Basic Statistics FBQT 1024 - Chapter 3
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What is the name of the course mentioned in the first page of the text?

BASIC STATISTICS (FBQT 1024)

By the end of the chapter, what are students expected to be able to do? (Select all that apply)

  • Compute and interpret the mean, median, and mode for a set of data (correct)
  • Differentiate ungrouped and grouped data (correct)
  • Calculate the standard deviation of data sets
  • Analyze the variability of data

    • Which of the following is NOT a measure of central tendency?

  • Mean
  • Range (correct)
  • Median
  • Mode

    • What is the formula for calculating the mean for population data?

    <p>μ = Σx/N</p> Signup and view all the answers

    The mean is always affected by extreme values (outliers).

    <p>True</p> Signup and view all the answers

    What is the mean of the 2002 payrolls of the five Major League Baseball teams listed in table 3.1?

    <p>78 million</p> Signup and view all the answers

    What is the mean age of the eight employees in the given example?

    <p>45.25 years</p> Signup and view all the answers

    The median is affected by extreme values (outliers).

    <p>False</p> Signup and view all the answers

    What is the median weight loss of the five members of the health club?

    <p>8 pounds</p> Signup and view all the answers

    What is the median revenue of the 12 top-grossing North American concert tours?

    <p>$84.45 million</p> Signup and view all the answers

    What is the mode of the speeds of the eight cars stopped on 1-95 for speeding violations?

    <p>74 miles per hour</p> Signup and view all the answers

    What is the term used to describe a data set with two modes?

    <p>Bimodal</p> Signup and view all the answers

    What is the formula for calculating the mean for grouped data in a population?

    <p>μ = Σfx / N or μ = Σfx / Σf</p> Signup and view all the answers

    What is the mean of the daily commuting times of the 25 employees?

    <p>21.40 minutes</p> Signup and view all the answers

    What is the mean number of orders received by a mail-order company during the past 50 days?

    <p>16.64 orders</p> Signup and view all the answers

    What is the formula for calculating the mode for grouped data?

    <p>X = L + ((f - f ) / ((f - f ) + (f - f ))) C</p> Signup and view all the answers

    What is the mode of the frequency distribution table given for class intervals?

    <p>13</p> Signup and view all the answers

    What is the median age of the 100 workers in company X?

    <p>31.5</p> Signup and view all the answers

    Study Notes

    Basic Statistics (FBQT 1024) - Chapter 3: Measures of Central Tendency

    • Learning Outcomes:
      • Students will be able to compute and interpret the mean, median, and mode for a set of data.
      • Students will be able to differentiate ungrouped and grouped data.

    Describing Data Numerically

    • Central Tendency:
      • Mean: Arithmetic average of all values. Affected by outliers.
      • Median: Middle value in ranked data. Not affected by outliers.
      • Mode: Value that appears most frequently. Not affected by outliers.

    Measures of Central Tendency for Ungrouped Data

    • Mean: Sum of values divided by the number of values.
    • Median: Middle value after ranking data from smallest to largest.
    • Mode: Most frequent value.
    • Relationships: The mean, median, and mode can give different insights into the center of a set of data.

    Mean

    • Ungrouped data: Divide the sum of all values by the number of values.
    • Population data: μ = Σx/N (Σx the sum of all values, N the number of values).
    • Sample data: x̄ = Σx/n (Σx the sum of all values, n the number of values).
    • Outliers: Mean is sensitive to extreme values.
      • Provide example to illustrate how outlier affects outcome

    Example 1 (2002 MLB Payroll)

    • The 2002 payrolls for five MLB teams were: 62, 93, 126, 75, 34.
    • Mean: $78 million

    Example 2 (Employee Ages)

    • Ages of eight employees: 53, 32, 61, 27, 39, 44, 49, 57.
    • Mean age: 45.25 years

    Example 3 (Pacific States Population)

    • Populations of five Pacific states (in thousands): 5894, 3421, 627, 1212, and 33,872.
    • Illustrates effect of outlier on mean: - Mean without California: 2788.5 thousand - Mean with California: 9005.2 thousand

    Median

    • Definition: The middle value in a ranked data set.
    • Location: Median position = (n + 1)/2, where n is the number of values.
    • Odd number of values: Median is the middle value.
    • Even number of values: Median is the average of the two middle values.
    • Example 1 (Weight loss): 3, 5, 8, 10, 19; Median = 8 pounds.
    • Example 2 (Concert Tour Revenue):
      • Median Revenue = $84.45 million

    Example 4 (Real Estate Broker)

    • Median selling prices of 10 houses.
    • Need to calculate Median

    Example 5 (Home Runs)

    • Number of home runs hit by teams in the Indian League in 2004..
    • Calculate median

    Mode

    • Definition: The value that occurs most frequently.
    • No mode or multiple modes:
      • Potential for a data set with no mode.
      • Potential for a data set with multiple modes.
    • Example 1 (Speeds of cars): 77, 69, 74, 81, 71, 68, 74, 73; Mode = 74 mph
    • Example 2 (Incomes of families): $36,150; $95,750; $54,985; $77,490; and $23,740. - No mode
    • Example 3 (TV Prices): $495, $486, $503, $495; $470, $505, $470 and $499. - Mode = $470 and $495 (Bimodal).
    • Exercise 1 (Ages of students): 21, 19, 27, 22, 29, 19, 25, 21, 22, and 30. - Mode = 19 and 21 (Bimodal)
    • Further example use of Histogram to illustrate how to find mode from graphical representations

    Mean for Grouped Data

    • Formula for calculating mean from grouped data.

    Median for Grouped Data

    • The formula for calculating median from grouped data.

    Which Measure is "Best"?

    • Mean (Sensitive to extreme values)
    • Median (Robust to extreme values, Good for skewed distributions)
    • Best choice depends on data characteristics (outliers, distribution)

    Shape of Distribution

    • Skewness:

      • Left-skewed (Mean < Median)
      • Symmetric (Mean = Median)
      • Right-skewed (Median < Mean)

    • Illustrates how each of these looks on a graph

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    Basic Statistics (FBQT 1024) Chapter 3 PDF

    Description

    This quiz covers Chapter 3 of Basic Statistics FBQT 1024, focusing on measures of central tendency including mean, median, and mode. Students will learn to compute and interpret these statistics for both ungrouped and grouped data. Understanding the differences in these measures will enhance data analysis skills.

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