Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.6d

Lesson 2.10Matching Center and Spread

Apply Day · Set BSecond form · new problems, same idea

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Learning target I can choose the best measure of center for a data set based on its shape.

Remember2.10 · Part II

Choosing Appropriate Measures of Center & Spread

  1. Symmetric Data (No Outliers): Use Mean and MAD
  2. Skewed Data (Has Outliers): Use Median and IQR (outliers distort the mean)
  3. Compare distributions using both center (typical value) and spread (variability)

Words: Mean (Media)Median (Mediana)Outlier (Valor atípico)Skewed (Sesgado)Data distribution (Distribución de datos)

  1. 1Complete each step, then write the final answer.

    Which measure better shows a typical value for 2, 3, 3, 4, 28: the mean or the median?

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    Final answer:
  2. 2Complete each step, then write the final answer.

    A player scored 18, 21, 19, 20, 22 and 20 points in 6 games. Which measure should you use for a typical game: the mean or the median?

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    Final answer:
  3. 3Complete each step, then write the final answer.

    A theater sold 48, 52, 50, 49 and 51 tickets on 5 nights. Which measure should you use for a typical night: the mean or the median?

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    Final answer:
  4. 4Complete each step, then write the final answer.

    A cat weighed 9, 10, 11, 10 and 10 pounds at 5 vet visits. Which measure should the vet use for a typical weight: the mean or the median?

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    Final answer:
  5. 5Complete each step, then write the final answer.

    Mo's trips to school took 15, 18, 16, 17, 14 and 60 minutes. The 60 was a snow day. Give the best typical time.

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    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.

    Six values have a mean of 20 and a median of 12. Does the data most likely have a high outlier, a low outlier, or no outlier?

    1. AA high outlier
    2. BA low outlier
    3. CNo outlier
    Show your work
  7. 7Circle the letter of the best answer. Show how you know.

    A gymnast's scores are: 8.5, 8.8, 8.7, 8.6, 8.9. There are no outliers. Which measure best represents a typical score?

    1. AMedian
    2. BNeither — the data is too small
    3. CBoth are equally bad
    4. DMean
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  8. 8Circle the letter of the best answer. Show how you know.

    A runner's mile times are: 7:10, 7:15, 7:12, 7:20, 12:00. The 12:00 was due to a cramp. Which measure best represents a typical mile?

    1. AMean — it uses all the data
    2. BMedian — the outlier 12:00 pulls the mean too high
    3. CMode — it shows the most common time
    4. DNeither measure works
    Show your work
  9. 9Circle the letter of the best answer. Show how you know.

    Data set: 5, 6, 7, 7, 8, 50. The mean is about 13.8 and the median is 7. Which better represents the typical value?

    1. AMean (13.8) — it includes all values
    2. BBoth are equally good
    3. CMedian (7) — the outlier 50 inflates the mean
    4. DNeither works for this data
    Show your work
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