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Calculating the Mean_ Median_ and Mode The mean_ median_ and mode

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					      Name: __________________________________________________________


Calculating the Mean, Median, and Mode
The mean, median, and mode are single numbers that help describe how the individual scores in a data set
are distributed in value. A data set consists of the observations for some variable is referred to as raw data
or ungrouped data.

The Mean

The arithmetic mean is another name for the average of a set of scores. The mean can be found by dividing
the sum of the scores by the number of scores. This best used when there are few outliers.

For example, the mean of 5, 8, 2, and 1 can be found by first adding up the numbers. 5 + 8 + 2 + 1 = 16.
The mean is then found by taking this sum and dividing it by the number of scores, called the count. Our
data set 5, 8, 2, and 1 has a count of 4 hence the mean is 16 ÷ 4 = 4.

The Median

The median of a set of data values is the middle value once the data set has been arranged in order of its
values. This is best used when there are outliers at both ends of the data or when the range is to great to
establish a mode

To find the mean of 2, 9, and 1, first arrange in order: 1, 2, 9. The median is the middle number or 2.

If you have an even number of values such as 1, 2, 5, and 8, the median is the average of the two middle
numbers. The median for 1, 2, 6, and 8 is the average of 2 and 6 = 4.

The Mode

The mode of a set of data values is the number in the set that appears most frequently. If no number
appears more than once, then the data set has no mode. Or if it has multiple modes and not a great deal of
data, true multiple modes are rare. It is best used when it is clustered and has outliers in the data.

For example, the number 5 appears three times in 1, 2, 5, 5, 5, 8, 8, 9. Since the number 5 appears the most
times, it is the mode. A set of numbers that can have more than one mode, as long as the number appears
more than once. In the data set 1, 2, 2, 3, 3, 4, 5. The mode is 2 and 3. We also can say that this data set is
bimodal.

The Outlier

A piece of data that extends the range well beyond the normal data, it affects the usefulness of the mean.

For example, 1, 56, 56 57,76, 67, 75, 64, 190 are a set of numbers. 1 and 190 are outliers. The skew the
numbers.




                                                        1
Name: __________________________________________________________


              Calculating the Mean, Median, and Mode
                                            (Answer ID # 1037143)
Calculate the values to the nearest hundredth. Select the most accurate measure of central
tendency and explain why. Use your notes.

1.   13, 137, 124, 55, 143, 111, 141, 174, 53, 38, and 111

median: _________                        mean: _________                         mode: _________
2.   150, 19, 156, 19, 48, 142, 41, 142, 41, and 102

Write the median: _________        Write the mean: _________            Write the mode: _________
3.   178, 77, 86, 85, 16, 45, 164, 26, 107, 49, 136, 161, and 170

Write the median: _________        Write the mean: _________            Write the mode: _________
4.   108, 90, 16, 2, 2, 3, 25, and 130

Write the median: _________        Write the mean: _________            Write the mode: _________
5.   Students with the following GPAs applied for a job: 3.5, 2.4, 2, 4, 2.4, 2.4, 2.4, 2.4, 3.2,
     and 2.6

Write the median: _________        Write the mean: _________            Write the mode: _________
6.   Given the following annual mutual fund returns:
      23.04         57.01           39.41             39.41         -40.87        13.45
      7.58          39.41           43.1              -43.25        51.17         -49.26
      14.53         19.21           23.75             -49.26        17.06         10.96
      19.77         -42.09          10.96             -48.44        2.3           42.58
      12.73         42.58           29.8              8.08          24.97         13.45
Write the median: _________        Write the mean: _________            Write the mode: _________
7.   The following temperatures were recorded: -3, -7, 62, -1, 53, -9, 12, 19, -6, and 45

Write the median: _________        Write the mean: _________            Write the mode: _________




                                                     2
Name: __________________________________________________________


Find the mean, median, mode and range for each set of data. Select the most accurate
measure of central tendency and explain why. Use your notes

1.                                                       2.




