### 5-3 Graph Frequency Distributions

```Graph Frequency Distributions
Section 5 - 3
Graph Frequency Distributions
 Why are graphs so important in math?
 What would happen if we surveyed everyone in
the school about the price of their car?
 What would the data look like?
 Would it be easy to understand?
Graph Frequency Distributions
 Today:
1) Create a frequency chart
a) Including an interval frequency chart
2) Find the mean from a frequency chart
Graph Frequency Distributions
 You want to purchase a car stereo. You find 33
ads for the stereo you want and arranged them
ascending order:
What is wrong with using this data?
\$540
\$600
\$700
\$700
\$870
\$990
\$1,200
\$550
\$600
\$700
\$750
\$900
\$990
\$1,200
\$550
\$600
\$700
\$775
\$900
\$990
\$1,200
\$550
\$675
\$700
\$775
\$990
\$990
\$550
\$700
\$700
\$800
\$990
\$1,000
\$540 \$550 \$550
How many car stereos
\$550 \$550 \$600
are priced below \$800?
\$600 \$600 \$675
\$700 \$700 \$700
How many car stereos
\$700 \$700 \$700
are priced below \$600?
\$700 \$750 \$775
\$775 \$800 \$870
How many car stereos
\$900 \$900 \$990
are priced above
\$990 \$990 \$990
\$1,000?
\$990 \$990 \$1,000
\$1,200 \$1,200 \$1,200
Price
P(\$)
\$540
\$550
\$600
\$675
\$700
\$750
\$775
\$800
\$870
\$900
\$990
\$1,000
\$1,200
Frequency
f
Graph Frequency Distributions
 The following data was collected on the weight of
packages shipped by a manufacturing company.
13
49
32
16
56
57
65
26
48
45
68
23
44
27
43
35
35
44
22
15
30
46
43
65
What is the major problem with creating a
frequency graph for this data?
How can this problem be resolved?
36
62
35
Graph Frequency Distributions
13
44
36
68
43
48
30
16
35
49
27
62
23
65
65
22
56
35
32
43
35
45
46
26
15
57
44
Weight
Frequency (f)
Graph Frequency Distributions
 Create an interval frequency distribution chart
containing the following data.
14
49
71
26
19
64
74
66
55
22
62
75
47
88
54
44
78
59
39
16
18
22
88
93
71
37
49
35
29
74
Graph Frequency Distributions
\$ Amount
10 – 19
20 – 29
30 – 39
40 – 49
50 – 59
60 – 69
Frequency (f)
3
4
4
8
2
3
Graph Frequency Distributions
 You are the manager of The Dress Code Boutique.
From the following data representing the dollar sales
of each transaction today, construct a frequency
distribution using classes with an interval of \$10.
14
49
71
26
19
64
74
66
55
22
62
75
47
88
54
44
78
59
39
16
18
22
88
93
71
37
49
35
29
74
Graph Frequency Distributions
\$ Amount
10 – 19
20 – 29
30 – 39
40 – 49
50 – 59
60 – 69
70 - 79
80 - 89
90 - 99
Frequency (f)
4
4
3
4
3
3
6
2
1
Graph Frequency Distributions
 Finding the mean from a frequency chart:
1) Multiply the price by the frequency
•
If the chart is an interval chart, use the midpoint of
the intervals
2) Find the sum of the products
3) Divide the sum by the total number of tally’s
Product
P(f)
Price
P(\$)
Frequency
f
\$540
1
\$550
4
\$540
\$2,200
\$600
3
\$1,800
\$675
1
\$700
7
\$750
1
\$775
2
\$675
\$4,900
\$750
\$1,550
\$800
1
\$870
1
\$900
2
\$800
\$870
\$1,800
\$990
6
\$5,940
\$1,000
1
\$1,200
3
\$1,000
\$3,60
2) Find the sum of
the products:
= \$26,425
3) Divide this sum
by the number of
tally’s
\$26,425
33
= \$800.76
Graph Frequency Distributions
How can we multiply the amount by the frequency?
\$ Amount
10 – 19
20 – 29
30 – 39
40 – 49
50 – 59
60 – 69
Frequency
3
4
4
8
2
3
938
Mean =
= 39.1
24
Midpt
Product
14.5
24.5
43.5
98
34.5
44.5
54.5
64.5
138
356
109
193.5
Graph Frequency Distributions
\$ Amount
10 – 19
20 – 29
30 – 39
40 – 49
50 – 59
60 – 69
70 - 79
80 - 89
90 - 99
Frequency Mid pt
4
14.5
4
24.5
3
34.5
4
44.5
3
54.5
3
64.5
6
74.5
2
84.5
1
94.5
Product
58
98
103.5
178
163.5
193.5
447
169
94.5
Mean = \$50.17
Graph Frequency Distributions
Section 5 - 3
Graph Frequency Distributions
 Below are prices you have found for different tints
for your car. Put them in an interval frequency chart
and find the mean price.
25
35
68
34
63
61
27
50
58
36
48
39
19
68
27
43
52
35
54
23
42
18
45
47
26
52
19
Graph Frequency Distributions
How can we multiply the amount by the frequency?
\$ Amount
10 – 19
20 – 29
30 – 39
40 – 49
50 – 59
60 – 69
Frequency
Midpt
3
14.5
5
24.5
5
34.5
44.5
5
54.5
5
64.5
4
1091.5
= \$40.43
Mean =
27
Product
43.5
122.5
172.5
222.5
272.5
258
Graph Frequency Distributions
 Yesterday:
1) Create a frequency chart
a) Including an interval frequency chart
2) Find the mean from a frequency chart
Today:
1) Read a stem & leaf plot
2) Graph box & whisker plots
Graph Frequency Distributions
1
0
2
2 4
3
8
5
9
7
8
10 15 17 18
22 24
38 39
Graph Frequency Distributions
1
2
3
4
8
0
0
2
9 9
2 3 3 4 4 4 4 6 8 9 9
1 2 4 5 6 7
3
Find the mean, mode, and 4 quartiles from this data:
Q1 = 23
Q 2 = 27
Mean = 28
Mode = 24
Q3 = 32.5
Q 4 = 43
Graph Frequency Distributions
 Steps to creating a box and whisker chart
1)
Find the four quartiles
2)
Draw a box from
3)
Draw a vertical line in the box at
4)
Draw whiskers out to your lowest and highest data
values
Q1 to Q3
Q2
Graph Frequency Distributions
Q1 = 23
Q 2 = 27
18
23
Q3 = 32.5
27
32.5
Q 4 = 43
43
Graph Frequency Distributions
 You are doing research on the number of gasoline price
changes per year. You have collected the following
data.
1
2
3
4
5
6
7
1
0
8
0
2
3
2
a) Put this data in a
box and whisker
graph
1 2 3 7 9
3 6 6
8 9 9 9 9 9
2
4
4
4
5
5
5
6
7
b) Are there any
outliers?
Graph Frequency Distributions
Q1 = 23
11
Q 2 = 39
23
Q3 = 55
39
Q 4 = 72
55
IQR: 55 – 23 = 32
Lower Boundary: 23 – (1.5) (32) = -25
Upper Boundary: 55 + (1.5) (32) = 103
72
Graph Frequency Distributions
\$3,000 \$5,200
\$7,000 \$9,100
\$15,000
What is the IQR? \$9,100 - \$5,200 = \$3,900
Lower Boundary: \$5,200 – (1.5)(3,900)= - \$650
Upper Boundary: \$9,100 + (1.5)(3,900)= \$14,950
Graph Frequency Distribution
 Page 236, 2-12
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