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Questions and Answers
What does it mean if you score in the 75th percentile on a standardized test?
What does it mean if you score in the 75th percentile on a standardized test?
- You are in the top 25% of test takers.
- You scored higher than 75% of the other students. (correct)
- You scored 75% on the test.
- 75% of the questions were answered incorrectly.
The median of a dataset always represents the 25th percentile.
The median of a dataset always represents the 25th percentile.
False (B)
What five values are needed to create a box plot?
What five values are needed to create a box plot?
minimum value, first quartile, median, third quartile, and maximum value
The shaded box in a box plot encompasses the first quartile, the median, and the ______.
The shaded box in a box plot encompasses the first quartile, the median, and the ______.
What is the purpose of the whiskers in a box plot?
What is the purpose of the whiskers in a box plot?
Given Q1 = 65 and Q3 = 86, what is the interquartile range (IQR)?
Given Q1 = 65 and Q3 = 86, what is the interquartile range (IQR)?
If a data point falls outside the whiskers in a box plot, it is always considered an error and should be removed from the dataset.
If a data point falls outside the whiskers in a box plot, it is always considered an error and should be removed from the dataset.
Match the following terms with their definitions:
Match the following terms with their definitions:
Flashcards
Percentile
Percentile
A measure indicating a value's position relative to others in a dataset.
Median
Median
The middle value, dividing the dataset into two equal halves; the 50th percentile.
Quartiles
Quartiles
Values that divide the dataset into four equal parts.
Box Plot
Box Plot
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First Quartile
First Quartile
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Third Quartile
Third Quartile
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Interquartile Range (IQR)
Interquartile Range (IQR)
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Outlier
Outlier
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Study Notes
- A percentile is a measure indicating whether a value is below or above a percentage of observations in a group.
- Scoring in the 75th percentile on a test means 75% of other students scored below.
- The median represents the 50th percentile, also known as the second quartile.
- Values at the 25th and 75th percentiles are the first and third quartiles, giving more information about the distribution of data.
- This data can be applied to a boxplot.
Boxplots
- A large data set of final exam scores can be plotted as percentiles.
- The first quartile is 65, the median is 79, and the third quartile is 86, with a minimum value of 32 and a maximum of 99.
- A 5-number summary of a data set can be plotted into a box plot, also known as a box-and-whisker plot.
- To create a box plot, first, plot all five numbers on a number line.
- A shaded box encompasses the first quartile, the median, and the third quartile, with a dashed line at the median value.
- Before adding whiskers, compute the interquartile range (IQR) by finding the difference between Q3 and Q1.
- The IQR is 86 minus 65, which equals 21.
- Aim to draw whiskers that reach both the maximum and minimum values: the length of both whiskers can be no longer than 1.5 times the IQR, or 31.5 units on either side.
- For the left whisker, draw a line from Q1 extending to 33.5 on the number line.
- For the right whisker, draw a line from Q3 extending to 99, the maximum value.
- If the minimum value, 32, is beyond the left whisker, mark it with an asterisk to indicate an outlier.
- If the maximum value, 99, is not an outlier since it sits within the length of the right whisker.
- With the median towards the right of the box and the left whisker longer than the right whisker, the distribution is negatively skewed.
- Also, the left whisker has an outlier, skewing the distribution in a negative direction even more.
- Percentiles and box plots represent certain qualities of a data set and are used in business and academic applications.
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Description
Explanation of percentiles and how they relate to data distribution. The median represents the 50th percentile. Boxplots are introduced as a visual way to represent data using a 5-number summary derived from percentiles.
