AFDA.7 The focus of this standard is on the interpretation of descriptive The student will use problem solving, mathematical communication, statistics, probabilities, and their relationship to the normal mathematical reasoning, connections, and representations to z-scores, curve in the context of a data set. Identify the properties of a normal distribution. (a) Descriptive statistics include measures of center (mean, median, and mode) Describe how the standard deviation and the mean affect the graph of and dispersion or spread (variance and standard deviation). the normal distribution. (a) Variance (σ 2) and standard deviation (σ) measure the spread of data about Given standard deviation and mean, calculate and interpret the the mean in a data set. for a data point. (b) z-score Standard deviation is expressed in the original units of measurement of the Compare two sets of normally distributed data a standard normal data. distribution and given mean and standard deviation. (b) z-scores, The greater the value of the standard deviation, the further the data tends to Represent probability as area under the curve of a standard normal be dispersed from the mean. distribution. (c) In order to develop an understanding of standard deviation as a measure Use a graphing utility or a table of Standard Normal Probabilities to of dispersion (spread), students should have experiences analyzing the determine probabilities associated with areas under the standard formulas for and the relationship between variance and standard normal curve. (c) deviation. Use a graphing utility to investigate, represent, and determine The normal distribution curve is the family of symmetrical, bell-shaped relationships between a normally distributed data set and its curves defined by the mean and the standard deviation of a data set. The descriptive statistics. (a, b, c) arithmetic mean (μ) is located on the line of symmetry of the curve and is approximately equivalent to the median and mode of the data set. The normal curve is a probability distribution and the total area under the curve is 1.
AFDA.7 The focus of this standard is on the interpretation of descriptive statistics, z-scores, probabilities, and their relationship to the normal curve in the context of a data set. Descriptive statistics include measures of center (mean, median, and mode) and dispersion or spread (variance and standard deviation). Variance (σ 2) and standard deviation (σ) measure the spread of data about the mean in a data set. Standard deviation is expressed in the original units of measurement of the data. The greater the value of the standard deviation, the further the data tends to be dispersed from the mean. In order to develop an understanding of standard deviation as a measure of dispersion (spread), students should have experiences analyzing the formulas for and the relationship between variance and standard deviation. The normal distribution curve is the family of symmetrical, bell-shaped curves defined by the mean and the standard deviation of a data set. The arithmetic mean (μ) is located on the line of symmetry of the curve and is approximately equivalent to the median and mode of the data set. The normal curve is a probability distribution and the total area under the curve is 1. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Identify the properties of a normal distribution. (a) Describe how the standard deviation and the mean affect the graph of the normal distribution. (a) Given standard deviation and mean, calculate and interpret the z-score for a data point. (b) Compare two sets of normally distributed data a standard normal distribution and z-scores, given mean and standard deviation. (b) Represent probability as area under the curve of a standard normal distribution. (c) Use a graphing utility or a table of Standard Normal Probabilities to determine probabilities associated with areas under the standard normal curve. (c) Use a graphing utility to investigate, represent, and determine relationships between a normally distributed data set and its descriptive statistics. (a, b, c)
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