WHS Math - Statistics

This course uses a standards-based approach to the study of statistics and probability. It is designed so that students will discover how to use probability and statistics to research and analyze data, compare results, and document how statistics are used and misused on a daily basis. A statistics calculator and statistical application software will be used. Connections to functions, both algebraic and trigonometric, will be introduced in the latter part of the course. Connections to real world and cross-curricular applications will be made. Prerequisite Courses: Algebra 1, Geometry, and Algebra 2 or Integrate 1, Integrated 2, and Integrated 3. This course meets the recommendations for a math class outlined in MassCore. (5 Credits)

Unit

Timeframe

Big Ideas (Statements or Essential Questions)

Major Learning Experiences from Unit 

1. Descriptive Statistics

Quarter 1

Descriptive Statistics

  • The definition of statistics

  • How to distinguish between a population and a sample and between a parameter and a statistic

  • How to distinguish between qualitative (categorical) data and quantitative data

  • How to collect data

  • How to construct a frequency distribution including limits, midpoints, relative frequency, cumulative frequency, and boundaries

  • How to construct frequency histograms

  • How to graph and interpret quantitative and categorical data sets

  • How to find the mean, median, mode of a sample

  • How to find a weighted mean of a frequency distribution

  • How to describe the shape of a distribution as uniform, symmetric, or skewed and how to compare the mean and median for each

  • How to find the range, variance, and standard deviation of a data set

2. The Normal Curve

Quarter 1

The Normal Curve

  • How to interpret graphs of normal probability distributions

  • How to use the Empirical Rule to interpret standard deviation

  • How to find and interpret the standard score (z-score)

  • How to find areas under the standard normal curve

  • How to find probabilities for normally distributed variables

  • How to find a z-score given the area under the normal curve

  • How to transform a z-score to an x-value

  • How to find a specific data value of a normal distribution given the probability

3. Probability

Quarter 2

Probability

  • How to use the Fundamental Counting Principle to find the number of ways two or more events can occur

  • How to find the probability of the complement of an event

  • How to use a tree diagram

  • How to find the probability of an event given that another event has occurred

  • How to distinguish between independent and dependent events

  • How to use the Multiplication Rule to find the probability of two events occurring in sequence or to find conditional probabilities

  • How to determine if two events are mutually exclusive

  • How to use the Addition Rule to find the probability of two events

  • How to find the number of ways groups of objects can be arranged in order

  • How to find the number of ways to choose several objects from a group without regard to order

  • How to use counting principles to find probabilities

4. Inferential Statistics - Probability Distributions

Quarter 3

Probability Distributions

  • How to distinguish between discrete and continuous random variables

  • How to construct a discrete probability distribution

  • How to determine if a distribution is a probability distribution

  • How to find the mean, variance, and standard deviation of a discrete probability distribution

  • How to find the expected value of a discrete probability distribution

  • How to determine if a probability experiment is a binomial experiment, finding binomial probabilities, graphing binomial distributions, and determining the mean, variance, and standard deviations of binomial probability distributions

  • How to find probabilities using the geometric distribution

  • How to find probabilities using the Poisson distribution

5. Inferential Statistics - Confidence Intervals

Quarter 3

Confidence Intervals

  • How to find a point estimate and a margin of error

  • How to construct and interpret confidence intervals for population mean

  • How to determine the minimum sample size required when estimating 𝜇

  • How to find a point estimate for the population proportion

  • How to construct a confidence interval for a population proportion

  • How to determine the minimum sample size required when estimating a population proportion

6. Personal Finance

Quarter 4

Personal Finance

  • Credit cards, credit scores, and credit card debt

  • Cost of living, supporting a family, paying bills

  • Car loans and car payments

  • Cost of living variances across the United States

  • Cost of college and student loans

  • starting salaries based on desired careers