Understanding Distributions and Transformations

This video tutorial introduces quantitative distributions, focusing on percentiles and Z-scores. It explains how to calculate and interpret these metrics using examples, such as Jenny's test score. The video also covers data transformation effects on distribution measures, including center, spread, and shape. Finally, it provides a practical assignment to reinforce learning.

What is a percentile used for in a distribution?

• To calculate the standard deviation

• To measure the average value

• To describe the location of a value

• To determine the spread of data

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CCSS.6.SP.B.5C

If Jenny's test score is at the 88th percentile, what does this mean?

• 88% of scores are lower than or equal to hers

• 88% of scores are higher than hers

• She scored 88 out of 100

• Her score is the highest in the class

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CCSS.HSS.ID.A.4

What does a positive z-score indicate?

• The value is the median

• The value is at the mean

• The value is above the mean

• The value is below the mean

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CCSS.HSS.ID.A.4

How is a z-score calculated?

• By multiplying the observation by the mean

• By adding the mean to the observation

• By subtracting the mean from the observation and dividing by the standard deviation

• By dividing the observation by the mean

What happens to the mean and median when a constant is added to all values in a distribution?

• They remain unchanged

• Only the mean changes

• They both increase by the constant

• They both decrease by the constant

Does multiplying all values in a distribution by a constant affect the shape of the distribution?

• Yes, but only if the constant is greater than 1

• No, it does not change the shape

• No, unless the constant is negative

• Yes, it changes the shape

What is the effect of subtracting a constant from all values in a distribution on the variability?

• It makes variability zero

• It does not affect variability

• It decreases variability

• It increases variability

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When converting measurements from inches to centimeters, what happens to the measures of spread?

• They remain the same

• They are divided by the conversion factor

• They are multiplied by the conversion factor

• They are subtracted by the conversion factor

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CCSS.6.SP.B.5C

What is the median of the given data set in the practical application section?

• 70.9375

• 73

• 19

• 11.43

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CCSS.HSF-LE.A.1B

What should you do with the scores entered in your calculator for the next class?

• Multiply them by a constant

• Add a constant to them

• Leave them as they are

• Delete them

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CCSS.HSF-LE.A.1B