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The 32 observations below are measurements of head length (in centimeters) of a sample of Australian and Indian crocodiles:

24.0, 24.0, 32.0, 32.3, 35.0, 35.0, 35.8, 37.5, 37.6, 37.6, 38.2, 38.3, 39.5, 40.0, 40.0, 45.9, 46.0, 48.0, 49.0, 50.7, 51.0, 52.0, 52.0, 53.5, 56.0, 60.5, 61.0, 62.0, 64.0, 71.0, 83.0

Calculate the five-number summary of this data, determine any outliers in the data, and construct a boxplot showing outliers (if any).

Answer :

Final answer:

To calculate the five-number summary of the given data, arrange the data in ascending order and find the minimum, Q1, Q2 (median), Q3, and maximum values. In this case, the five-number summary is: Minimum - 24.0, Q1 - 35.0, Median - 40.0, Q3 - 52.0, Maximum - 83.0. There are no outliers in the data.

Explanation:

The five-number summary consists of the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value of a dataset. To calculate the five-number summary of the given data, you need to:

  1. Arrange the data in ascending order: 24.0, 24.0, 32.0, 32.3, 35.0, 35.0, 35.8, 37.5, 37.6, 37.6, 38.2, 38.3, 39.5, 40.0, 40.0, 45.9, 46.0, 48.0, 49.0, 50.7, 51.0, 52.0, 52.0, 53.5, 56.0, 60.5, 61.0, 62.0, 64.0, 71.0, 83.0
  2. Find the minimum value: 24.0
  3. Find Q1, which is the median of the lower half of the data. In this case, the lower half is the values up to and including the median (Q2). Q1 = 35.0
  4. Find Q2, the median of the entire dataset. In this case, Q2 = 40.0
  5. Find Q3, which is the median of the upper half of the data. In this case, the upper half is the values starting from and including the median (Q2). Q3 = 52.0
  6. Find the maximum value: 83.0

The five-number summary is:

Minimum: 24.0

Q1: 35.0

Median: 40.0

Q3: 52.0

Maximum: 83.0

No outliers are present in the data. You can construct a boxplot using these values to visualize the distribution of the data.

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