Measures of Position for Grouped Data Quiz and Flashcards

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Questions and Answers

What is the main purpose of measures of position in data analysis?

To describe the distribution of a dataset (correct)

To calculate the mean of a dataset

To find the range of a dataset

To identify the middle value of a dataset

Which of the following is an example of a measure of position?

Mean

Median

90th percentile (correct)

Mode

What is the formula to find the kth percentile for grouped data?

$P_k = LB + \frac{kN - cf_b}{fP_k} \times i$ (correct)

$Q_k = LB + \frac{kN}{10} \times i$

$Q_k = LB + \frac{kN - cf_b}{100} \times i$

$D_k = LB + \frac{10kN}{fD_k} \times i$

What is the definition of a decile?

A measure of position that divides the distribution of data into 10 equal parts Signup and view all the answers

What is the value of $Q_2$ in percent?

75% Signup and view all the answers

What is the lower boundary for the 40th percentile?

80.5 Signup and view all the answers

What is the cumulative frequency used to solve for the 7th decile?

90 Signup and view all the answers

What is the main difference between a quartile and a decile?

A quartile divides the data into 4 equal parts, while a decile divides the data into 10 equal parts Signup and view all the answers

What is the purpose of finding the measure of position in a dataset?

To understand the distribution of the dataset Signup and view all the answers

In a dataset with 15 observations, what is the position of the 20th percentile?

4th Signup and view all the answers

What is the purpose of using the Mendelhall and Sincich Method in data analysis?

To solve for quartiles, deciles, and percentiles of a dataset Signup and view all the answers

In a dataset, what does the 35th percentile separate?

The lowest 35% from the highest 65% Signup and view all the answers

What is the formula to find the kth percentile?

$P_k = (n + 1) / 100$ Signup and view all the answers

What is the value of $D_4$ in the example given?

10 Signup and view all the answers

Which of the following is an example of a measure of position in a dataset?

Median Signup and view all the answers

What is the purpose of finding the 80th percentile in a dataset?

To separate the lowest 80% from the highest 20% Signup and view all the answers

What is the relationship between the median and the 50th percentile?

The median and the 50th percentile are equal Signup and view all the answers

In a dataset, what is the main purpose of finding the quartiles?

To separate the dataset into four equal parts Signup and view all the answers

What is the value of $P_{80}$ in the example given?

12 Signup and view all the answers

Study Notes

Measures of Position for Grouped Data

The measures of position for grouped data include quartiles, deciles, and percentiles.

Quartiles

A quartile is a measure of position that divides the distribution of data into four equal parts.
The formula for quartile is: 𝑘𝑁 4 𝑄𝑘 = 𝐿𝐵 + [ − 𝑐𝑓 𝑏 𝑓𝑄𝑘 ] ×𝑖

Deciles

A decile is a measure of position that divides the distribution of data into ten equal parts.
The formula for decile is: 𝑘𝑁 𝐷𝑘 = 𝐿𝐵 + [ 10 − 𝑐𝑓 𝑏 𝑓𝐷𝑘 ] ×𝑖

Percentiles

A percentile is a measure of position that divides the distribution of data into hundred equal parts.
The formula for percentile is: 𝑘𝑁 𝑃𝑘 = 𝐿𝐵 + [100 − 𝑐𝑓 𝑏 𝑓𝑃𝑘 ] ×𝑖

Steps to Calculate Measures of Position

Construct the cumulative frequency column.
Determine the kth class (Use: 𝑘𝑁 for quartile, 𝑘𝑁 for decile, 𝑘𝑁 for percentile).
Determine the values of each of the variables in the formula.
Substitute the values into the formula then solve.

Example Problems

Calculate quartile, decile, and percentile using the frequency distribution table.
Solve problems involving quartile, decile, and percentile.

What I Need to Know

Calculate a specified measure of position (e.g. 90th percentile) of a set of data.
Interpret measures of position.

What I Can Do

Calculate a specified measure of position: quartile, decile, and percentile of grouped data.
Interpret measures of position.

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Description

Solve problems on calculating measures of position using a frequency distribution of math test scores. Determine class boundaries, total frequency, and deciles from the given data.