Gr 10 Math Ch 9: Measures of Dispersion

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What is another name for the 25th percentile?

Upper quartile

Lower quartile (correct)

Decile

Median

How many groups does the decile divide an ordered data set into?

Eleven groups

Nine groups

Five groups

Ten groups (correct)

What does the interquartile range measure?

The dispersion of the middle half of the data set (correct)

The closure of the data set

The variance of the data set

The range of all data values

What is the semi-interquartile range?

Half of the interquartile range Signup and view all the answers

In grouped data, where do the percentiles lie?

Within a range of values Signup and view all the answers

What do we define as the full data range?

The difference between the 100th and 0th percentiles Signup and view all the answers

What does the range of a data set measure?

The difference between the maximum and minimum values Signup and view all the answers

In a data set, the 25th percentile is also known as which quartile?

First quartile (Q1) Signup and view all the answers

How is the rank of the pth percentile calculated in an ordered data set?

$r = rac{p}{100} (n - 1) + 1$ Signup and view all the answers

What happens to the range if outliers are present in the data set?

It is enhanced and can give inflated results Signup and view all the answers

When calculating the pth percentile, what should be done if the rank is not an integer?

Take the value halfway between the two closest ranks Signup and view all the answers

Which statement is true concerning quartiles?

The third quartile (Q3) captures the top 25% of data Signup and view all the answers

What is the relationship between percentiles and quartiles?

Quartiles are specific percentiles Signup and view all the answers

What does it mean if a data point is in the 90th percentile?

It is lower than 90% of the data points Signup and view all the answers

What does the range of a data set represent?

The difference between the maximum and minimum values Signup and view all the answers

Which of the following statements is true regarding percentiles?

Each percentile indicates a specific rank in the data set. Signup and view all the answers

How many quartiles divide an ordered data set?

Four quartiles Signup and view all the answers

If the rank of the pth percentile in an ordered dataset is 4.5, what should be done to find the value of the percentile?

Average the 4th and 5th values Signup and view all the answers

Which of the following best describes the relationship between quartiles and percentiles?

Quartiles represent specific percentiles. Signup and view all the answers

What is the role of outliers in determining the range of a data set?

Outliers significantly influence the calculation of the range. Signup and view all the answers

What is the median in relation to quartiles?

The second quartile (Q2), which is also known as the 50th percentile Signup and view all the answers

What is the correct formula for calculating the rank of the pth percentile in an ordered data set with n values?

r = p(n - 1)/100 + 1 Signup and view all the answers

What is the primary purpose of using deciles in data analysis?

To divide an ordered data set into ten equal parts Signup and view all the answers

Which calculation accurately reflects the interquartile range?

Q3 - Q1 Signup and view all the answers

In grouped data, percentiles are typically found within what kind of range?

A range based on ranks Signup and view all the answers

What is the semi-interquartile range a representation of?

It is half of the interquartile range Signup and view all the answers

How is the full data range calculated in terms of percentiles?

By subtracting the 0th percentile from the 100th percentile Signup and view all the answers

What denotes the first quartile in terms of percentiles?

25th percentile Signup and view all the answers

What is true about the interquartile range (IQR)?

It measures the dispersion of the middle half of the data set. Signup and view all the answers

Which of the following statements regarding deciles is accurate?

There are ten deciles, with each separating 10% of the data. Signup and view all the answers

How is the semi-interquartile range calculated?

By dividing the interquartile range by two. Signup and view all the answers

In an ordered data set, what is the rank of the 75th percentile if there are 40 values?

32 Signup and view all the answers

What does the full data range represent?

The maximum value minus the lowest value in a data set. Signup and view all the answers

Where do percentiles generally lie in grouped data?

Within a range rather than at a specific value. Signup and view all the answers

What is indicated by the 50th percentile in a data set?

The median value of the data set Signup and view all the answers

How is the rank of the 25th percentile calculated in an ordered data set?

r = rac{25}{100}(n - 1) + 1 Signup and view all the answers

Which characteristic does the range of a data set exhibit?

It represents the difference between the maximum and minimum values. Signup and view all the answers

What happens if the rank calculated for a percentile is not an integer?

Take the average of the values at the two surrounding ranks. Signup and view all the answers

What does the term 'percentile' specifically refer to in a data set?

The value based on the percentage of data points below it. Signup and view all the answers

Why is the range considered sensitive to outliers?

Outliers affect the distribution of values. Signup and view all the answers

When calculating a percentile, what is the significance of the parameter 'p' in the formula?

It indicates the percentage of values below the desired value. Signup and view all the answers