Mastering Data Analysis: Techniques and Biases

Jeopardy 2.4 Bias 2.5 Measures of Central Tendency 2.1 Data Analysis with Graphs 2.3 Sampling Techniques 2.6 Measures of Spread Q $100 Q $100 Q $100 Q $100 Q $100 Q $200 Q $200 Q $200 Q $200 Q $200 Q $300 Q $300 Q $300 Q $300 Q $300 Q $400 Q $400 Q $400 Q $400 Q $400 Q $500 Q $500 Q $500 Q $500 Q $500 Final Jeopardy

$100 Question from 2.1 Explain the problem with the following frequency table:

$100 Answer from 2.1 The interval size must be the same for all set of intervals.

$200 Question from 2.1 A bar graph and pie graph can be used to display _____________.

$200 Answer from 2.1 Categorical Data

$300 Question from 2.1 • Would you choose a histogram or a bar graph • to illustrate the following scenarios? • Sum of the values of 2-six sided dice when they are rolled • The heights of all players in a junior lacrosse league • The numbers from 100 rolls of a standard die

$300 Answer from 2.1 • Histogram • Histogram • Bar Graph

$400 Question from 2.1 What is the sum of all the relative frequencies of a data set? Explain why this occurs.

$400 Answer from 2.1 The sum is 100% or 1. this occurs because relative frequencies are a percent of the total.

$500 Question from 2.1 The following table lists the relative frequencies and examination scores of a class of 25 students. Construct the frequency-distribution table for the students’ scores.

$500 Answer from 2.1 Your Text Here

$100 Question from 2.3 What is the most common type of sampling technique?

$100 Answer from 2.3 Voluntary –Response Sample

$200 Question from 2.3 A telephone company is planning a marketing survey of its 760 000 customers. The company wants a sample size of about 250. Suggest a method for selecting a systematic sample.

$200 Answer from 2.3 Interval size: 3040 2. The company could randomly select one of 3040 names on the list, then choose every 3040th customer from that point on.

$300 Question from 2.3 What is an advantage and a disadvantages of simple random sample?

$300 Answer from 2.3

$400 Question from 2.3 • What is the sampling method used in each of the following scenarios? • The Heritage Ministry selects a sample of immigrants such that the proportions from each country of origin are the same for all immigrants. • A reporter stops people on a downtown street to ask what they think of the city’s lakefront. • A radio show host invites listeners to call in with their views on banning smoking in restaurants.

$400 Answer from 2.3 • Stratified sample • Convenience sample • Voluntary-response sample

$500 Question from 2.3 Before booking bands for the school dances, the students’ council at Sandalwood Heights wants to survey the music preferences of the student body. The following table shows the enrolment at the school. Design a stratified sample for a survey of 25% of the student body.

$500 Answer from 2.3 Your Text Here

$100 Question from 2.4 Non-response bias is a form of ____________.

$100 Answer from 2.4 Sampling Bias

$200 Question from 2.4 Identify the bias in the following survey: A survey asked students at Sandalwood Heights’ football game whether a fund for extra-curricular activities should be used to buy new equipment for the football team or instruments for the school band.

$200 Answer from 2.4 Sampling Bias

$300 Question from 2.4 A talk show host conducts an on-air survey about re-instituting capital punishment in Canada. Six out of ten callers voice their support for capital punishment. The next day, the host claims that 60% of Canadians are in favour of capital punishment. Is this claim statistically valid? Explain.

$300 Answer from 2.4 No; the sample may contain sample and response bias. Also, the radio station may have a conservative audience.

$400 Question from 2.4 Reword the following question to eliminate the bias: Do you plan to support the current government at the next federal election, in order that they can continue to implement their effective policies?

$400 Answer from 2.4 Do you plan to support the current government at the next federal election?

$500 Question from 2.4 Why do leading and loaded questions produce biased results?

$500 Answer from 2.4 Leading and loading questions contain language that can influence respondents’ answers.

$100 Question from 2.5 Which central tendency is the most affected by outliers? Least affected?

$100 Answer from 2.5 Most Affected: Mean Least Affected: Mode

$200 Question from 2.5 List a set of 8 values that has a median that is not one of the data values.

$200 Answer from 2.5 Answers may vary. For example: 8 9 10 11 12 13 14 15

$300 Question from 2.5 How do you determine the mean, median, and mode of grouped data?

$300 Answer from 2.5 Find the midpoint of all the intervals. Median Divide the total number of elements by 2. Determine, in which this number occurs. Find the midpoint of this interval. Mode Find the midpoint of the interval with the highest frequency Mean Use weighted average

$400 Question from 2.5 How would you calculate the weighted average for grouped data?

$400 Answer from 2.5 Find the midpoints for the intervals Use the weighted average formula

$500 Question from 2.5 Marie has the following marks in her Data Management course. Calculate her weighted average. Tests (%): 74, 89, 68 Quizzes (%): 38, 92, 77 Exam: 89 Tests: 60% Quizzes: 10% Exam: 30%

$500 Answer from 2.5 Weighted Average: (74)(60) + (89)(60) + (68)(60) + (38)(10) + (92)(10) + (77)(10) + (89)(30) 60 + 60 + 60 + 10 + 10 + 10 + 30 = 77.5%

$100 Question from 2.6 What is the difference between a box-and-whisker plot and a modified box-and-whisker plot?

$100 Answer from 2.6 Box-and-whisker plot: Illustrates the spread of a data set Modified box-and-whisker plot: Excludes the outliers from the main plot

$200 Question from 2.6 Determine the Z-scores for the following data set obtained after surveying people about the number of first cousins they had: 18 15 26 20 21

$200 Answer from 2.6 -0.49, -1.23, -1.48, 0, 0.25

$300 Question from 2.6 The following data was collected from students after they were asked how many cousins they had: 19 1 4 6 7 6 5 3 2 8 7 2 Calculate the Q1, Q2, Q3, IQR, and the semi-interquartile range.

$300 Answer from 2.6 Q1: 2.5 Q2: 5.5 Q3: 7 IQR: 4.5 SIQR: 2.25

$400 Question from 2.6 Identify the outlier in the following set of data: 4 8 13 1 3 7 2 9 6 9

$400 Answer from 2.6 There is no outlier in the data set.

$500 Question from 2.6 These were the hours worked by the nurses at the General hospital. Use your graphing calculator to calculate the mean, variance, and standard deviation for the following set of data. Assume this is a population.

Mastering Data Analysis: Techniques and Biases

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