## Intermediate Math 1 - Statistics and Probability

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## 1- Expressions and Equations 2- Geometry 3- Number Systems

4- Ratios and Proportions 5- Statistics and Probability

## Use random sampling to draw inferences about a population.

7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. |
7.SP.1.a I understand that information can be gathered about a population from a sample of the population. For example: To estimate the amount of time the students at Mt. View JHS spend on homework, every 5th student in the lunch room was surveyed.7.SP.1.b I understand that the generalizations made are only valid if the sample is representative of the population.7.SP.1.c I understand that random sampling tends to produce representative samples and support valid inferences. |

7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. |
7.SP.2.a I can use data from a random sample to draw inferences about a population with an unknown characteristic of interest (the desired information).For example: Students can use a random sample of students to estimate the average height of all students in the school. (The average height of the students is the unknown characteristic of interest.)7.SP.2.b I can generate multiple samples of the same size from the same population to gauge the variation in estimates or predictions of the parameter.Note: Parameter is the true value of the population’s unknown characteristic. A statistic is calculated from the sample and is only an estimate of the population’s parameter. For example: Students create additional random samples from the same population to determine the variation in their prediction of the average height of the students. (Using different samples of the same population will give slightly different results.) |

## Investigate chance processes and develop, use, and evaluate probability models.

7.SP.3 Informally assess the degree of visual overlap of two data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. |
7.SP.3 I can use visual representations (box & whisker plots, dot plots, etc.) to compare the centers(mean and median) and variability (interquartile range, mean absolute deviation) of two data sets (This standard builds on 6.SP.5 where mean absolute deviation is introduced.). Note – How to find the Mean Absolute Deviation from a data set.The Mean Absolute Deviation is calculated in three simple steps. 1) Determine the Mean: Add all numbers and divide by the count example: the weights of the following three people, denoted by letters are A - 56 Kgs B - 78 Kgs C - 90 Kgs Mean = (56+78+90)/3= 74.6 2) Determine deviation of each variable from the Mean i.e 56-74.6 = -18.67 78-74.6= 3.33 90-74.6 =15.33 3) Find the average of the absolute values of the deviations. i.e eliminate the negative aspect Thus the Mean Absolute Deviation is (18.67 +3.33+15.33)/3 =12.44 Alternatively, you can use the excel formula =AVEDEV(56,78,90) to obtain the result. http://wiki.answers.com/Q/How_do_you_calculate_mean_absolute_deviation#ixzz1UAVheVZn Note: For a detailed example please see pages 22-24 of Arizona’s Grade 7 explanation of the Common Core. http://www.ade.az.gov/standards/math/2010MathStandards/Gradelevel/MathGr7.pdf |

7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. |
7.SP.4 I can use measures of center (mean and median) and variability (interquartile range, mean absolute deviation) from random samples to make informal comparative inferences about two populations. For example - Decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. |

## Investigate chance processes and develop, use, and evaluate probability models.

7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. |
7.SP.5 I can understand the probability of a chance event is the likelihood of the event occurring and is expressed as a number between 0 and 1.For example: A probability near 0 represents an unlikely event, a probability of ½ represents an equally likely chance, and probability near 1 represents a near certainty. |

7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. |
7.SP.6.a I can approximate the probability of an event by collecting data and observing its long-run relative frequency.For example: Rolling a number cube 40 times and approximating the likelihood of rolling a six on any single roll.7.SP.6.b I can predict the approximate relative frequency given the theoretical probability.For example: When rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. |

7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? |
7.SP.7.a I can develop a uniform probability model (all outcomes equally likely) and use it to determine the likelihood of a given event. For example: The probability of choosing any one student in a class. The probability of rolling a 2 on a number cube.7.SP.7.b I can create a probability model, e.g. bar graph, circle graph, table (which may not be uniform) by observing frequencies in data generated from an experiment.For example: Toss a paper cup 20 times and observe how many times it lands open face down. Then draw a probability model based on your results. |

7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? |
7.SP.8.a I can understand that just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.7.SP.8.b I can create representations (organized lists, tables and tree diagrams) of sample spaces for compound events.7.SP.8.b.1 I can identify the outcomes for a given event.For example: Flipping two coins has possible outcomes of HH, HT, TH, TT.7.SP.8.c I can design and use a simulation to generate frequencies for compound events. For example: Use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? |