Upper quartile is the lowest value ofa)lowest 25%.b)lowest 50%.c)top 2...
Upper Quartile Definition:
The upper quartile, also known as the third quartile (Q3), is a statistical measure used to divide a dataset into four equal parts. It is the value below which 75% of the data falls.
Explanation:
To understand why option 'C' is the correct answer, let's break down the quartiles and their corresponding percentages.
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First Quartile (Q1): The first quartile is the value below which 25% of the data falls. It represents the lower boundary of the second quarter of the data. In other words, 25% of the data points are smaller than or equal to Q1.
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Second Quartile (Q2) or Median: The second quartile is the value that separates the data into two equal halves. It represents the middle value of the dataset. 50% of the data points are smaller than or equal to Q2, and 50% are larger.
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Third Quartile (Q3) or Upper Quartile: The third quartile is the value below which 75% of the data falls. It represents the upper boundary of the third quarter of the data. In other words, 75% of the data points are smaller than or equal to Q3.
Answering the Question:
Now, let's relate this information to the answer options provided:
a)
Lowest 25%: This option refers to the first quartile (Q1), not the upper quartile (Q3). Therefore, it is not the correct answer.
b)
Lowest 50%: This option refers to the second quartile (Q2) or the median, not the upper quartile (Q3). Therefore, it is not the correct answer.
c) Top 25%: This option correctly identifies the upper quartile (Q3). It is the value below which 75% of the data falls, representing the top 25% of the dataset. Therefore, this is the correct answer.
d)
Top 75%: This option refers to the entire dataset, not just the upper quartile (Q3). Therefore, it is not the correct answer.
Conclusion:
The upper quartile (Q3) represents the value below which 75% of the data falls. Therefore, option 'C' correctly identifies the upper quartile as the lowest value of the top 25% of the dataset.