Transcript Section 1.1 (Thurs Feb 3)

1.1 Constructing and Interpreting Visual Displays of Data
Number of Pirates
Number of Pirates
Cambridge
Number of Pirates
Kitchener
Waterloo
City
Frequency
Waterloo
100
Kitchener
200
Cambridge
50
Waterloo
0
Kitchener
= 50 pirates
Cambridge
Height of Cambridge Pirates
20
Number of Pirates
15
250
10
200
5
150
0
100
100
110
120
130
140
150
Centimeters
50
0
Waterloo
Kitchener
Cambridge
There are a surprising number of pirates in the local area. The most pirates are in Kitchener.
Cambridge pirates are generally short.
160
170
180
Example 1
Imagine that only 10,000 people in the three cities
were studied to gather the data. Identify the
population, data, & sample.
The population is all people living in Kitchener, Waterloo
and Cambridge.
The data is number of pirates found in each city (100, 200 and 50)
The sample is the 10,000 people who were studied.
Number of Pirates
City
Frequency
Waterloo
100
Kitchener
200
Cambridge
50
Example 2
Calculate the angles for the pie graph corresponding to
the data.
Total = 350
Number of Pirates
City
Frequency
Waterloo
100
Kitchener
200
Cambridge
50
Waterloo: 100 / 350 = 0.285… x 360 =102.9
Kitchener: 200 / 350 = 0.571… x 360 = 205.7
Cambridge: 50 / 350 = 0.142… x 360 = 51.4
Number of Pirates
Waterloo
Kitchener
Cambridge
Example 3
Height of Cambridge Pirates
Is this a bar graph or a histogram?
20
15
This is a histogram because the data is continuous.
This means that every possible number including
decimals can be represented with the data.
10
5
0
100
110
120
130
140
150
160
170
180
Centimeters
What are the class intervals?
100 – 109.99…. , 110 – 119.99 … , 120 – 129.99 … , etc
100 – 110, 110 – 120, 120 – 130, etc
is an acceptable answer. Just realize that the second
number in each interval is not included.
Height of Cambridge Pirates
A corresponding bar graph might look something like this.
16
14
12
10
8
6
4
2
0
105
115
125
135
145
155
165
175
Example 4
Height of Pirates
Interval
Create a box and whisker diagram for the height data.
STEP 1: Find the median (middle value) of the data
50 data values, the middle is the average of 25th and 26th
Both are in 120 – 130. Assume they are both 125.
Therefore the median is 125
STEP 2: Find the medians of the bottom half and top half
13th
25 data values in each half. Need the
in each half.
th
13 value in the bottom half is in 110 – 120 … assume 115
13th value (38th overall) in the top half is in 130 - 140 … assume 135
Frequency
100-110
5
110-120
10
120-130
15
130-140
10
140-150
5
150-160
2
160-170
2
170-180
1
STEP 3: Draw it
100
110
120
130
140
150
160
170
180
Technically I “cheated” to find the medians. The “cheating” may will
get you a 4- only. Here is the proper way … its complicated
Height of Pirates
Interval
Median is average of 25th and 26th piece of data …
Need 10th and 11th in 120 – 130 and there are 15 numbers in the
interval and the interval is 10 units long.
10 / 15 = 0.666 ... X 10 = 6.66 + 120 = 126.66
11 / 15 = 0.733 … X 10 = 7.33 + 120 = 127.33
Average of 126.66 and 127.33 is 127 (instead of 125)
Frequency
100-110
5
110-120
10
120-130
15
130-140
10
140-150
5
150-160
3
160-170
2
170-180
1
Bottom half median is 13th piece of data
Need 8th in 110 – 120 and there are 10 numbers in the interval and the interval is 10 units long.
8/10 = 0.8 x 10 = 8 + 110 = 118
Median of the bottom half is 118 (instead of 115)
Top half median is 38th piece of data
Need 8th in 130 – 140 and there are 10 numbers in the interval and the interval is 10 units long.
8/10 = 0.8 x 10 = 8 + 130 = 138
Median of the bottom half is 138 (instead of 135)
Important Facts
Your homework is: Read: Pg 3 – 10 and Do: Pg 11 # 2, 4 -10
• population, sample, class interval, median are important terms
• 6 types of charts/graphs appeared in the lesson
• there are 2 other types to know as well.
• The only two that require any calculations are pie graph, box and whisker
• Make sure you can do the calculations
• Pirates are very interesting