Statistics

Quantitative Methods

Q1
Professor Pshenychna was interested in the study habits of students in her Statistics class. She asked the students to fill out a survey which included answering the question: “When is your best time to study math?”
The responses are reported in the following table (EM = Early Morning, LM = Late Morning, EA = Early Afternoon, LA = Late Afternoon, EV = Evening, NT = Night):
LA EV EM EA LA EA EV EV
EM EA NT EV EA NT NT NT
LA EA EA EM EM NT NT LA
EM EM EA NT LM LM NT LA
EA EA NT EV NT EM LA EM
NT LM LM NT LA LA NT NT
LA EM NT LA EM LA LA EM
________________________________________
a. Fill in the following frequency distribution and relative frequency percent table for the data.
Round to one decimal place if necessary
Time to Study Frequency Relative Frequency (%)
Early Morning
%

Late Morning
%

Early Afternoon
%

Late Afternoon
%

Evening
%

Night
%

Total 5656 100%100%
________________________________________
b. What percent of the students study Statistics in the afternoon?
%
Round to one decimal place if necessary
________________________________________
c. What percent of the students study Statistics at night or early morning?
%
Round to one decimal place if necessary
Q2
A group of 40 students in a library was sampled and the type of laptop they were using was examined. It was found that 14 were using HP, 9 were using Lenovo, 8 were using Dell, 4 were using Microsoft, and 5 were using Apple.
________________________________________
a. Use the given information to complete the following table:
Laptop Type HP Lenovo Dell Microsoft Apple
Frequency

Relative Frequency

________________________________________
b. How many degrees will the segment representing “Lenovo” have on a pie chart?
°
________________________________________
c. What proportion of the students use HP?
%
________________________________________
d. What is the relative frequency for Apple?
%
Q3
The owner of Blackstone Inc. opened 3 stores in different parts of the city and would like to compare the number of sales transactions made after 2 months of operation. The number of sales transactions at the 3 stores are displayed in the chart below:

________________________________________
a. What type of chart is being used to compare the data?

________________________________________
b. Fill in the following two-way frequency table for the data.
Store 1 Store 2 Store 3 Total
Month 1

Month 2

Total

________________________________________
c. How many transactions were made in the first month?

________________________________________
d. How many transactions were made in total (in both months at all 3 stores)?

________________________________________
e. What percent of the total transactions were made by Store 3?
%
Round to one decimal place
________________________________________
f. What percent of the total transactions were made by Store 3 in Month 2?
%
Round to one decimal place
________________________________________
g. What percent of the transactions at Store 2 were made in Month 1?
%
Round to one decimal place
________________________________________
h. What percent of the transactions in Month 1 were made at Store 2?
%
Round to one decimal place
________________________________________
i. Which store has the highest percentage increase from Month 1 to Month 2?

Q4
The ungrouped frequency table below shows the number of students absent in a statistics class in a fall semester.
Number Absent Number of Classes
0 3
1 3
2 5
3 7
4 6
5 3
6 2
________________________________________
a. Is it possible to recover the raw data from this table?

________________________________________
b. What is the total number of absenteeism recorded in the course that semester?

________________________________________
c. What number of absent students occurred most often?

________________________________________
d. In how many classes were 2 students absent?

________________________________________
e. How many times were no more than 2 students absent?

________________________________________
f. How many times were more than 4 students absent?

________________________________________
g. What proportion of classes were exactly 4 students absent?

%
Round to two decimal places
________________________________________
h. What proportion of classes were up to 3 students absent?

%
Round to two decimal places
________________________________________
i. What proportion of classes were more than 3 students absent?

%
Round to two decimal places
Q5
The amount of time (minutes) a sample of students spent on online social media in a 4-hour window is organized in a frequency distribution with 7 class intervals. The class intervals are 0 to < 10, 10 to < 20, ..., 60 to < 70. The number of observations (frequencies) for the classes are 6, 11, 18, 17, 15, 13, and 7 respectively. ________________________________________ a. Complete the following frequency table for the distribution showing frequency, relative frequency, cumulative frequency, and cumulative relative frequencies. Round to four decimal places when necessary Class Interval Frequency Relative Frequency Cumulative Frequency Cumulative Relative Frequency 0 to < 10 10 to < 20 20 to < 30 30 to < 40 40 to < 50 50 to < 60 60 to < 70 ________________________________________ b. How many students spent between 40 and 60 minutes on social media? ________________________________________ c. What percent of the students spent between 50 and 60 minutes on social media? % Round to two decimal places ________________________________________ d. What percent of the students spent no more than 40 minutes on social media? % Round to two decimal places ________________________________________ e. What percent of the students spent no less than 50 minutes on social media? % Round to two decimal places The histogram below summarizes the grades (out of 50) of all students who wrote a midterm exam. ________________________________________ a. How many class intervals were used in the histogram? ________________________________________ b. How many students wrote midterm exam? ________________________________________ c. What is the modal class? ________________________________________ d. What is the midpoint of the last class interval? ________________________________________ e. How many students scored between above 15 but no more than 20? ________________________________________ f. What percent of students scored above 40? % ________________________________________ g. What percent of students scored no more than 30? % ________________________________________ h. Is it possible to determine individual student grades from this histogram? Q6 A3 To determine the distribution of the height of female grade 6 students in a developing country, a researcher collected height data (in inches) from one grade 6 class and reported them as follows: 58 54 61 56 64 67 58 68 65 54 58 58 56 60 69 51 60 61 50 59 64 63 64 67 56 Calculate the mean, median and mode. ________________________________________ Mean=Mean= Round to 2 decimal places ________________________________________ Median=Median= ________________________________________ Mode : Mode : • + Q 7 The frequency table shows the number of items returned daily for a refund at a convenience store over the last 29 days of operation: Number of items Returned (x) frequency (f) 2 3 3 9 4 8 5 5 6 4 Determine the mean, median, and mode. ________________________________________ Mean: Round to 2 decimal places ________________________________________ Median: ________________________________________ Mode: Q8 The following are the starting salaries (in thousands of dollars) of a sample of new research analysts: 3649505151545868697070727374767778798083848788899036495051515458686970707273747677787980838487888990 Use the intuitive approach to determine the quartiles. Q1=Q1= Q2=Q2= Q3=Q3= Q9 The following data consists of birth weights (pounds) of a sample of newborn babies at a local hospital: 8.57.710.39.46.17.2710.17.36.77.38.57.710.39.46.17.2710.17.36.77.3 Calculate the following: ________________________________________ a. Range Range=Range= ________________________________________ b. Variance s2=s2= Round to 2 decimal places ________________________________________ c. Standard Deviation s=s= Round to 2 decimal places Q 10 Given Samples A and B below, Sample A: 4.1 2.2 2.7 3.4 3.9 3.7 4.7 3.7 4.7 Sample B: 2.2 4.9 3.5 3.5 4.4 4.5 3.0 4.5 2.1 ________________________________________ a. Calculate the mean and standard deviation for each sample. Sample A: x̄ A = x̄ A = ; s A = ; s A = Sample B: x̄ B = x̄ B = ; s B = ; s B = Round to two decimal places if necessary ________________________________________ b. Calculate the coefficient of variation for each sample. Sample A: CV A =CV A = % Sample B: CV B =CV B = % Round to two decimal places if necessary ________________________________________ c. Which sample is more variable? Sample A Sample B Neither sample is more variable than the other Q11 The recommended minimum credit card payment for a sample of 100 credit card holders is summarized below: Minimum Payment ($) Frequency 15 to under 30 38 30 to under 45 30 45 to under 60 18 60 to under 75 4 75 to under 90 10 ________________________________________ a. Estimate the mean minimum payment. Mean: Round to 2 decimal places. ________________________________________ b. Using that median class, estimate the median minimum payment. Median: ________________________________________ c. What is the modal class? Modal Class: ________________________________________ d. Describe the shape of the distribution in terms of symmetry/skewness. Skewness: Q12 A search on Best Barryo Mobile's website for "smartwatch" produced ninety-two results, 40 of which are actual smartwatches. Their prices are summarized in the frequency table below: Price ($) Number of Watches 50 to under 100 5 100 to under 150 5 150 to under 200 9 200 to under 250 6 250 to under 300 10 300 to under 350 5 ________________________________________ a. Calculate an approximate value for the sample variance. s2=s2= Round to two decimal places if necessary ________________________________________ b. Calculate an approximate value for the sample standard deviation. s=s= Round to two decimal places if necessary Q13 The hourly pay of a sample of nurses is approximately normal with a mean of $37.75 and a standard deviation of $3.25. Approximately what percent of the nurses make: ________________________________________ a. More than $44.25? % ________________________________________ b. Less than $47.50? % ________________________________________ c. Between $41.00 and $44.25? % Q 14 standard deviation of 8 seconds. Suppose call completion times are approximately normal. The shortest 2.5% of the completed calls will last less than how many seconds? seconds Q 15 standard deviation of 8 seconds. Suppose call completion times are approximately normal. The shortest 2.5% of the completed calls will last less than how many seconds? seconds Q 16 The hourly pay of a sample of city bus drivers has a mean of $42.50 and a standard deviation of $2.75. If the distribution of the data is unknown, determine what percent of the drivers make between $28.75 and $56.25? % Q 17 Incoming calls to the main line at a call centre are transferred within an average of 45 seconds with a standard deviation of 4 seconds. Find an interval (in seconds) centered around the mean, during which at least 36% of the calls are transferred. seconds −− Seconds Q18 Professor Pshenychna was interested in the study habits of students in her Statistics class. She asked the students to fill out a survey which included answering the question: "When is your best time to study math?" The responses are reported in the following table (EM = Early Morning, LM = Late Morning, EA = Early Afternoon, LA = Late Afternoon, EV = Evening, NT = Night): LA EV EM EA LA EA EV EV EM EA NT EV EA NT NT NT LA EA EA EM EM NT NT LA EM EM EA NT LM LM NT LA EA EA NT EV NT EM LA EM NT LM LM NT LA LA NT NT LA EM NT LA EM LA LA EM ________________________________________ a. Fill in the following frequency distribution and relative frequency percent table for the data. Round to one decimal place if necessary Time to Study Frequency Relative Frequency (%) Early Morning % Late Morning % Early Afternoon % Late Afternoon % Evening % Night % Total 5656 100%100% ________________________________________ b. What percent of the students study Statistics in the afternoon? % Round to one decimal place if necessary ________________________________________ c. What percent of the students study Statistics at night or early morning? % Round to one decimal place if necessary