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Lesson 1

1. Lesson 1

1.7. Explore 3

Mathematics 30-3 Module 4

Module 4: Statistics

 

Self-Check 2

 

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Check your understanding of mode and median by selecting the best response for questions 1 to 3 based on what you did in Try This 2. Be sure to read the feedback provided when you check your answers. In question 4, attempt to explain each question and then check your answer.

  1. What did you do with numbers that repeated themselves? Do you include the numbers in the list multiple times when ordering them from smallest to largest, or simply discard them?
    1. Leave repeated numbers in the list.
    2. Discard repeated numbers.

       

    Answer

  2. When calculating the mode, did you have values that repeated themselves the same number of times? How does this affect the mode?
    1. There is no mode.
    2. There is more than one mode.

       

    Answer

  3. In the case of finding the mode, what happens if none of the data values repeat themselves?
    1. There is no mode.
    2. There is more than one mode.

       

    Answer

  4. When you generated the list of 15 numbers, it was probably easier to find the median (middle point) than it was with the list of 20 numbers.
    1. Can you explain why this is so? Answer
    2. How is the median determined when given a data set with an even number of terms? Answer

From Try This 2, you hopefully discovered the following information about median:

  • The middle number is the median if the ordered data has an odd number of elements.
  • The average (arithmetic mean) of the two middle numbers is the median if the ordered data has an even number of elements.

From Try This 2, you hopefully discovered the following information about mode:

  • If each value occurs once, then there is no mode. If two or more values appear the same number of times, and this is the greatest number of occurrences in the data set, then they are all considered modes.
Self-Check 3

 

Determine the mean, median, and mode of each of the following sets of data.

  1. {5, 6, 7, 8, 9, 10, 12} Answer
  2. {20, 12, 49, 15, 28, 32, 15, 49, 29, 4, 2} Answer
  3. {5, 6, 7, 7, 8, 9, 10, 12} Answer