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The mean, median and mode are not always sufficient to represent or compare sets of data.

You can draw inferences from numerical data by examining how the data is distributed around the mean or the median.

When analyzing two sets of data, it is important to look at both similarities and differences in the data.

Demonstrate an understanding of normal distribution, including:

• standard deviation

• z-scores.

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Page 240

Questions #2

Resources:

Mean -- http://www.brightstorm.com/math/algebra/introduction-to-statistics/mean/

Mode – http://www.brightstorm.com/math/algebra/introduction-to-statistics/mode/

Median – http://www.brightstorm.com/math/algebra/introduction-to-statistics/median/

Range-- http://www.brightstorm.com/math/algebra/introduction-to-statistics/range/

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Large sets of data can be difficult to interpret. Organizing the data into intervals and tabulating the frequency of the data in each interval can make it easier to interpret the data and draw conclusions about how the data is distributed.

A frequency distribution is a set of intervals and can be displayed as a table, a histogram, or a frequency polygon.

Demonstrate an understanding of normal distribution, including:

• standard deviation

• z-scores.

There are no achievement indicators

NO AFL’s

Resources:

Main Concepts in Lesson:

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The standard deviation,, is a measure of the dispersion of data about the mean.

You can calculate the standard deviation using your graphing calculator, but algebraically as well.

When data is concentrated close to the mean, the standard deviation, , is low. When data is spread far from the mean, the standard deviation is high.

Show the steps to solving the standard deviation algebraically.

Standard deviation is often used as a measure of consistency. When

data is closely clustered around the mean, the process that was used to generate the data can be interpreted as being more consistent than a process that generated data scattered far from the mean.

1.1 Explain, using examples, the meaning of standard deviation.

1.2 Calculate, using technology, the population standard deviation of a data set.

1.3 Explain, using examples, the properties of a normal curve, including the mean, median, mode, standard deviation, symmetry and area under the curve.

1.5 Compare the properties of two or more normally distributed data sets.

1.6 Explain, using examples that represent multiple perspectives, the application of standard deviation for making decisions in situations such as warranties, insurance or opinion polls.

1.7 Solve a contextual problem that involves the interpretation of standard deviation.

Page 261 - 265

Questions #5, 7, 9 (Key Question) and 12

Resources:

Standard Deviation -- http://www.khanacademy.org/video/statistics--standard-deviation?playlist=Statistics

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You can make reasonable estimates about data that approximates a normal distribution, because data that is normally distributed has special characteristics.

The mean determines the location of the centre of the curve on the horizontal axis,

The standard deviation determines the width and height of the curve.

The properties of a normal distribution can be summarized as follows:

- The graph is symmetrical. The mean, median, and mode are equal(or close) and fall at the line of symmetry.

- The normal curve is shaped like a bell, peaking in the middle, sloping down toward the sides, and approaching zero at the extremes.

- About 68% of the data is within one standard deviation of the mean.

- About 95% of the data is within two standard deviations of the mean.

- About 99.7% of the data is within three standard deviations of the mean.

- The area under the curve can be considered as 1 unit, since it represents 100% of the data.

99

Generally, measurements of living things (such as mass, height, and length) have a normal distribution.I

1.3 Explain, using examples, the properties of a normal curve, including the mean, median, mode, standard deviation, symmetry and area under the curve.

1.4 Determine if a data set approximates a normal distribution, and explain the reasoning.

1.5 Compare the properties of two or more normally distributed data sets.

1.7 Solve a contextual problem that involves the interpretation of standard deviation.

1.9 Solve a contextual problem that involves normal distribution.

Page 279 - 282

Questions #4, 6, 7, 10, 11 (Key Question) and 13

Resources:

Main Concepts in Lesson:

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The standard normal distribution is a normal distribution with mean, , of 0 and a standard deviation, , of 1.

The area under the curve of a normal distribution is 1.

Z-scores indicated the number of standard deviations that a data value lies from the mean.It is used to compare data from different normally distributed sets by converting it to the standard normal distribution.

A positive z- score means the data value lies above the mean.

A negative z-score means the data value lies below the mean.

You can find the area to the left of the z-score by using a z-score chart.

1.5 Compare the properties of two or more normally distributed data sets.

1.6 Explain, using examples that represent multiple perspectives, the application of standard deviation for making decisions in situations such as warranties, insurance or opinion polls.

1.7 Solve a contextual problem that involves the interpretation of standard deviation.

1.8 Determine, with or without technology, and explain the z-score for a given value in a normally distributed data set.

1.9 Solve a contextual problem that involves normal distribution.

Page 292 - 294

Questions #5b and d, 6c and d, 8b, 9, 11, 13 (Key Question), and 16

Resources:

Main Concepts in Lesson:

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When data approximates a normal distribution, a confidence interval indicates the range in which the mean of any sample of data of a given size would be expected to lie, with a stated level of confidence. This confidence interval can then be used to estimate the range of the mean for the population.

Sample size, confidence level, and population size determine the size of the confidence interval for a given confidence level.

A confidence interval is expressed as the survey or poll result, plus or minus the margin of error.

The margin of error increases as the confidence level increases (with a constant sample size). The sample size that is needed also increases as the confidence level increases (with a constant margin of error).

The sample size affects the margin of error. A larger sample results in a smaller margin of error, assuming that the same confidence level is required.

1.5 Compare the properties of two or more normally distributed data sets.

1.6 Explain, using examples that represent multiple perspectives, the application of standard deviation for making decisions in situations such as warranties, insurance or opinion polls.

1.9 Solve a contextual problem that involves normal distribution.

2.1 Explain, using examples, how confidence levels, margin of error and confidence intervals may vary depending on the size of the random sample.

2.2 Explain, using examples, the significance of a confidence interval, margin of error or confidence level.

2.3 Make inferences about a population from sample data, using given confidence intervals, and explain the reasoning.

2.4 Provide examples from print or electronic media in which confidence intervals and confidence levels are used to support a particular position.

2.5 Interpret and explain confidence intervals and margin of error, using examples found in print or electronic media.

2.6 Support a position by analyzing statistical data presented in the media.

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Questions #4, 7 (Key Question) and 8

Resources: