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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