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Inside Collection (Textbook):

Textbook by: Barbara Illowsky, Ph.D., Susan Dean. E-mail the authors

# Practice 1: Center of the Data

Summary: This module provides students with opportunities to apply concepts related to descriptive statistics. Students are asked to take a set of sample data and calculate a series of statistical values for that data.

## Student Learning Outcomes

• The student will calculate and interpret the center, spread, and location of the data.
• The student will construct and interpret histograms an box plots.

## Given

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars.

## Complete the Table

Table 1
Data Value (# cars) Frequency Relative Frequency Cumulative Relative Frequency

## Discussion Questions

### Exercise 1

What does the frequency column sum to? Why?

65

### Exercise 2

What does the relative frequency column sum to? Why?

1

### Exercise 3

What is the difference between relative frequency and frequency for each data value?

### Exercise 4

What is the difference between cumulative relative frequency and relative frequency for each data value?

## Construct a Histogram

Determine appropriate minimum and maximum x and y values and the scaling. Sketch the histogram below. Label the horizontal and vertical axes with words. Include numerical scaling.

## Data Statistics

Calculate the following values:

### Exercise 5

Sample mean = x¯ x =

4.75

### Exercise 6

Sample standard deviation = sx s x =

1.39

### Exercise 7

Sample size = nn =

65

## Calculations

Use the table in section 2.11.3 to calculate the following values:

Median =

4

Mode =

4

First quartile =

4

### Exercise 11

Second quartile = median = 50th percentile =

4

Third quartile =

6

### Exercise 13

Interquartile range (IQRIQR) = _____ - _____ = _____

#### Solution

6 - 4 = 2 6 - 4 = 2

### Exercise 14

10th percentile =

3

### Exercise 15

70th percentile =

6

### Exercise 16

Find the value that is 3 standard deviations:

• a. Above the mean
• b. Below the mean

• a. 8.93
• b. 0.58

## Box Plot

Construct a box plot below. Use a ruler to measure and scale accurately.

## Interpretation

Looking at your box plot, does it appear that the data are concentrated together, spread out evenly, or concentrated in some areas, but not in others? How can you tell?

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#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

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#### Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks