# OpenStax-CNX

You are here: Home » Content » Descriptive Statistics: Practice

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

# Descriptive Statistics: Practice

Summary: Note: This module is currently under revision, and its content is subject to change. This module is being prepared as part of a statistics textbook that will be available for the Fall 2008 semester.

Note: You are viewing an old version of this document. The latest version is available here.

## Practice 1:

Calculating & interpreting the center, spread & location of data constructing & interpreting histograms and 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

## Discussion questions

1. What does the frequency column sum to? Why? ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________
2. What does the relative frequency column sum to? Why? ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________ ____________________________________________________________________________________________________________
3. What is the difference between relative frequency and frequency for each data value?
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

sample mean = x¯ x = __________

sample standard deviation = sx s x = _________

sample size = n = __________

## Use the table on the first page of this practice to answer the following

1. median = _________
2. mode = ___________
3. fist quartile = ___________
4. second quartile = median = 50th percentile = _____________
5. third quartile = _____________
6. interquartile range (IQR) = ____________________ - ________________ = ________________
7. 10th percentile = _______________
8. 70th percentile = _______________
9. Find the value that is 3 standard deviations: a. above the mean ______________ b. below the mean _____________

## 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?

## Practice 2:

Understanding theoretical symbols

## Given

The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976-77 through 2004-2005. (Source: Graphically Speaking by Bill King, LTCC Institutional Research, December 2005). Use these values to answer the following questions:

• μμ = 1000 FTES
• median - 1014 FTES
• σσ = 474 FTES
• first quartile = 528.5 FTES
• third quartile = 1447.5 FTES
• n = 29 years
1. A sample of 11 years is taken. About how many are expected to have a FTES of 1014 or above? Explain how you determined your answer _____________________________________________________
2. 75% of all years have a FTES: a) at or below _______________________ b) at or above _________________
3. The population standard deviation = _______________________
4. What percent of the FTES were from 528.5 to 1447.5? _______________________ How do you know?
5. What pis the IQR? ____________________ What does the IQR represent?
6. How many standard deviations away from the mean is the median? ____________

## Content actions

### Give feedback:

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