                                                              39   40   41   42   43   44   45   46   47
     68   69   70   71   72   73   74

3.                                                       4.




     41   42   43   44   45   46   47    48
                                                              26   27   28   29
Complete.
1.                                                       2.


                                                               2   3    4    5    6    7    8
      1   2    3    4    5    6
                                                              Mean_____ Median _____ Mode _____
     Mean _____ Median _____            Mode _____            What is wrong with this graph?
       High Temperatures in October             a. How can we improve this data?                           .
3.            Stem Leaves
                 47 4 5 2 8
                 51 0 3
                 60 2 5                         b. Is there an outlier? If there is, what is the
                                                outlier?
                 72 4 1 0


                                                c. What is the mean median and mode?




                                                     3
Name: __________________________________________________________


Complete.
6.           Length of Pieces of Rope               a. What is the difference between the lengths
                                                    of the blue rope and the red rope?



                                                    b. If it takes twenty-one inches of rope to go
                                                    all the way around the fence post, how many
                                                    times will the orange rope go around the
                                                    post?



                                                    c. What is the mean median and mode?




Complete.
7.       Color of Cars in a Parking Lot             a. How many cars are there in this study?



                                                    b. What is the mean median and mode?



                                                    c. Which color has the least amount of cars in
                                                    the parking lot?




Make a vertical bar graph using the data in the table.
10.         Points Scored          Player Points                Points Scored
                                   Steven   6    a. What is the mean for points for all
                                   Austin   9    players?
                                     Isaac     16
                                     Luis      10
                                     Olivia    3     b. What is the median for points scored?
                                     Morgan    18
                                     Jacob     13
                                     Natalie   12   c. Are there any outliers? What is the mode?




                                                4
Name: __________________________________________________________



Complete.
11. This stem-and-leaf plot shows that        a. Is there an outlier? If so, then what is it?
    grades that students received on a
    math quiz.
                 Test Scores
             Stem Leaves                      b. What is the median of the high temperatures
                 38                           recorded?
                 4
                 5
                 65 1                         c. What is the mode of the data?
                 74 8 8 4 8 4
                 86 2 8 0
                 95 4 8 6 6 3 1 7
                10 0
Complete.
12.          Money Spent on Sneakers                a. What is the mode? Is there an outlier?


                                                    b. What is the average amount spent on all 6
                                                    sneakers? Round your answer to the nearest
                                                    cent.


                                                    c. What is the median of the data?




Complete.
14.   What Students                                  a. What number of 1000 students drank
    Drank for Breakfast A      Milk 50%              orange juice for breakfast?
                        B      Water 25%
                               Orange Juice
                           C
                               16%                   b. What is the most popular drink?
                           D   Soda 9%




                                                5
Name: __________________________________________________________


What sort                                     4. Using the scatter plot and the trend
of trend is                                   line, find the gravity to the nearest
shown in                                      tenth, when the altitude is 125 km.
the scatter                                   Describe the scatter plot.
plot?




A wholesale dealer of stationery
products plots the scatter diagram of
his income through the years 1985 to
2000. Is the data linear? What is your
prediction for 2005?




                                              5. Using the scatter plot and the line of
3. The scatterplot shows the details of       fit, describe the scatterplot. Predict the
a survey on population of 10 cities and       number of hours a student needs to
the number of educational institutes in       study to get a score of 92.
these cities.




                                          6
Name: __________________________________________________________


6. Describe each graph below. Does
the line of fit agree with the graph?            9. Describe this scatter plot. What is
                                                 your prediction for 2002?




                                                 10. Create a table that shows the
                                                 weight of each child as he ages. State
                                                 which of these graphs are linear, which
7. Describe each graph. Does the line            is curved.
fit as the correlation for the data points
given.




8. The scatter plot displays Sam's
weight as he ages. What can you
conclude from this data?




                                             7

				
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