Statistics - Mod 1
What are the two meanings of the term statistics?
A group of methods used to collect, analyze, present, and interpret data to make decisions Numerical facts from sample data, such as the age of a student or the income of a family
Parameter
A numerical measure that represents a population
Statistic
A numerical measure that represents a sample
Representative Sample
A sample that represents the characteristics of the population as closely as possible
Sampling without Replacement
A sampling method in which the item selected at each selection is not put back in the population before the next selection
Sampling with Replacement
A sampling method in which the item selected at each selection is put back in the population before the next item is drawn
Which of the following quantitative variables are continuous? Number of people in line for a roller coaster Amount of time a student spends studying for a test Family size Amount of snowfall each day A person's weight
Amount of time a student spends studying for a test Amount of snowfall each day A person's weight
The State Education Department requires local school districts to keep these records on all students: age, race or ethnicity, days absent, current grade level, standardized test scores in reading and mathematics, and any disabilities or special educational needs the student may have. Which of the following are categorical (or qualitative) variables in these records? Student Name Mathematics Test Score Reading Test Score Current Grade Level (Freshman, Sophomore, Junior, or Senior) Days Absent Age Disabilities or Special Needs Race or Ethnicity
Current Grade Level Disabilities or Special Needs Race or Ethnicity
A data set consists of the ages of death of selection of 29 past United States presidents.
Do these data represent a sample or a population? sample Are the data qualitative or quantitative? quantitative
Which of the following are quantitative variables?
Number of students in a calculus class Amount of time it takes to assemble a puzzle
The data below give the amount of money spent on fast food by 14 individuals over a one week period. Calculate the percentile rank of 8 and 52. Round solutions to one decimal place, if necessary. 7, 7, 8, 8, 13, 17, 34, 44, 45, 45, 48, 51, 52, 55
Percentile Rank of 8 = 21.4% (2+0.5(2))/14 * 100 Percentile Rank of 52 = 89.3% (12+0.5(1))/14 * 100 (x + 5y)/n * 100
The data below give the ages of a random sample of 12 people. Calculate the first, second, and third quartiles of the data. Also determine the interquartile range. 23, 24, 34, 46, 52, 63, 67, 73, 75, 82, 85, 87
Q1 = 40 (34+46)/2 Q2 = 65 (63+67)/2 Q3 = 78.5 (75+82)/2 IQR = (78.5 - 40)
Which of the following are qualitative variables?
State in which a person lives Rating of a customer service representative (excellent, good, fair, poor)
population
The collection of all elements whose characteristics are being studied
Steam-and-leaf plot 1 - 0,1,1,2,8,8 2 - 1,2,4,5,6,6 3 - 0,1,2,6,6,9 4 - 0,1,1,1,6,6 5 - 1,2,2,4,4,7
The data is uniform
The following table gives the Test 1 scores for 6 randomly selected statistics students. (Student / Test 1 Score) Student 1 / 92 Student 2 / 91 Student 3 / 85 Student 4 / 97 Student 5 / 75 Student 6 / 94
This data set contains: 6 elements 6 observations What is the variable of this data set? Test 1 Score
"Frequency" is how many times a random variable occurs in the data set.
True
The following table gives the favorite color of each student in a large statistics class. (color / frequency) Blue / 69 Yellow / 94 Red / 69 Green / 91 Purple / 74 Pink / 86
What is the variable of this data set? color How many observations are in this data set? 483 The data in the table are Population and Qualitative
Sample
a subset of the population selected for study
A survey of families living in a certain city was conducted to collect information on the following variables: age of the oldest person living in the family, number of family members, number of males in the family, number of females in the family, whether or not the they own a house, income of the family, whether or not the family took vacations during the past year, whether or not they are happy with their financial situation, and the amount of their montly mortgage or rent. a) Which of the variables are qualitative? b) Which of the variables are quantitative? c) Which of the variables are discrete? d) Which of the variables are continuous?
