Unit E: Statistics and Probability

Chapter 1: Statistics

Practice


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  1. Eleven starting salaries for a company are listed in the table. The mean is $54 000, the median is $45 000, and the mode is $35 000.


    New Employee Starting Salary
    (in thousands of dollars)
    $31
    $35
    $35
    $39
    $44
    $45
    $49
    $61
    $73
    $85
    $97
     
    Which measure of central tendency best represents the average starting salary?

  2. Determine which measure of central tendency should be used in each of the following scenarios.

    1. The amount of spending money (per week) of a group of grade 12 students is stated in the table of values below. Which measure of central tendency should be used to calculate the average amount of spending money per student?

      Spending Money
      (dollars)
      5
      10
      10
      10
      20
      20
      30
      40
      500





    2. Parks Canada would like their mascot, Parka, to hold a sign on main street to advertise an upcoming event.

      Time of Day
      		Number of Pedestrians
      8:00 AM – 10:00 AM
      		175
      10:00 AM – 12:00 PM 92
      12:00 PM – 2:00 PM 110
      2:00 PM – 4:00 PM 205
      4:00 PM – 6:00 PM 158



      Which measure of central tendency should be used to find the two-hour time slot that has the greatest amount of pedestrian traffic?

    3. The fuel consumptions for 10 hybrid cars of the same model were tested. The data is listed in the table below.

      Fuel Consumption
      (L/100 km)
      5.6
      4.4
      4.5
      4.2
      4.5
      4.5
      4.8
      5.9
      4.5
      5.1



      Which measure of central tendency should be used to calculate the average fuel consumption in L/100 km?
Eleven starting salaries for a company are listed in the table. The mean is $54 000, the median is $45 000, and the mode is $35 000.

New Employee Starting Salary
(in thousands of dollars)
$31
$35
$35
$39
$44
$45
$49
$61
$73
$85
$97
 
Which measure of central tendency best represents the average starting salary?
 

From the 11 salaries, there are 7 data values that are lower than the mean of $54 000. The mean gives an inflated average starting salary. The extreme values of $85 000 and $97 000 cause the mean value to be higher than the typical values in the set of data.

The mode value of $35 000 is lower than 8 data values from the 11 salaries. Therefore, mode is not representative of the average starting salary.

Since there are extremely high values in the data, the middle value of $45 000 would be the best choice to represent the average starting salary. Therefore, the best measure of central tendency is the median.
Determine which measure of central tendency should be used in each of the following scenarios.

  1. The amount of spending money (per week) of a group of grade 12 students is stated in the table of values below. Which measure of central tendency should be used to calculate the average amount of spending money per student?

    Spending Money
    (dollars)
    5
    10
    10
    10
    20
    20
    30
    40
    500





  2. Parks Canada would like their mascot, Parka, to hold a sign on main street to advertise an upcoming event.

    Time of Day
    		Number of Pedestrians
    8:00 AM – 10:00 AM
    		175
    10:00 AM – 12:00 PM 92
    12:00 PM – 2:00 PM 110
    2:00 PM – 4:00 PM 205
    4:00 PM – 6:00 PM 158




    Which measure of central tendency should be used to find the two-hour time slot that has the greatest amount of pedestrian traffic?

  3. The fuel consumptions for 10 hybrid cars of the same model were tested. The data is listed in the table below.

    Fuel Consumption
    (L/100 km)
    5.6
    4.4
    4.5
    4.2
    4.5
    4.5
    4.8
    5.9
    4.5
    5.1



    Which measure of central tendency should be used to calculate the average fuel consumption in L/100 km?


  1. Median would be the best choice since the value of $500 inflates the mean. Mean would not be an accurate average to represent the data. Mode could also be used since $10 is the most common value for the amount of spending money.

  2. Mode is the only measure of central tendency to summarize the most popular time slot for pedestrian traffic. Mean and median could be used to find the average pedestrian traffic per hour.

  3. Mean is the best measure of central tendency to use since there are not extreme values in the data.