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Common Core Standard HSS-ID.A.3 Questions

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

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Grade 9 Histograms CCSS: HSS-ID.A.1, HSS-ID.A.3

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Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.3
For a left-skewed, unimodal distribution, which of the following is generally true?
  1. Mode < Median < Mean
  2. Median < Mean < Mode
  3. Mean < Mode < Median
  4. Mean < Median < Mode
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.3
Sam goes running the same distance every weekend and records how long it takes to run this distance. Usually it takes between 45 minutes and 55 minutes. On one run, however, it took 75 minutes. Which of the following would be good a reason to remove this outlier from the data set? Choose all correct answers.
  1. Sam got distracted while he was running, and ran a longer route than he normally does.
  2. Sam accidentally recorded the time incorrectly.
  3. Sam was running more slowly that weekend.
  4. Sam knows what his approximate average running time should be, and this one value alters his average.
Grade 11 Range, Median, Mean, and Mode CCSS: HSS-ID.A.3
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.3
For a right-skewed, unimodal data distribution, which of the following is generally true?
  1. Median < Mode < Mean
  2. Mode < Median < Mean
  3. Mean < Median < Mode
  4. Mean < Mode < Median
Grade 11 Range, Median, Mean, and Mode CCSS: HSS-ID.A.3
Which value changed the most (according to percentage increase or decrease)?
  1. Mean
  2. Median
  3. Mode
  4. They all changed by the same amount.
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.3
Which of the following is generally true for a roughly symmetric, unimodal data distribution (one with no skew)?
  1. Mean [math]~~ \ [/math] Median [math]~~ \ [/math] Mode
  2. Mean [math]~~ \ [/math] Median > Mode
  3. Mean [math]~~ \ [/math] Median [math]~~ \ [/math] Mode [math]~~ \ [/math] 0
  4. Mean [math]~~ \ [/math] Median < Mode
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.3
A study is being conducted to determine the total income of people who graduated from university within the past two years. After the data is collected, most values lie in the range of $40,000 to $50,000 dollars per year. One value stands out, which is a yearly income of $105,000. Which of the following would be a valid reason for removing this data point from the set? There may be more than one correct answer.
  1. One recent graduate received a very high paying job because of a family connection.
  2. The person with this income graduated from university several years ago.
  3. This person's income is actually the combination of income from three different jobs.
  4. This person never went to university, but is about the same age as other people in the study.
Grade 11 Range, Median, Mean, and Mode CCSS: HSS-ID.A.3
Which value changed the least (according to percentage increase or decrease)?
  1. Mean
  2. Median
  3. Mode
  4. They all changed by the same amount.
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.3
Which of the following best describes the dot plot?
Line Plot 2
  1. Symmetric Unimodal
  2. Skewed Right
  3. Skewed Left
  4. Uniform
Grade 11 Collecting and Interpreting Data CCSS: HSS-ID.A.3
Grade 11 Range, Median, Mean, and Mode CCSS: HSS-ID.A.3
Which of the following statements is true, concerning the removal of a single outlier on the mean, median, and mode of any given data set?
  1. The median will usually be most affected after removing an outlier.
  2. The mean will usually be most affected after removing an outlier.
  3. The mode is the only measure of center that can remain unaffected after removing an outlier.
  4. The median will always change, but it will only be a relatively small change.
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