a) house owned or not happy with financial situation or not Vacation in the past year or not b) Family income Number of females in the family Number of males in the family Age of oldest person in the family Amount of monthly mortgage or rent c) Number of females in the family Vacation in the past year or not House owned or not Happy with financial situation or not Number of males in the family Age of oldest person in the family d) Family income Amount of monthly mortgage or rent
Data were collected for 494 fish from Fort Pierce Inlet. The length of the fish (in mm) is summarized in the table below. (Lengths (mm) / Frequency) 200 - 203 / 43 204 - 207 / 78 208 - 211 / 42 212 - 215 / 44 216 - 219 / 39 220 - 223 / 89 224 - 227 / 29 a) What is the class boundary between the first and second classes? b) What is the lower limit of the sixth class? c) What is the midpoint of the fifth class? d) What is the upper limit of the sixth class?
a) 203.5 b) 212 c) 217.5 d) 207
The following table gives all Test 2 scores for a statistics class. Complete the stem-and-leaf plot below. Describe the shape of the distribution. 79 71 79 91 64 71 97 82 54 65 99 99 99 99 93 84 69 90 81 89 88 76 82 94 88
a) Data were collected for 1 quantitative variable b) Do these data constitute a population or sample? population c) Complete the stem-and-leaf plot below. 5 - 4 6 - 4, 5, 9 7 - 1, 1, 6, 9, 9 8 - 1, 2, 2, 4, 8, 8, 9 9 - 0, 1, 3, 4, 7, 9, 9, 9, 9 d) In regard to shape, the data are left-skewed
Twenty students were asked about their favorite college class. The results are listed below. Let A = Astronomy, B = Biology, C = Chemistry, M = Mathematics, and E = English. A B C M A E B A E C E B E E B A M B M B a) The data in the table above are b) Complete the frequency distribution for the data. c) Complete the relative frequency distribution for the data. Round solutions to three decimal places, if necessary.
a) qualitative b) (Class / Frequency) Astronomy / 4 Biology / 6 Chemistry / 2 Math / 3 English / 5
The following data set contains the Test 1 scores of all students in a statistics class. 53 56 57 58 59 59 64 64 70 71 72 76 77 77 78 78 79 80 81 82 82 83 83 84 86 88 88 89 90 99 a) The data in the table above are b) Complete the frequency distribution for the data. c) Complete the cumulative frequency distribution for the data. d) Complete the relative frequency distribution for the data. Round solutions to two decimal places, if necessary.
a) quantitative and discrete b) (score / frequency) 50-59 / 6 60-69 / 2 70-79 / 9 80-89 / 11 90-99 / 2 c) 50-59 / 6 60-69 / 8 70-79 / 17 80-89 / 28 90-99 / 30 d) 50-59 / 0.2 60-69 / 0.07 70-79 / 0.3 80-89 / 0.37 90-99 / 0.07
Determine whether the value is a parameter or statistic: a) 20% of vehicles sold are compact cars. b) In a weight loss research study the sample of 50 men lost an average of 2.5 pounds. c) Caldwell Community College determined that 89% of students who took MAT 152 successfully completed the course. d) In a recent sample of 250 people, it was found that 25% do not bathe everyday.
a. parameter b. statisitc c. parameter d. statisitc
In a study, the data you collect is Hair Color. These data are:
categorical
A data set of monthly expenditures (rounded to the nearest dollar) incurred at coffee shops by a sample of 800 households has a minimum value of $12 and a maximum value of $210. Suppose we want to group these data into six classes of equal widths. Assuming we take the lower limit of the first class as $1 and the upper limit of the sixth class as $210, determine the class limits, boundaries, and midpoints for a grouped quantitative data table. Hint: To determine the class width, divide upper limit of the sixth class (210) by the number of classes (6).
