Data Dynamics
Find the mean of this data set: 4, 8, 12, 16.
What is 10?
The sum is 40; 40 \ 4 = 10
True or False: On a dot plot, the height of a column of dots directly represents the frequency of that specific data value.
What is true?
The theoretical probability of rolling a number greater than 4 on a standard 6-sided die.
What is 1/3?
The successful outcomes are 5 and 6, giving 2/6, which simplifies to 1/3.
If you flip a coin once and roll a standard 6-sided die once, how many total possible outcomes exist in the sample space?
What is 12 outcomes?
2 coin outcomes x 6 die outcomes = 12
A data set consists of the following numbers: 3, 5, 5, 7, 10, 12, 15. What is the median?
What is 7 (It is the exact middle value of the ordered data set).
If a dot plot shows a heavy cluster of data points on the left side with a long, sparse "tail" stretching out to the right, how is the distribution described?
What is Skewed right (or positively skewed)?
A bag contains 4 red marbles, 5 blue marbles, and 3 green marbles. What is the probability of randomly selecting a marble that is not blue?
What is 7/12
Total marbles = 12. Non-blue marbles = 4 red + 3 green = 7
A fair coin is flipped twice in succession. What is the probability of getting heads on both flips?
What is 1/4 or 25%?
1/2 x 1/2 = 1/4
If the mean of four numbers is 15, and three of the numbers are 10, 12, and 18, what is the fourth number?
What is 20 (The total sum must equal 15 x 4 = 60. Since 10 + 12 + 18 = 40, the missing number is 60 - 40 = 20)
A dot plot tracks how many books students read over the summer. It shows 3 dots on 0 books, 5 dots on 1 book, 4 dots on 2 books, and 2 dots on 3 books. How many total students were surveyed?
What is 14 students?
3 + 5 + 4 + 2 = 14
During a probability experiment, a coin is flipped 50 times. It lands on heads 28 times. The experimental probability of landing on tails is?
What is 11/25 or 44%
Tails appeared 50 - 28 = 22 times. Experimental probability is 22/50 = 11/25
A drawer holds 3 black socks and 2 white socks. If you randomly select a sock, do not replace it, and then select a second sock, what is the probability that both socks are black?
What is 3/10 or 30%?
P(Black first) x P(Black second) = 3/5 x 2/4 = 6/20 = 3/10
Identify both the mode and the range of this data set: 14, 11, 14, 19, 22, 14, 11.
What is Mode = 14; Range = 11 (14 appears the most frequently. The range is the maximum minus the minimum: 22 - 11 = 11)
Using the same book data from the $300 clue (3 dots on 0, 5 dots on 1, 4 dots on 2, 2 dots on 3), find the median number of books read.
What is 1 book?
With 14 total data points, the median is the average of the 7th and 8th values. Listing them out: 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3. Both positions are 1
The probability of a certain event occurring is 0.35. What is the probability of its complementary event? (Hint: complementary events = 1)
What is 0.65?
The sum of an event and its complement is always 1; 1 - 0.35 = 0.65
A fair coin is tossed and a 4-sided die (numbered 1–4) is rolled. Describe or construct the sample space diagram to find the probability of getting Tails and an odd number.
What is 1/4 or 25%?
The sample space has 8 total pairs: (H,1), (H,2), (H,3), (H,4), (T,1), (T,2), (T,3), (T,4). The successful outcomes are (T,1) and (T,3), which is 2/8 = 1/4
A class of 20 students took a math quiz. 12 students scored an average of 80%, and the remaining 8 students scored an average of 90%. What is the weighted mean score for the entire class?
What is 84%?
Name two specific visual advantages a dot plot has over a raw, unorganized list of numerical data.
What is it clearly reveals the shape/distribution of data, instantly highlights gaps and outliers, makes finding the mode effortless, and preserves every single raw data point visually?
A prize spinner is divided into unequal sectors: Red, Blue, and Yellow. If the probability of spinning Red is 1/4 and Blue is 2/5, what is the probability of spinning Yellow?
What is 7/20 or 35%?
1 - (1/4 + 2/5) = 1 - (5/20 + 8/20) = 1 - 13/20 = 7/20
Two standard 6-sided dice are rolled simultaneously. What is the probability that the sum of the two numbers showing face up is exactly 9?
What is 1/9?
There are 36 total outcomes. The combinations that sum to 9 are (3,6), (4,5), (5,4), and (6,3). That gives 4/36, which simplifies to 1/9.