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  1. The five-number summary of the distribution of scores on the final exam in Psych 001 last semester was: 18,
    39, 62, 76, and 100. Which of the following best describes the location
    of the 80th percentile?
    a.
    The 80th percentile is 76.
    b. The 80th percentile is between 18 and 39.
    C.
    d.
    e.
    The 80th percentile is between 62 and 76.
    The 80th percentile is between 76 and 100.
    The 80th percentile is between 39 and 76.
    ing does not change?

Verified Answer :

GinnyAnswer

The five-number summary provides five critical values from a dataset:

1. Minimum value (smallest value)
2. First quartile (Q1) – the value below which 25% of the data fall
3. Median (Q2) – the middle data point, which divides the data into two halves
4. Third quartile (Q3) – the value above which 25% of the data fall, or equivalently, below which 75% of the data fall
5. Maximum value (largest value)

In the given five-number summary, the values are:

1. Minimum: 18
2. Q1: 39
3. Median (Q2): 62
4. Q3: 76
5. Maximum: 100

The percentile of a value is the percent of observations that lie below that value. Thus, the 80th percentile will be a value such that 80% of the data points are at or to the left of it on the number line.

Since Q3 (76) is the point where 75% of the data is to its left, and the maximum (100) is the point where 100% of the data is to its left, the 80th percentile must be larger than Q3 and smaller than the maximum because 80% is greater than 75% but less than 100%.

This means that the 80th percentile should fall between Q3 and the maximum value:

e. The 80th percentile is between 76 and 100.

So the correct answer is:

e. The 80th percentile is between 76 and 100.

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