class width = 35 (210/6) (Class Limits / Lower Boundary / Upper Boundary / Class Midpoint) 1 - 35 / 0.5 / 35.5 / 18 36 - 70 / 35.5 / 70.5 / 53 71 - 105 / 70.5 / 105.5 / 88 106 - 140 / 105.5 / 140.5 / 123 141 - 175 / 140.5 / 175.5 / 158 176 - 210 / 175.5 / 210.5 / 193
Is the following value from a discrete or continuous data set? The number of children a person has
discrete (# of possible values is countable)
Categorical variables are the same as quantitative variables.
false categorical - data represents groups quantitative - data represents amounts
Calculate the 17th and 74th percentiles of the data set shown below. 1, 9, 10, 14, 15, 18, 19, 20, 23, 25
i = P / 100 (N + 1) i = 49/100 (10+1) i = 5.39 (5)
Determine what the key terms refer to in the following survey.To determine the average number of classes Oxnard College students were taking, a group of 32 Oxnard College students were given and answered the following survey.How many classes you are taking this semester?
parameter - The average number of classes of all students in Oxnard College is 2.7 statistic - The average number of classes of those 32 students in the sample is 3 sample - The 32 Oxnard College students who were surveyed population - All students in Oxnard College
In a study, the data you collect is Air pressure (psi).This data is:
quantitative
In a study, the data you collect is Wage per hour.This data is:
quantitative
In a study, the data you collect is Weight in pounds. This data is:
quantitative
In a study, the data you collect is The GPAs of some students at IRSC. These data constitute a
sample
In a study, the data you collect is The number of manatees in some of Florida's counties. These data constitute a
sample
Suppose you want to know what high school incoming freshman at a particular college came from. To estimate the percentage of incoming freshman from each of the area's high schools you take a sample of 200 incoming college freshman. Match the following:
sample - 200 incoming college freshman parameter -percentage of all incoming freshman who graduated from each area high school individual - an incoming college freshman statisitc - percentage of the 200 incoming college freshmen who graduated from each area high school variable - high school graduated from population - all incoming college freshmen
In 2010, the Pew Research Center questioned 709 adults in the U.S. to estimate the proportion of the population favoring marijuana use for medical purposes. It was found that 77% are in favor of using marijuana for medical purposes. State the individual, variable, population, sample, parameter and statistic.
sample - The 709 adults in the U.S. surveyed individual - one adult in the U.S. variable - Favoring marijuana use for medical purposes population - All adults in the U.S. statistic - The 77 % in favor of using marijuana in the study. parameter - The 77 % in favor of using marijuana in the U.S.
Determine whether the value is a parameter or statistic. In a weight loss research study the sample of 50 women lost an average of 2.5 pounds
statisitc
Determine whether the value is a parameter or statistic:In a random sample of 100 students who passed statistics, 60% used statistics in their future careers
statisitc
m - 42, 22, 58, 13, 71 f - 10, 66, 28, 22, 38
∑mf = 6480 (42)(10) + (22)(66) + (58)(28) + (13)(22) + (71)(38) ∑m2f = 339052 (42)^2(10) + (22)^2(66) + (58)^2(28) + (13)^2(22) + (71)^2(38) (∑mf)^2 = 41990400 6480^2
Use the data below to complete the following calculations. 85, 79, 35, 82, 32, 79, 91, 50
∑x = 533 (85 + 79 + 35 + 82 + 32 + 79 + 91 + 50) ∑x^2 = 39,461 (7225 + 6241 + 1225 + 6724 1024 + 6241 + 8281 + 2500) (∑x)^2 = 284,089 (533 * 533)
Use the data below to complete the following calculations. x - 96, 21, 17, 10, 45, 78, 97, 94 y - 3, 70, 68, 29, 10, 94, 21, 48
∑xy = 17,535 (96*3)+(21*70)+(17*68)+(10*29)+(45*10)+(78*94)+(97*21)+(94+48) ∑x^2y = 1,294,933 (96^2*3)+(21^2*70)+(17^2*68)+(10^2*29)+(45^2*10)+(78^2*94)+(97^2*21)+(94^2+48) (∑xy)2 = 307,476,225 17,535^2
