Measures of Central Tendency
Find the mean, median, mode, and range of:
8, 10, 12, 14, 16
What is:
Mean=12
Median=12
No mode
Range=8
Mia's quiz scores are:
72%, 84%, 88%, 76%
What is her current average in the class?
What is 80%?
A bag contains:
4 red marbles, 3 blue marbles, and 3 green marbles.
Find:
a) P(red). Write your answer as a fraction in simplest form, using proper notation.
What is P(red)=2/5?
What is the difference between experimental and theoretical probability?
What is:
Theoretical probability is what you expect to happen.
Experimental probability is what actually happens when you do the experiment.
Two standard coins are flipped.
a) list the sample space
b) how many outcomes are possible?
What is:
a) {HH, HT, TH, TT}
b) 4
Find the mean, median, mode, and range of:
24, 19, 32, 19, 28, 24, 19, 31
What is:
Mean=24.5
Median=24
Mode=19
Range=13
The daily temperatures for a week were:
12°C, 15°C, 14°C, 13°C, 16°C
a) What is the mean temperature that week?
b) If a temperature of 18°C is added, will the mean increase or decrease?
What is:
a)Mean=14°C
b)18°C is higher than the original mean, so it will increase the mean.
A spinner has 8 equal sections numbered 1–8.
Find:
P(spinning an even number). Write your answer as a fraction in simplest form, using proper notation.
What happens to the experimental probability as the number of trials increases?
What is:
The experimental probability will become closer to the theoretical probability?
A coin is tossed and a die is rolled.
a) List the sample space.
b) How many outcomes are possible?
What is:
a) {(H,1),(H,2),(H,3),(H,4),(H,5),(H,6),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}
b) 12
a) Find the mean and median:
45, 47, 48, 50, 52, 90
b) Which measure better represents the data?
What is:
a) mean=55.3, median=49
b) Median because it is not as affected by the outlier (90)
The number of books read by a student over five months was: 3, 5, 4, 6, 7
a) What is the mean number of books read per month?
b) If a sixth month is added in which the student reads 9 books, what is the new mean?
What is:
a)Mean=5
b)Mean=5.7
A jar contains 10 chocolate candies, 5 strawberry candies, and 5 lemon candies.
Find the probability of selecting:
a) A strawberry candy
Write answer as a fraction, decimal, and percent.
What is P(strawberry)=1/4=0.25=25%
A coin was flipped 20 times and landed on heads 11 times.
What is the experimental probability of heads?
What is:
P(heads)=11/20
A spinner has three equal sections labeled:
Red, Blue, Green
The spinner is spun twice.
a) Draw a tree diagram.
b) List all possible outcomes.
c) What is the probability of getting the same colour twice?
What is:
a)
├── Red
│ ├── Red (RR)
│ ├── Blue (RB)
│ └── Green (RG)
├── Blue
│ ├── Red (BR)
│ ├── Blue (BB)
│ └── Green (BG)
└── Green
├── Red (GR)
├── Blue (GB)
└── Green (GG)
b) {RR, RB, RG, BR, BB, BG, GR, GB, GG}
c) P(same colour)=1/3
Which measure (mean, median, or mode) would best describe each of the following and why:
a) Most common shoe size sold at a store
b) Typical monthly rent in a city with a few extremely expensive apartments
c) Average height of Grade 7 students
What is:
a) Mode-which is sold most frequently
b) Median-outliers
c) Mean-heights are typically fairly evenly spread without extreme outliers
Sophia has test scores of:
78%, 82%, 85%, 91%
What score does she need on her fifth test to have an average of 84%?
What is 84%?
A standard die is rolled.
Find the theoretical probability of:
a) Rolling a 3
b) Rolling an odd number
c) Rolling a number greater than 4
What is:
a) P(3)=1/6
b) P(odd)=1/2
c) P(>4)=1/3
A spinner has 4 equal sections labeled A, B, C, and D.
The spinner was spun 40 times and landed on A 12 times.
a) What is the theoretical probability of landing on A?
b) What is the experimental probability of landing on A?
What is:
a) P(A)=1/4
b) P(A)=3/10
Three different sandwiches (Ham, Turkey, Veggie) and two different drinks (Water, Juice) are available for lunch.
a) Draw a tree diagram showing all possible meal combinations.
b) How many combinations are possible?
c) What is the probability of randomly choosing a meal that includes Juice?
What is:
a) ├── Ham
│ ├── Water (Ham, Water)
│ └── Juice (Ham, Juice)
├── Turkey
│ ├── Water (Turkey, Water)
│ └── Juice (Turkey, Juice)
└── Veggie
├── Water (Veggie, Water)
└── Juice (Veggie, Juice)
b)6
c) P(juice)=1/2
Explain how an outlier affects:
a) The mean
b) The median
c) The range
a) Greatly affected- pulls the mean in the direction of the outlier
b)Very little or not at all
c)Greatly affected- increases the range significantly
Liam has scores of:
70%, 80%, 85%, 90%
What score does he need on his fifth test to have an average of 84%?
What is 95%?
One card is selected at random from a standard deck of 52 playing cards.
Find the theoretical probability of:
a) Drawing a heart
b) Drawing a face card (Jack, Queen, or King)
c) Drawing a black card that is greater than 10 (J, Q, K)
What is:
a) P(heart)=1/4
b)P(face card)=3/13
c) P(black, >10)=3/26
A jar contains:
a) What is the theoretical probability of selecting a strawberry candy?
A student randomly selects a candy 40 times (replacing it each time) and gets a strawberry candy 10 times.
b) What is the experimental probability of selecting a strawberry candy?
c) which is higher?
What is:
a) P(strawberry)=3/10
b) P(strawberry)=1/4
c) Theoretical
A student is creating a lunch combo. They can choose:
a) List the sample space.
b) What is the probability of randomly choosing a lunch that includes Milk?
c) What is the probability of randomly choosing a lunch that includes Turkey or Chicken?
What is:
a) {(Ham,Water), (Ham,Juice), (Ham,Milk), (Turkey,Water), (Turkey,Juice), (Turkey,Milk), (Veggie,Water), (Veggie,Juice), (Veggie,Milk), (Chicken,Water), (Chicken,Juice), (Chicken,Milk)}
b)P(milk)=1/3
c)P(turkey or chicken)=1/2