Vocabulary
Sampling and Bias
Empirical Rule
Z-Scores
Bell Curve Facts
100
What is this unit about?
Bell curve / normal distribution, statistics, population sampling, creating non-bias data, and more!
100
AMC surveyed all the customers in theater 1 and 5 on their movie experience. What type of sampling did they do?
Cluster
100
What are the 3 magic numbers from the Empirical Rule?
68, 95, 99.7
100
If the mean is 67 and the standard deviation is 3. Then what is the value of
mu + 3sigma
76
100
What is another name for the Bell Curve?
Normal Distribution
200
What is a sample and a population?
A sample is a portion of the population, and ideally without bias the sample will be REPRESENTATIVE of the population. The population is the whole of a group of people.
200
Every 10th login to the NBA 2k online game has the gamer engage with a survey. What kind of sampling technique is this?
Systematic
200
If my score is m and your score is n, what is the probability that a random score, p, is
m < p < n?
68%
200
A set of normally distributed data has a mean of 82 and a standard deviation of 5. If the z score is -1 for a data point, what is the data point?
77
200
What is the symbol used for standard deviation and what is the symbol used for the mean?
A lowercase sigma,
sigma
Lowercase mu,
mu
300
What is the mean? What z-score does the mean have?
A value gathered by adding up all the data points, and then dividing by the amount of data points. It is the middle of a bell curve. The mean has a z-score of 0.
300
Everyone writes down on a slip of paper which type of phone he or she has and drops it in a bucket. Of the 125 slips of paper, 30 are randomly selected. What type of sampling is this?
Simple Random
300
If the mean of a standardized test with a normal distribution is 54.3 and the standard deviation is 4.6, what is the best approximation of the percent of the scores that fall within two standard deviations above the mean?
47.5% aka (34% + 13.5%)
300
A data set is normally distributed with a mean of 78 and a standard deviation of 6.5. An element in this set is 72. Which is closest to the z-score for 72?
-0.92
300
What do you type in Desmos if you need to create a bell curve to find the percentage of a population/sample between two values or below/above a singular value?
normaldist(
400
What is a normal distribution?
It is the most common type of distribution, and as a sample increases in size the sample is more likely to display the normal bell curve shape.
400
What type of data gathering is described as an equal number of samples being taken from each level?
Stratified
400
On a standardized test with normal distribution. The mean is 75 and the standard deviation is 6. If 1,200 students took the test, approximately how many students would be expected to score between 69 and 81?
816, 68% of 1200
400
What is the Z-Score formula?
Z= (x-mu)/sigma
400
The figure shows the normal distribution curve. What is the significance of the intersection of the vertical line and the curve?
It is the mean, median, and mode
500
What is standard deviation?
A specially calculated value relevant to the data that shows how spread out a normal distribution is. Also it determines how flat or tall the normal distribution is.
Extra:
sigma = sqrt((sum (x_i - mu)^2)/N)
500
You are gathering data to determine the probability that a random person considers himself or herself a sports fan. To collect data, you ask people as they enter a sporting goods store. Is there bias in this sample. Why or why not?
Bias because of location
500
A normally distributed set of 1,010 values has a mean of 103 and a standard deviation of 12. What integer value is closest to the number of values expected to be below 88?
107
500
A set of data is normally distributed with a mean of 18. If the z-score corresponding to a value of 28 is 1.25, then what is the standard deviation of the set?
sigma = 8
500
As standard deviation increases, what happens to the bell curve?
It flattens, or the peak becomes less tall.