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The Mean

Section A – All the review questions in this section are selected response.

  1. What is the mean of the following numbers? 10, 39, 71, 42, 39, 76, 38, 25
    1. 42
    2. 39
    3. 42.5
    4. 35.5
  2. What name is given to a value in a data set that is much lower or much higher than the other values?
    1. A sample
    2. An outlier
    3. A population
    4. A tally
  3. What symbol is used to denote the mean of a population?
    1. \sum
    2. \overline{x}
    3. x_n
    4. \mu
  4. What measure of central tendency is calculated by adding all the values and dividing the sum by the number of values?
    1. median
    2. mean
    3. mode
    4. typical value
  5. The mean of 4 numbers is 71.5. If 3 of the numbers are 58, 76, and 88, what is the value of the 4^{\text{th}} number?
    1. 64
    2. 60
    3. 76
    4. 82

Section B – All questions in this section require you to show all the work necessary to arrive at a correct solution.

  1. Determine the means of the following sets of numbers:
    1. 20, 14, 54, 16, 38, 64
    2. 22, 51, 64, 76, 29, 22, 48
    3. 40, 61, 95, 79, 9, 50, 80, 63, 109, 42
  2. The mean weight of 5 men is 167.2 pounds. The weights of 4 of the men are 158.4 pounds, 162.8 pounds, 165 pounds, and 178.2 pounds. What is the weight of the 5^{\text{th}} man?
  3. The mean height of 12 boys is 5.1 feet. The mean height of 8 girls is 4.8 feet.
    1. What is the total height of the boys?
    2. What is the total height of the girls?
    3. What is the mean height of the 20 boys and girls?
  4. The following data represents the number of advertisements received by 10 families during the past month. Calculate the mean number of advertisements received by each family during the month. 43 \qquad 37 \qquad 35 \qquad 30 \qquad 41 \qquad 23 \qquad 33 \qquad 31 \qquad 16 \qquad 21
  5. The following table of grouped data represents the weight (in pounds) of all 100 babies born at a local hospital last year. Calculate the mean weight for a baby.
Weight (pounds) Number of Babies
[3 - 5) 8
[5 - 7) 25
[7 - 9) 45
[9 - 11) 18
[11 - 13) 4
  1. A group of grade 6 students each earned a mark on an in-class assignment. The marks for the boys were 90, 50, 70, 80, and 70. The marks for the girls were 60, 20, 30, 80, 90, and 20.
    1. Find the mean mark for the boys.
    2. Find the mean mark for the girls.
    3. Find the mean mark for all the students.
  2. The mean of 4 numbers is 31. (a) What is the sum of the 4 numbers? The mean of 6 other numbers is 28. (b) Calculate the mean of all 10 numbers.
  3. The following numbers represent the weights (in pounds) of 9 dogs: 22 \qquad 19 \qquad 26 \qquad 18 \qquad 29 \qquad 33 \qquad 20 \qquad 16 \qquad 30
    1. What is the mean weight of the dogs?
    2. If the heaviest and the lightest dogs are removed from the group, find the mean weight of the remaining dogs.
  4. To demonstrate her understanding of the concept of mean, Melanie recorded the daily temperature in degrees Celsius for her hometown at the same time each day for a period of 1 week. She then calculated the mean daily temperature.
Day Sun Mon Tues Wed Thurs Fri Sat
Temperature (^\circ \text{C}) -7^\circ \text{C} 0^\circ \text{C} -1^\circ \text{C} 1^\circ \text{C} -4^\circ \text{C} -6^\circ \text{C} 3^\circ \text{C}

\overline{x} &= \frac{-7+-1+1+-4+-6+3}{6}\\\overline{x} &= \frac{-14}{6}\\\overline{x} &= -2.3^\circ  \text{C}

Melanie reported the mean daily temperature to be -2.3^\circ \text{C}.

(a) Is Melanie correct? Justify your answer.

(b) If you do not agree with Melanie’s answer, can you tell Melanie what mistake she made?

  1. Below are the points scored by 2 basketball teams during the regular season for their first 12 games:

&\text{Honest Hoopers} && 93 && 78 && 84 && 106 && 116 && 93 && 90 && 75 && 104 && 100 && 123 && 57\\&\text{Bouncy Baskets}  && 110 && 89 && 91 && 121 && 84 && 79 && 114 && 66 && 50 && 101 && 106 && 114

Which team had the higher mean score?

Section C – Match the words in the left column with the correct symbol from the right column.

The Median

Section A – All the review questions in this section are selected response.

