1) Analyze box plots to determine median ages, ranges of different BMW models. 2) Construct line graphs comparing book sales over time for two publishers. 3) Calculate measures of center and spread, and interpret box plots for additional data sets.

1. Chapter 2
D E S C R I P T I V E S TA T I S T I C S
SECTIONS 1 - 5

2. 2.1 Descriptive Statistics
Goals:
 Be able to display data graphically and interpret graphs
correctly.
 Calculate and interpret measures of the center, location and
spread of data.

3. 2.3 Line Graph
 Line graphs represent each piece of data by a point on a
graph. Categories are shown on the horizontal axis and the
associated frequencies or data values are shown on the
vertical axis. The points are then connected to allow us to
look for trends.
 Line graphs are generally used for quantitative data and
work particularly well for showing how things change over
time.

4. 2.3 Line Graph

5. 2.3 Line Graph
Height Comparison for Girls and Boys to Age Four (Line Graph)
42
40
38
36
Hieght (inches)
34
Girls
Boys
32
30
28
26
24
0 1 2 3 4 5
Age (years)

6. 2.3 Line Graph
Height Comparison for Girls and Boys to Age Four (line graph)
45
40
35
30
Hieght (inches)
25
Girls
Boys
20
15
10
5
0
0 1 2 3 4 5
Age (years)

7. EXAMPLE number of
year
dolphins
The following data
set shows the 1996 1827
number of dolphins
sited in Santa 1997 7290
Barbara Channel
from 1996 to 2001. 1998 4941
Create a line graph
using the following 1999 6154
data
2000 5011
2001 7768

8. 2.3 Bar Graph
 Bar Graphs are similar to line graphs but categories can be
shown on either the vertical or horizontal axis and the
frequencies or values are represented by rectangles (or
rectangular boxes) instead of points.
 On a bar graph the bars generally do not touch.
 Bar graphs work particularly well for showing frequencies or
relative frequencies of qualitative or quantitative discrete
catagories.

9. 2.3 Bar Graph
How often do you wear a seat belt when riding in a
car driven by someone else?
3000
2500
2000
1500
1000
500
0
Never Rarely Sometimes Most of the Always
time

10. 2.3 Bar Graph
How often do you wear a seat belt when riding in a
car driven by someone else?
Always
Most of the time
Sometimes
Rarely
Never
0 500 1000 1500 2000 2500 3000

11. 2.3 Bar Graph
How often do you wear a seat belt when riding in a car
driven by someone else?
3000
2500
2000
1500
1000
500
0

12. EXAMPLE color frequency
Create a bar graph RED 44
using the following
data ORANGE 14
YELLOW 12
GREEN 30
BLUE 66
PURPLE 34

13. 2.4 Histograms
 A histogram is similar to a bar graph but is used to
represent quantitative categories. Categories should be
placed along the horizontal axis.
 The bars in a histogram always touch.

14. EXAMPLE
1. What is the most frequent number of cars
A car salesman
sold in a week?
records the number
of sales made per
week for the past 2. What is the highest number of cars sold
year and constructs in a week.
the following
histogram. Answer
each question using 3. For how many weeks were two cars sold?
the histogram.
4. Determine the percentage of the time
that 6 cars were sold.

15. 2.4 Histograms
Car Sales
14
12
10
frequency
8
6
4
2
0
0 1 2 3 4 5 6 7 8 9 10
cars sold in one week

16. Number of Cars Frequency
EXAMPLE Sold per week
60-69 2
The following
frequency table
70-79 3
represents the IQ 80-89 13
scores of a random 90-99 42
sample of seventh-
grade students. IQ
100-109 58
scores are measured 110-119 40
to the nearest whole 120-129 31
number. Construct a
histogram 130-139 8
representing this 140-149 2
data. 150-159 1

17. 2.5 Measures of Location
 The median of a data set is the value that falls in the center
of the data set when arranged in ascending order. If there
are an even number of values the median will be the average
of the two central values. The median can also be thought
of as the second quartile of the data set.
 The first quartile and the third quartile can be found by
dividing the data into two sets consisting of the numbers
above and below the median and finding the central values
of each of theses new sets. The median of the lower half
of the data set is the first quartile and the median of the
upper half is the third quartile.

18. EXAMPLE
Find the 1. 4.5, 10, 1, 1, 9, 14, 4, 8.5, 6, 1, 9
minimum, maximum
, median, first
quartile, and third 2. 49.2, 53.3, 55.9, 48. 1, 43.2, 49.6, 47.7, 52.3
quartile of each data
set.

19. 2.5 Box Plot
 A box plot is a graphical representation of a quantitative
data set that tells us about the location of the data. It gives
a visual summary of the minimum value, first
quartile, median, third quartile, and maximum value of the
data.
 The graph is shown in relation to one axis representing the
values of the data. A box is drawn extending from Q1 to Q3
with a vertical bar dividing it at the median.
Whiskers, horizontal lines, are drawn extending from the
sides of the box to the minimum and maximum values.

20. EXAMPLE
Draw a box plot 1. 4.5, 10, 1, 1, 9, 17, 4, 8.5, 5, 1, 9
representing each
data set.
2. 49.2, 53.3, 55.9, 48. 1, 43.2, 49.6, 47.7, 52.3

21. EXAMPLE
#2.13.20 A survey was conducted of 130 purchasers of
new BMW 3 series cars, 130 purchasers of
BMW 5 series cars, and 130 purchasers of
BMW 7 series cars. In it, people were asked
the age they were when they purchased their
car. The following box plots display the
results.

22. HOMEWORK

23. HOMEWORK

24. HOMEWORK
2.13 #s 4a, b, c, 7, 10, 12, 13a, b, d, e, f, also construct a line
graph for the data from Publisher A and Publisher B, 16a part
i and iii, 16b, 21, 29, 30, 31