Algebra 2 Statistics and Probability Review

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Questions and Answers

What is a sample?

a subset selected to represent the population

What is a random sample?

each member of the population has an equal chance of being selected as a part of the sample

What is a self-selected sample?

members volunteer to be included in the sample

What is a convenience sample?

members that are readily available or easy to reach Signup and view all the answers

What is the mean?

the average of a set of data, obtained by adding the data values and then dividing by the number of data Signup and view all the answers

What is the median?

the middle number in a set of data values that are listed in order Signup and view all the answers

What are measures of central tendency?

numbers that are used to describe the center of a set of data Signup and view all the answers

What is the range of a set of data?

the difference between the minimum and maximum values within a set of data Signup and view all the answers

What is the interquartile range (IQR)?

the difference between the third and first quartiles Signup and view all the answers

What are independent events?

the outcome of one event does not affect the outcome of the second event Signup and view all the answers

What is a probability distribution graph?

the probabilities of all the possible outcomes for a random variable Signup and view all the answers

What does a z-score indicate?

how many standard deviations a value is from the mean Signup and view all the answers

What is a standard normal curve?

a graph of probability distribution shaped like a symmetrical, bell-shaped curve Signup and view all the answers

What is the mode of the set of data values {6.1, 9.5, 3.8, 4.6, 6.1, 2.0, 3.7, 2.1}?

6.1 Signup and view all the answers

What is the median of the set of data values {6.1, 9.5, 3.8, 4.6, 6.1, 2.3, 3.7, 2.1}?

4.2 Signup and view all the answers

What is the standard deviation for the set of data values {25, 29, 21, 19, 30, 26, 28}?

3.81 Signup and view all the answers

Find the margin of error (moe) for the sample proportion, given the sample size n = 300. Round to the nearest percent.

+/- 6% Signup and view all the answers

Find the margin of error (moe) for the sample proportion, given the sample size n = 125. Round to the nearest percent.

+/- 9% Signup and view all the answers

What is the probability that all her friends are available to meet for lunch on three different days if there is a 20% chance that all of her friends will be available?

5.12% Signup and view all the answers

Estimate the percent of scores that were 90 or higher if the mean score on a quiz is 82 and the standard deviation is 4.

2.5% Signup and view all the answers

Find the sample proportion (as a %) given 27 out of 60 shoppers prefer generic brands when available.

45% Signup and view all the answers

What number of pieces of checked luggage is 3 standard deviations above the mean when the mean is 380 and the standard deviation is 20?

440 Signup and view all the answers

Find the P(boy and reads horror stories) if 59% of respondents are girls and the percentage of boys reading horror stories is 49%.

20% Signup and view all the answers

What is the participant's bowling score whose z-score is -2.5 if the mean bowling score is 205 and the standard deviation is 14?

170 Signup and view all the answers

Approximately how many students receive grades of 61 or below in a university class of 174 students, if the mean score is 68.5 and the standard deviation is 7.3?

28 Signup and view all the answers

Study Notes

Statistical Sampling Methods

Sample: A subset chosen to represent a larger population.
Random Sample: Every member of the population has an equal chance of selection, akin to drawing names from a hat.
Self-Selected Sample: Participants choose themselves to be included, like customers taking a survey at a store.
Convenience Sample: Comprises members that are easily accessible, such as students on a specific bus.

Measures of Central Tendency

Mean: The average value calculated by summing data points and dividing by the total number of data.
Median: The middle number in a sorted list of data values.
Mode: The number that appears most frequently in a dataset.

Data Range and Distribution

Range: The difference between the maximum and minimum values in a dataset.
Interquartile Range (IQR): The difference between the third quartile (Q3) and the first quartile (Q1).

Probability Concepts

Independent Events: Two events where the outcome of one does not influence the other.
Probability Distribution Graph: Visual representation showing the probabilities of all possible outcomes for a random variable, with total probability summing to 1.

Statistical Measurements

Z Score: Indicates how many standard deviations a data point is from the mean.
Standard Normal Curve: A symmetrical bell-shaped graph representing a normal distribution, with 50% of data below the mean and 50% above.

Statistical Calculations and Applications

Margin of Error (MOE): Reflects the potential error in sample proportions, calculated based on sample size.
Probability Calculations: For example, for Jean, the chance of all friends being available across three days is 5.12%.
Standard Deviation: Measures the dispersion of a dataset. For example, the standard deviation from a set of data values might be 3.81.

Contextual Data Problems

Sample Proportion: For 27 out of 60 shoppers preferring generic brands, the sample proportion is 45%.
Checked Luggage: 3 standard deviations above a mean of 380 luggage pieces results in 440 pieces.
Survey Analysis: In a survey, the probability that a boy reads horror stories can be calculated based on given percentages.
Z-Score Application: The z-score of -2.5 for bowling indicates a participant's score of 170 for a mean of 205 and standard deviation of 14.
Exam Score Distribution: In a class with a mean of 68.5, it's estimated that approximately 28 students scored 61 or below.

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