CEMC's Open Courseware - Lesson 1: Mean, Median, and Mode

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Exercises

Determine the mean, median, and mode for each data set.
1. Minutes practising piano each day: $30,~50,~20,~50,~15,~45,~0$
2. Number of points scored in basketball games: $14,~4,~15,~17,~2,~18,~10,~12,~15,~10$
3. Grades on a report card: $76\%,~ 72\%,~64\%,~78\%,~72\%,~72\%,~82\%,~78\%$
4. Cost of lunch each day: $$7.99,~$10.99,~$5.79,~$8.50,~$6.99,~$4.49$
5. Daily low temperatures: $-7^\circ$C, $-5^\circ$C, $-7^\circ$C, $-3^\circ$C, $2^\circ$C, $0^\circ$, $-1^\circ$C
Fill in each blank with one of the following three words: sometimes, always, or never. Explain why the resulting statement is true.
1. The mean is a value in the data set.
2. The mode is a value in the data set.
3. The median is a value in the data set.
During a census, data was collected about the number of people in each household in the country. The measure of central tendency was calculated to be $2.9$ people. Would this be a calculation of the mean, median, or mode of the data set? Explain.
Different types of data sets are described below. Create two different data sets that match the description given.
1. Seven pieces of data with two modes and a median of $8$.
2. Five pieces of data with a mean of $28$ and a median of $20$.
3. Eight pieces of data with a median of $15$ and with a mode that is larger than the median.
4. Six pieces of data with a mean of $2$, a median of $3$, and no mode.

Below is data collected from a Grade 7 class about the number of hours they sleep each night. Determine the mean, median, and mode of the data.

Number of Hours	Number of Students
$6$	$3$
$7$	$8$
$8$	$12$
$9$	$8$
$10$	$1$
$11$	$1$

1. Create a data set of five numbers that includes the numbers $2$, $2$, and $4$, for which the mean of the data set is $20$.
2. The mean, median, and mode for this data set with five numbers are all equal:\[15,~40,~25,~20,~\boxed{\phantom \square}\]What is the missing value in the box?
1. What can you say about the numbers in a data set if the mean is significantly larger than the median?
  For example, consider race times with a mean of $20$ minutes and a median of $11$ minutes.
2. What can you say about the numbers in a data set if the three central tendencies are all very close in value?
  For example, consider race times with a mean of $12.7$ seconds, a median of $12.8$ seconds, and a mode of $12.9$ seconds.
At one track and field meet, Fadi had the following six shot-put results:
$10.38$ m

$10.46$ m

$11.06$ m

$10.21$ m

$10.79$ m

$10.92$ m

At a second meet, Fadi had the following three shot-put results:

$10.95$ m

$11.29$ m

$10.86$ m
1. Calculate the mean shot-put result for the first meet (six distances). Calculate the mean shot-put result over the second meet (three distances).
2. Can Fadi find the mean of all shot-put results (nine distances) by calculating the mean of the two values found in part a)? Explain.
Source: Shot-put - Wavebreakmedia/iStock/
Getty Images
The mean of five positive integers is $20$.
1. What is the largest possible value of one of these five numbers?
2. If this set of five positive integers has no mode, then what is the largest possible value of one of these five numbers?

Number of Hours	Number of Students
\(6\)	\(3\)
\(7\)	\(8\)
\(8\)	\(12\)
\(9\)	\(8\)
\(10\)	\(1\)
\(11\)	\(1\)