High S

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duatio

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Revie

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Domai

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a Anal

ysis

How is data presented, compared and used to predict future outcomes?

The standards for this domain…

MM1D1

Students will determine the number of outcomes related to a given event.

MM1D2

Students will use the basic laws of probability.

MM1D3

Students will relate samples to a population.

MM2D1

Using sample data, students will make informal inferences about population means and standard deviations.

MM2D2

Students will determine an algebraic model to quantify the association between two quantitative variables.

MM

1D3

STUDEN

TS W

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RELATE

SAM

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O A

POPULATI

ON.

SAMPLES– MM1D3

• Summary Statistics• Population vs Sample• Representative Sample -- Random

Summary Statistics

Mean5 number

summary (Box & Whisker Plot)

Range

Mean

Average

5 NUMBER SUMMARY – BOX & WHISKER PLOT

Range

How far from the lowest value to the highest value

(subtract)

Now you try one…

Linda's first five Math II tests scores were 75, 82, 74, 95, and 89. If her mean semester average was 85, what score did she make on her sixth and last test?

95

Which would be better median or mean?

If each of the 20 random samples collected contains several outliers, which of the following will give the best estimate of where the center of the actual population lies?

Median because it is more resistant to outliers.

Population vs Sample

Sample is the PART of the population that you survey for your study. The key is selecting a representative sample.

Representative Sample

• The sample must be Random!

• The larger the sample the closer to the population.

• If a small sample, the more samples the closer to the population.

Example

A population was sampled ten times. The medians of the samples are:

17, 17, 17, 18, 19, 19, 20, 20, 21, 21

Can we use these sample medians to predict the median of the population?

Example answer

YES – take the mean of the sample medians which would be 18.9

So a good estimate of the median of the actual population would be 19.

Representative Sample

Random is always representative.

Sample Types

Self selected – volunteerSystematic – rule or patternConvenience – easy to contactBiased – skewed – not

representativeUnbiased – representative of

the population

Example…

Janet is surveying students at her school. Which of the following would most likely give her a representative sample?

  a. Surveying only her homeroom b. Surveying the first 60 students who walk up to her at lunch c. Surveying only the members of the school chorus d. Surveying 50 students from each grade who have been randomly selected by a computer.

D – why?

WHY? what type of sample…

What type of samples are these and what is wrong with them?

  a. Surveying only her homeroom -- convenience b. Surveying the first 60 students who walk up to her at lunch-- volunteer c. Surveying only the members of the school chorus -- biased d. Surveying 50 students from each grade who have been randomly selected by a computer. -- systematic

Now you try one…

A principal is surveying the parents of his students to find out if they would support extending the school day by 20 minutes. Which method would most likely result in a representative sample?  

a. Surveying every 20th name from a list of all school parents b. Surveying 50 parents of ninth graders. c. Surveying parents that attend the monthly PTO meeting d. Surveying parents who volunteer in the media center.

A

More Practice

Handout