Statistics and Probability - Manitoba Education

Gr ade 7 Mathematics

Statistics and Probability

Statistics and Probability (Data Analysis) (7.SP.1, 7.SP.2)

Enduring Understanding(s): Data can be described by a single value used to describe the set.

General Learning Outcome(s): Collect, display, and analyze data to solve problems.

Specific Learning Outcome(s):

Achievement Indicators:

7.SP.1 Demonstrate an understanding of central tendency and range by n determining the measures of central tendency (mean, median, mode) and range n determining the most appropriate measures of central tendency to report

findings [C, PS, R, T]

Determine the mean, median, and mode for a set of data, and explain why these values may be the same or different.

Determine the range of a set of data. Provide a context in which the mean,

median, or mode is the most appropriate measure of central tendency to use when

reporting findings. Solve a problem involving the measures of

central tendency.

7.SP.2 Determine the effect on the mean, median, and mode when an outlier is included in a data set. [C, CN, PS, R]

Analyze a set of data to identify any outliers.

Explain the effect of outliers on the measures of central tendency for a data set.

Identify outliers in a set of data and justify whether or not they are to be included in the reporting of the measures of central tendency.

Provide examples of situations in which outliers would or would not be used in determining the measures of central tendency.

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Prior Knowledge

Students may have had experience with the following: QQ Differentiating between first-hand and second-hand data. QQ Comparing the likelihood of two possible outcomes occurring, using words such as

QQ less likely QQ equally likely QQ more likely QQ Creating, labelling, and interpreting line graphs to draw conclusions. QQ Selecting, justifying, and using appropriate methods of collecting data, including QQ questionnaires QQ experiments QQ databases QQ electronic media QQ Graphing collected data and analyzing the graph to solve problems.

For more information on prior knowledge, refer to the following resource: Manitoba Education and Advanced Learning. Glance Across the Grades: Kindergarten to

Grade 9 Mathematics. Winnipeg, MB: Manitoba Education and Advanced Learning, 2015. Available online at .mb.ca/k12/cur/math/glance_k-9/index.html.

Related Knowledge

Students should be introduced to the following: QQ Comparing and ordering fractions, decimals (to thousandths), and integers by using

QQ benchmarks QQ place value QQ equivalent fractions and/or decimals QQ Constructing, labelling, and interpreting circle graphs to solve problems. QQ Expressing probabilities as ratios, fractions, and percents. QQ Identifying the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events. QQ Conducting a probability experiment to compare the theoretical probability (determined using a tree diagram, table, or another graphic organizer) and experimental probability of two independent events.

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Grade 7 Mathematics: Suppor t Document for Teacher s

Background Information

Students live in an information age that abounds with data. Various media continually offer information on fashion, entertainment, sports, finances, safety, health, and world events. Students encounter data regularly at school, in their marks, in science experiments, in social studies information, and so on. To be helpful, data needs to be categorized and understood.

Statistics help reduce large quantities of data to single values. The single value makes it much simpler to conceptualize and communicate about the information contained in the data. Statistics, however, are sometimes manipulated or presented in a manner that uses facts to mislead people and sway their opinions. By studying statistics, students develop their ability to understand and evaluate information presented in advertising, politics, and news reports, and to communicate their experience with data.

Measures of Central Tendency

In previous grades, students collected data first hand and from electronic sources, and learned when to use each source. In Grade 7, students are introduced to three statistical measures of central tendency: mean, median, and mode. Each is a numeric value attempting to represent an entire set of data. Each measure is an average with its own focus, strengths, and weaknesses. The more symmetrical the set of data is, the closer the measures of central tendency will be to one another. The more skewed the set of data is, the greater the difference between the values will be. The different measures are best used in different situations, although sometimes all three measures provide meaningful representations of the data.

The measures of central tendency and range are discussed below:

n Mean: The arithmetic mean is commonly referred to as average, and is commonly used to assign student grades. The mean is the measure of central tendency most affected by outliers; therefore, it is best used when the range of values in the set is narrow. To find the mean, combine all the values in the set and then evenly redistribute them. The algorithm for calculating the mean is to sum all values in the set, and divide the combined value by the number of values in the set. The mean can also be found by finding the central balance point on a number line.

Example:

Given the numbers 3, 4, 6, 3, 3, 9, 7,

a) plot the numbers on a number line

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