8.1.0: Exercises

Contemporary Mathematics · LibreTexts

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    From LibreTexts, under not declared, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    For the following exercises, data are collected on a sample of items found in a grocery store. Classify each of these datasets obtained from that sample as being categorical or quantitative.

    Exercise \(\PageIndex{1}\)

    Price

    Exercise \(\PageIndex{2}\)

    Calories per serving

    Exercise \(\PageIndex{3}\)

    Whether the product is gluten-free

    Exercise \(\PageIndex{4}\)

    Package weight

    Exercise \(\PageIndex{5}\)

    Country of origin

    For the following exercises, decide whether random samples are being selected. If they are, decide whether they are simple, systematic, cluster, or stratified.

    Exercise \(\PageIndex{6}\)

    A newspaper asks its readers to answer an online poll about proposed zoning changes in their city.

    Exercise \(\PageIndex{7}\)

    An electronics retailer uses a computer to randomly select customers in its rewards club to take a survey about their interest in a new product.

    Exercise \(\PageIndex{8}\)

    The student affairs office at a university wants to make sure students who live on campus are satisfied with their access to laundry facilities. They select five students at random from each residence hall to take the survey.

    Exercise \(\PageIndex{9}\)

    A professor wants to gauge how much time her students spend on homework, so she asks that question of each student who comes to her office hours that day.

    Exercise \(\PageIndex{10}\)

    The management at a restaurant wants feedback about its new menu. They choose ten tables at random, and survey each person seated at that table.

    Exercise \(\PageIndex{11}\)

    The transit authority in a large city wants to know about usage on a particular train route. They choose a number between 1 and 5 at random, and get 4. They then count the number of people on the fourth train to pass through the station, and then count every fifth train after that.

    Exercise \(\PageIndex{12}\)

    A candidate for a seat in the U.S. Congress wants to learn which issues are most important to her potential constituents. She chooses 50 people at random from each zip code in her district to survey.

    For the following exercises, you have been tasked with surveying a sample of 100 registered voters who live in your town. You have access to a spreadsheet containing the following data on every registered voter: name, address, age, phone number. The spreadsheet also can generate a unique random number for each person.

    Exercise \(\PageIndex{13}\)

    Describe how you might choose a simple random sample from this population.

    Exercise \(\PageIndex{14}\)

    Describe how you might choose a stratified random sample from this population to ensure that all age groups are represented.

    Exercise \(\PageIndex{15}\)

    Assume that there are 50,000 registered votes on your list. Describe how you might choose a systematic random sample from this population.

    Exercise \(\PageIndex{16}\)

    A sample of students was asked, “Which social media platform, if any, do you use most frequently?” The raw responses are given in this table:

    None Twitter Snapchat Snapchat Twitter Facebook
    Instagram Snapchat Twitter None Snapchat Instagram
    Instagram Facebook None Instagram Snapchat Twitter
    Snapchat Instagram Instagram Twitter Snapchat Twitter
    Facebook None Instagram Instagram Twitter Instagram

    Create a categorical frequency distribution to summarize these data.

    Exercise \(\PageIndex{17}\)

    A sample of students at a large university were asked whether they were full-time students living on campus (Full-Time Residential, FTR), full-time students who commuted (FTC), or part-time students (PT). The raw data are in the table below:

    FTR FTR FTC PT FTR PT FTR FTC FTC PT FTC FTC PT FTR FTC PT
    FTR FTC FTC FTR FTR PT FTC FTC FTC PT FTR PT FTC FTC FTR PT

    Give the categorical frequency distribution for these data.

    Exercise \(\PageIndex{18}\)

    A survey of students in a math class asked for the respondents’ birth months. The table below lists the responses:

    Dec Feb Apr Sep Nov Dec Aug Feb Feb Sep Oct Feb Jun Jan
    Jul May May Jan Mar Feb Nov Oct Apr Oct Aug Jan May Jan

    Give the categorical frequency distribution of the birth months.

    Exercise \(\PageIndex{19}\)

    Students in a statistics class were asked how many countries (besides their home countries) they had visited. The table below gives the raw responses:

    0 2 1 1 3 2 0 0 0 2 1 1 0 1 1
    0 2 0 1 0 1 0 2 0 1 1 0 0 1 0

    Create a frequency distribution to summarize the data.

    Exercise \(\PageIndex{20}\)

    The following table contains the top 25 receivers (by number of receptions) in the NFL during the 2020 season, along with their teams and the number of fumbles each made over the course of the season:

    Player Team Fumbles Player Team Fumbles
    Stefon Diggs BUF 0 Calvin Ridley ATL 1
    Davante Adams GNB 1 Robert Woods LAR 2
    DeAndre Hopkins ARI 3 Justin Jefferson MIN 1
    Darren Waller LVR 2 Diontae Johnson PIT 2
    Travis Kelce KAN 1 Tyreek Hill KAN 1
    Allen Robinson CHI 0 Terry McLaurin WAS 1
    Keenan Allen LAC 3 Alvin Kamara NOR 1
    Tyler Lockett SEA 1 D.K. Metcalf SEA 1
    JuJu Smith-Schuster PIT 3 Cole Beasley BUF 0
    Robby Anderson CAR 1 Brandin Cooks HOU 0
    Amari Cooper DAL 0 J.D. McKissic WAS 3
    Cooper Kupp LAR 1 Tyler Boyd CIN 1
    Curtis Samuel CAR 1      
    Create a frequency distribution for the number of fumbles made by these players.
    Exercise \(\PageIndex{21}\)

    A public opinion poll about an upcoming election asked respondents, “How many political advertisements do you recall seeing on television in the last 24 hours?” The responses were as follows

    6 2 5 5 2 2 4 1 3 0 1 2 1 6 2
    5 2 4 8 6 3 3 4 2 5 3 4 2 2 3

    Create a frequency distribution for these data.

    For the following exercises, use the following table of data on the top 15 receivers (by number of receptions) in the NFL during the 2020 season:

    Player Team Age Receptions Yards Yds/Rec TD Long
    Stefon Diggs BUF 27 127 1535 12.1 8 55
    Davante Adams GNB 28 115 1374 11.9 18 56
    DeAndre Hopkins ARI 28 115 1407 12.2 6 60
    Darren Waller LVR 28 107 1196 11.2 9 38
    Travis Kelce KAN 31 105 1416 13.5 11 45
    Allen Robinson CHI 27 102 1250 12.3 6 42
    Keenan Allen LAC 28 100 992 9.9 8 28
    Tyler Lockett SEA 28 100 1054 10.5 10 47
    JuJu Smith-Schuster PIT 24 97 831 8.6 9 31
    Robby Anderson CAR 27 95 1096 11.5 3 75
    Amari Cooper DAL 26 92 1114 12.1 5 69
    Cooper Kupp LAR 27 92 974 10.6 3 55
    Calvin Ridley ATL 26 90 1374 15.3 9 63
    Robert Woods LAR 28 90 936 10.4 6 56
    Justin Jefferson MIN 21 88 1400 15.9 7 71
    (source)
    Exercise \(\PageIndex{22}\)

    Make a binned frequency distribution for receiving yards (“Yards”) using bins of width 200.

    Exercise \(\PageIndex{23}\)

    Make another binned frequency distribution for receiving yards (“Yards”), but this time use bins of width 250.

    Exercise \(\PageIndex{24}\)

    Make a binned frequency distribution for number of yards per reception (“Yds/Rec”), using bins of width 1.

    Exercise \(\PageIndex{25}\)

    Make a binned frequency distribution for longest reception (“Long”), using bins of width 10.

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