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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