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An Introduction to Statistics

Homework for Statistics Lesson 3

    Find the mean, mode, median, and midrange for the following four data sets.
    Please use the statistics mode on your calculator only for the large data set.

  1. Fabricated data based on annual earnings of select individuals related to producing this homework assignment: $36,000, $360,000, $3,600,000, $36,000,000, and $360,000,000 (math teacher, notebook computer assembler, Netscape® programmer, Windows® programmer, Bill Gates).

     

     

  2. Data set with mixed precision: 1, 1.1, 2.7, 3.14, 1.618.

     

     

  3. Data set with an even number of elements: 1, 2, 3, 4, 5, 6, 7, 8.

     

     

  4. Data set with lots of data (inauguration ages of U.S. presidents): 57, 61, 57, 57, 58, 57, 61, 54, 68, 51, 49, 64, 50, 48, 65, 52, 56, 46, 54, 49, 51, 47, 55, 55, 54, 42, 51, 56, 55, 51, 54, 51, 60, 62, 43, 55, 56, 61, 52, 69, 64, 46, 54. Please use your graphing calculator and save the data for a few days.

     

     

  5. Assume four students drive from Michigan to Florida (2000. km) at 100.0 kph and return at 80.0 kph. Find the arithmetic mean of these two speeds.

     

     

  6. Use the arithmetic mean speed from the previous problem and the total distance travelled to obtain a false value for how long it took. (Speed is distance divided by time. Hence time is distance divided by speed.)

     

     

  7. Velocity is displacement per unit time. Using the data from the problems just above, calculate the true value for their time in hours for each leg of their journey. Contrast this with the previous problem.

  8. Now, divide their total distance travelled by their true total time. This is their true average speed and is the harmonic mean. It will be defined and derived in lesson 4.

     

     

  9. Examine lesson 11.8 in your Geometry book and do problems 1–4, and 9–10.

     

    1. Find the mean temperature if the high is 20°C and the low is 12°C.

       

    2. Find the mean temperature if the high is 6°C and the low is -7°C.

       

    3. Find the mean temperature if the high is -1°C and the low is -9°C.

       

    4. Suppose you score 95 and 87 on two tests. What is your mean score.

       

    1. Give the coordinates of the midpoint of line segment TW, where T=(-1, -1) and W=(9, 3).

       

    2. Give the coordinates of the midpoint of the segment with endpoints (a, b) and the origin.

       

  10. Give a formula for the coordinates of the midpoint of the segment connecting (x1,y1,z1) and (x2,y2,z2).

     

  11. Give a formula for the coordinates of the midpoint of the segment connecting (x1, y1, z1, ict1) and (x2, y2, z2, ict2).

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