MEAN, MEDIAN, MODE EXERCISES |
1/ For some strange reason, the grade 9 class at LCC decided to have
an egg eating contest to raise money for a school project.
The rules stated that each sponsor had to pay 10 cents for each egg eaten
after the first 5 eggs (they figured anyone can eat 5 eggs.)
The table shows the results of the competition:
Egg eater | number eaten | # of sponsors |
Jaclyn | 13 | 3 |
Alex | 22 | 2 |
Viviane | 10 | 4 |
Zach | 25 | 9 |
Norman | 32 | 7 |
Ryan | 22 | 3 |
Samantha | 22 | 3 |
Josh | 16 | 5 |
Michael | 12 | 3 |
Find:
a) the mean number of eggs eaten | b) the mean number of sponsors | ||
c) the median number of eggs eaten | d) the median number of sponsors | ||
e) the mode number of eggs eaten | f) the mode number of sponsors | ||
g) amount raised by each student | h) the total money raised | ||
i) the mean amount of money raised | j) the median of the money raised | ||
k) the mode value of money raised | |||
l) the range of: | eggs eaten | # of sponsors | money raised |
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2/ A group of 40 people went on an apple picking outing. At the end of the day,
they tabulated the number of baskets of apples picked:
# of baskets picked | frequency |
1 | 8 |
2 | 10 |
3 | 12 |
4 | 3 |
5 | 3 |
6 | 3 |
7 | 1 |
a) Find the median # of baskets.
b) Find the mean # of baskets.
c) What is the mode of this distribution?
d) What is the range of this distribution?
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3/ After a marathon in Toronto in which 50 people participated,
the following data was presented to the media:
distance (km) | frequency |
[ 0, 10 [ | 5 |
[ 10, 20 [ | 5 |
[ 20, 30 [ | 21 |
[ 30, 40 [ | 14 |
[ 40, 50 [ | 5 |
a) Find the estimated mean distance run.
b) What is the modal class of this data?
c) In which class do we find the median value?
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4/ Where (in what position 5th? 7th? etc.) is the median in a distribution with:
a) 27data items | b) 32 data items | c) 107 data items | d) 350 data items |
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Solutions:
1)
a) mean number of eggs eaten = 19.3 | b) the mean number of sponsors = 4.3 | ||
c) the median number of eggs eaten = 22 | d) the median number of sponsors = 3 | ||
e) the mode number of eggs eaten = 22 | f) the mode number of sponsors = 3 | ||
g) amount raised by each student (see table below) | h) the total money raised = $62.50 | ||
i) the mean amount of money raised = $6.94 | j) the median of the money raised = $5.10 | ||
k) the mode value of money raised = $5.10 | |||
l) the range of: | eggs eaten = 22 | # of sponsors = 7 | money raised = $16.90 |
Egg eater | money raised |
Jaclyn | C$2.40 |
Alex | C$3.40 |
Viviane | C$2.00 |
Zach | C$18.00 |
Norman | C$18.90 |
Ryan | C$5.10 |
Samantha | C$22.00 |
Josh | C$16.00 |
Michael | C$12.00 |
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2)
a) median = 3 | b) mean = 2.9 baskets | c) mode = 3 | d) range = 11 |
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3) (data in classes)
a) estimated mean = 26.8 km | b) modal class = [20, 30[ | c) median class = [20, 30[ |
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4)
a) 14th data value | b) between 16th & 17th | c) 54th data value | d) mean of 175th & 176th |
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