# 2.12 Univariate descriptive statistics: practice 1

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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 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

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

## Discussion questions

What does the frequency column sum to? Why?

65

What does the relative frequency column sum to? Why?

1

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

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:

Sample mean = $\overline{x}$ =

4.75

Sample standard deviation = $s_{x}$ =

1.39

Sample size = $n$ =

65

## Calculations

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

Median =

4

Mode =

4

First quartile =

4

Second quartile = median = 50th percentile =

4

Third quartile =

6

Interquartile range ( $\mathrm{IQR}$ ) = _____ - _____ = _____

$6-4=2$

10th percentile =

3

70th percentile =

6

Find the value that is 3 standard deviations:

• Above the mean
• Below the mean

• 8.93
• 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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