  1. What is the median of the following numbers? 10, 39, 71, 42, 39, 76, 38, 25
    1. 42.5
    2. 39
    3. 42
    4. 35.5
  2. The front row in a movie theatre has 23 seats. If you were asked to sit in the seat that occupied the median position, in what number seat would you have to sit?
    1. 1
    2. 11
    3. 23
    4. 12
  3. What is the median mark achieved by a student who recorded the following marks on 10 math quizzes? 68, 55, 70, 62, 71, 58, 81, 82, 63, 79
    1. 68
    2. 71
    3. 69
    4. 79
  4. A set of 4 numbers that begins with the number 32 is arranged from smallest to largest. If the median is 35, which of these could possibly be the set of numbers?
    1. 32, 34, 36, 38
    2. 32, 35, 38, 41
    3. 32, 33, 34, 35
    4. 32, 36, 40, 44
  5. The number of chocolate bars sold by each of 30 students is as follows: 32, 6, 21, 10, 8, 11, 12, 36, 17, 16, 15, 18, 40, 24, 21, 23, 24, 24, 29, 16, 32, 31, 10, 30, 35, 32, 18, 39, 12, 20 What is the median number of chocolate bars sold by the 30 students?
    1. 18
    2. 21
    3. 24
    4. 32

Section B – All questions in this section require you to show all the work necessary to arrive at a correct solution.

  1. The following table lists the retail price and the dealer’s costs for 10 cars at a local car lot this past year: Deals on Wheels
Car Model Retail Price Dealer’s Cost
Nissan Sentra $24,500 $18,750
Ford Fusion $26,450 $21,300
Hyundai Elantra $22,660 $19,900
Chevrolet Malibu $25,200 $22,100
Pontiac Sunfire $16,725 $14,225
Mazda 5 $27,600 $22,150
Toyota Corolla $14,280 $13,000
Honda Accord $28,500 $25,370
Volkswagen Jetta $29,700 $27,350
Subaru Outback $32,450 $28,775

(a) Calculate the median for the data on the retail prices for the above cars.

(b) Calculate the median for the data on the dealer’s costs for the above cars.

  1. Due to high winds, a small island in the Atlantic suffers frequent power outages. The following numbers represent the number of outages each month during the past year: 4 \quad 5 \quad 3 \quad 4 \quad 2 \quad 1 \quad 0 \quad 3 \quad 2 \quad 7 \quad 2 \quad 3 What is the median number of monthly power outages?
  2. The Canadian Coast Guard has provided all of its auxiliary members with a list of 14 safety items (flares, fire extinguishers, life jackets, fire buckets, etc.) that must be aboard each boat at all times. During a recent check of 15 boats, the number of safety items that were aboard each boat was recorded as follows: 7 \quad 14 \quad 10 \quad 5 \quad 11 \quad 2 \quad 8 \quad 6 \quad 9 \quad 7 \quad 13 \quad 4 \quad 12 \quad 8 \quad 3 What is the median number of safety items aboard the boats that were checked?
  3. A teacher’s assistant who has been substituting has been recording her biweekly wages for the past 13 pay periods. Her biweekly wages during this time were the following: & \$700 \qquad  \$550 \qquad  \$760 \qquad  \$670 \qquad  \$500 \qquad  \$925 \qquad  \$600\\ & \$480 \qquad  \$390 \qquad  \$800 \qquad  \$850 \qquad  \$365 \qquad  \$525 What is her median biweekly wage?
  4. A minor hockey league has 50 active players who range in age from 10 years to 15 years. The following table shows the ages of the players:
Age of Players(yrs) Number of Players
10 6
11 8
12 7
13 11
14 10
15 8

Use the TI-83 calculator to determine the median age of the players.

  1. A die was thrown 14 times, and the results of each throw are shown: What is the median score for the 14 rolls of the die?
  2. At a local golf club, 100 players competed in a 1-day tournament. The fifth hole of the course is a par 6. The scores of each player on this hole were recorded, and the results are shown below: &\text{Score}  && 2 \quad  3 \quad  4  \quad \ \ 5  \quad \ 6 \quad \ 7  \quad \ 8\\&\text{Number of Players}  &&  3 \quad 8 \quad 22 \quad 29 \quad 20 \quad 8 \quad 10 What is the median score for the players?
  3. A math teacher at a local high school begins every class with a warm-up quiz based on the work presented the previous day. Each test consists of 6 questions valued at 1 point for each correct answer. The results of Monday’s quiz for the 40 students in the class are shown below: &\text{Mark}  && 0 \quad 1 \quad 2 \quad 3 \quad \ 4 \quad 5 \quad 6\\& \text{Number of Students}  && 2 \quad 6 \quad 7  \quad 10 \quad 5 \quad 3 \quad 7 What is the median score for Monday’s quiz?
  4. In Canada, with the loonie and the toonie, you could have a lot of coins in your pocket. A number of high school students were asked how many coins they had in their pocket, and the results are shown in the following table: &\text{Number of Coins}  && 0 \quad 1 \quad 2 \quad 3 \quad 4 \quad 5 \quad 6 \quad 7\\&\text{Number of Students}  && 2 \quad 5 \quad 8 \quad 9 \quad 6 \quad 4 \quad 9 \quad 7 What is the median number of coins that a student had in his or her pocket?
  5. A group of 12 students participated in a local dirt bike race that required them to cover a 1-mile course in the fastest time possible. The times, in minutes, of the 12 participants are shown below: &3.5 \ \text{min} \quad 4.2 \ \text{min} \quad 3.1 \ \text{min} \quad 5.3 \ \text{min} \quad 6.2 \ \text{min} \quad 4.6 \ \text{min}\\&5.1 \ \text{min} \quad  6.7 \ \text{min} \quad 5.4 \ \text{min} \quad 4.4 \ \text{min} \quad  3.9 \ \text{min} \quad 5.0 \ \text{min} What is the median time of the participants in the race?

The Mode

Section A – All the review questions in this section are selected response.

  1. Which of the following measures can be determined for quantitative data only?
    1. mean
    2. median
    3. mode
    4. none of these
  2. Which of the following measures can be calculated for qualitative data only?
    1. mean
    2. median
    3. mode
    4. all of these
  3. What is the term used to describe the distribution of a data set that has 1 mode?
    1. multimodal
    2. unimodal
    3. nonmodal
    4. bimodal
  4. What is the mode of the following numbers, which represent the ages of 8 hockey players? 12, 11, 14, 10, 8, 13, 11, 9
    1. 11
    2. 10
    3. 14
    4. 8
  5. Which of the following measures can have more than 1 value for a set of data?
    1. median
    2. mode
    3. mean
    4. none of these

Section B – All questions in this section require your answer to be a complete sentence.

  1. What are the modes of the following sets of numbers?
    1. 3, 13, 6, 8, 10, 5 6
    2. 12, 0, 15, 15, 13, 19, 16, 13, 16, 16
  2. A student recorded her scores on weekly English quizzes that were marked out of a possible 10 points. Her scores were as follows: 8, 5, 8, 5, 7, 6, 7, 7, 5, 7, 5, 5, 6, 6, 9, 8, 9, 7, 9, 9, 6, 8, 6, 6, 7 What is the mode of her scores on the weekly English quizzes?
  3. The following table represents the number of minutes that students spent studying for a math test:
Studying Time (minutes) Number of Students
[0 - 10) 2
[10 - 20) 10
[20 - 30) 6
[30 - 40) 4
[40 - 50) 3

What is the mode of the amounts of time spent studying for the math test?

  1. A pre-test for students entering high school mathematics was given to 48 students. The following table shows the number of questions attempted out of 50 by each of the students taking the test:  & 43 \quad 39  \quad  40 \quad 40 \quad 41 \quad 44\\& 42 \quad 41 \quad 41  \quad 41  \quad 42  \quad  44\\& 43 \quad  41 \quad  40  \quad 41  \quad 42  \quad   41\\& 42  \quad  41 \quad 42  \quad 42  \quad 41  \quad  44\\& 41 \quad  42 \quad 43  \quad 40  \quad 42  \quad  39\\& 42  \quad 40 \quad 39  \quad 42 \quad 43  \quad  42\\& 42 \quad 39  \quad 41  \quad 41 \quad  42  \quad   40\\& 43 \quad  44 \quad 40  \quad 42  \quad 44  \quad   39 What number of questions was attempted the most by the students?
  2. A die was tossed 14 times. What is the mode of the numbers that were rolled?
  3. The following table represents the number of times that 24 students attended school basketball games during the year:

&\text{Number of Games} && 5 \quad 6 \quad 7 \quad 8 \quad 9\\&\text{Number of Students} &&  1  \quad 5 \quad  3 \quad  9 \quad  6

What is the mode of the numbers of games that students attended?

  1. The newly-formed high school soccer team is playing its first season. The following table shows the number of goals it scored during each of its matches:

&\text{Number of Goals} && 1 \quad  2 \quad 3\\&\text{Number of Matches} && 8 \quad 8 \quad m

If the mean number of goals scored is 2.04, what is the smallest possible value of m if the mode of the numbers of goals scored is 3?

  1. What is the mode of the following numbers, and what word can be used to describe the distribution of the data set? 5, 4, 10, 3, 3, 4, 7, 4, 6, 5, 11, 9, 5, 7
  2. List 3 examples of how mode could be useful in everyday life?
  3. The temperature in ^\circ \text{F} on 20 days during the month of June was as follows: 70^\circ \text{F}, \ 76^\circ \text{F}, \ 76^\circ \text{F}, \ 74^\circ \text{F}, \ 70^\circ \text{F}, \ 70^\circ \text{F}, \ 72^\circ \text{F}, \ 74^\circ \text{F}, \ 78^\circ \text{F}, \ 80^\circ \text{F}\\ 74^\circ \text{F}, \ 74^\circ \text{F}, \ 78^\circ \text{F}, \ 76^\circ \text{F}, \ 78^\circ \text{F}, \ 76^\circ \text{F}, \ 74^\circ \text{F}, \ 78^\circ \text{F}, \ 80^\circ \text{F}, \ 76^\circ \text{F} What is the mode of the temperatures for the month of June?

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Feb 23, 2012

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