / 66.5 / 88.5 / 77.5 89 - 110 / 88.5 / 110.5 / 99.5

The following data set shows the bank account balance for a random sample of 16 IRSC students. −18,−2,67,67,80,135,223,239,239,239,239,309,309,309,309,321

mean = 191.56 median = 239 mode = 239, 309

A data set consists of the marital status of all 15 students in a class. Do these data represent a sample or a population? Are the data qualitative or quantitative?

population qualitative

The following data are the final exam scores of the 13 students in a small calculus class. 60, 69, 69, 70, 73, 74, 75, 76, 87, 90, 91, 92, 93

range = 33 variance = 109.006 standard deviation = 10.441

Use the data below to complete the following calculations. (m / f) 28 / 96 61 / 73 26 / 83 83 / 7 27 / 19

∑mf= 10,393 (2,688)+(4,453)+(2,158)+(581)+(513) ∑m^2f= 465,079 (28^2 * 96) + (61^2 * 73) + (26^2 * 83) + (83^2 * 7) + (27^2 * 19) (∑mf)^2= 108,014,449 10,393^2

Use the data below to complete the following calculations. 169, 236, 115, 346, 104

∑x= 970 169 + 236 + 115 + 346 + 104 ∑x^2= 228,014 28,561 + 55,696 + 13,225 + 119,716 + 10,816 (∑x)^2= 940,900 (970 * 970)