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Statistics Class 3 Jan 30, 2012
Statistics Class 3
Jan 30, 2012
Group Quiz 21. The Statistical Abstract of the United States includes the
average per capita income for each of the 50 states. When those 50 values are added, then divided by 50, the result is $29,672.52. Is $ 29,672.52 the average per capita income for all individuals in the United States? Why or why not?
2. A classroom consists of 36 students seated in six different rows, with six students in each row. The instructor rolls a die to determine a row, then rolls the die again to select a particular student in the row. This process is reapeated until a sample of 6 students is obtained. Does this sampling plan result in a random sample? Simple random Sample? Explain.
Frequency Distributions
We recorded the pulses of 40 women. Here it is!
76 64 72 80 88 76 60 76 72 7668 80 80 104 64 88 68 60 68 7680 72 76 72 68 88 72 80 96 60 72 72 68 88 72 88 64 124 80 64
This data is hard to make sense of so we (you) are going to organize it using a Frequency Distribution (Table)
Frequency Distributions
A frequency Distribution shows how a data set is partitioned among all of several categories (or classes) by listing all of the categories along with the number of data values in each of the categories.
Lower class limits are the smallest numbers that can belong
to the different classes. Upper class limits are the largest numbers that can belong to
the different classes.
Class boundaries are the numbers used to separate the classes, but without the gaps created by class limits
Frequency Distributions
Class midpoints are the values in the middle of the classes.
Class width is the difference between two consecutive lower class limits.
Procedure for constructing a frequency Distribution.
1. Determine the number of classes.2. Calculate the class width.
class width= (max data value-min data value)/number of classes.
3. Choose either the min data value or convenient value below the min data value as the first lower class limit.
4. Using the first lower class limit and class width, list the other lower class limits. Do this vertically and add in the upper class limits
5. Tally up the data values in each class.
Example 1 Frequency table by hand.
76 64 72 80 88 76 60 76 72 76 68 80 80 104 64 88 68 60 68 76 80 72 76 72 68 88 72 80 96 60 72 72 68 88 72 88 64 124 80 64 1. Lets Have 7 classes. 2. Find the width.
Example 1 Frequency table by hand.
76 64 72 80 88 76 60 76 72 76 68 80 80 104 64 88 68 60 68 76 80 72 76 72 68 88 72 80 96 60 72 72 68 88 72 88 64 124 80 64 1. Lets Have 7 classes. 2. Find the width. 124-60= 64 64/7=9.14
List the min data value or convenient data value
60
List the lower values
60
70
List the lower values
60
70
80
90
100
110
120
Add in the upper limit values
60-69
70-79
80-89
90-99
100-109
110-119
120-129
Tally Ho!
76 64 72 80 88 76 60 76 72 76 68 80 80 104 64 88 68 60 68 76 80 72 76 72 68 88 72 80 96 60 72 72 68 88 72 88 64 124 80 64
60-69 12
70-79
80-89
90-99
100-109
110-119
120-129
Tally Ho!
76 64 72 80 88 76 60 76 72 76 68 80 80 104 64 88 68 60 68 76 80 72 76 72 68 88 72 80 96 60 72 72 68 88 72 88 64 124 80 64
60-69 12
70-79 14
80-89
90-99
100-109
110-119
120-129
Tally Ho!
Pulse Rate Freq
60-69 12
70-79 14
80-89 11
90-99 1
100-109 1
110-119 0
120-129 1
Relative Frequency
In a relative frequency the frequency is replaced with a relative frequency (proportion) or a percentage frequency (percent).
Relative frequency=class frequency/sum of all frequencies
Percentage freq=(class freq/sum of all freq)*100%
Pulse Rate Relative Frequency
60-69 12/40
70-79 14/40
80-89 11/40
90-99 1/40
100-109 1/40
110-119 0/40
120-129 1/40
Change into a relative frequency
Pulse Rate Relative Frequency
60-69 12/40=0.3
70-79 14/40=0.35
80-89 11/40=0.27
90-99 1/40=0.025
100-109 1/40=0.025
110-119 0/40=0
120-129 1/40=0.025
Change into a relative frequency
Pulse Rate Relative Frequency
60-69 0.3
70-79 0.35
80-89 0.275
90-99 0.025
100-109 0.025
110-119 0
120-129 0.025
Change into a relative frequency
Pulse Rate Freq
60-69 12
70-79 14
80-89 11
90-99 1
100-109 1
110-119 0
120-129 1
Change into cumulative frequency
Pulse Rate Cumulative Freq
60-69 12
70-79 12+14
80-89 12+14+11
90-99 12+14+11+1
100-109 12+14+11+1+1
110-119 12+14+11+1+1+0
120-129 12+14+11+1+1+0+1
Change into cumulative frequency
Pulse Rate Cumulative Freq
69 or less 12
79 or less 12+14=26
89 or less 12+14+11=37
99 or less 12+14+11+1=38
109 or less 12+14+11+1+1=39
119 or less 12+14+11+1+1+0=39
129 or less 12+14+11+1+1+0+1=40
Change into cumulative frequency
Pulse Rate Cumulative Freq
69 or less 12
79 or less 26
89 or less 37
99 or less 38
109 or less 39
119 or less 39
129 or less 40
Frequency DistributionsLast Digit of female pulses Frequency
0 9
1 0
2 8
3 0
4 6
5 0
6 7
7 0
8 10
9 0
Frequency Distributions
IQ Frequency
50-69 24
70-89 228
90-109 490
110-129 232
130-149 26
IQ Scores from 1000 adults were randomly selected. The results are summarized below. Notice the frequencies start low, increase then decrease.
HistogramsA histogram is a graph consisting of bars of equal width drawn
adjacent to each other (without gaps). The Horizontal scale represents classes of quantitative data value and the vertical scale represents frequencies. The heights of the bars correspond to the frequency values.
60-69 70-79 80-89 90-99 100-109 110-119 120-12902468
10121416
Female Pulse Rates
Pulse Rate
Freq
uenc
y
Relative Frequency Histogram
A relative frequency histogram is the same as a histogram with relative frequencies instead of frequencies.
60-69 70-79 80-89 90-99 100-109
110-119
120-129
00.05
0.10.15
0.20.25
0.30.35
0.4
Female Pulse Rates
Pulse Rate
Rela
tive
Freq
Cumulative Histogram
69 or less
79 or less
89 or less
99 or less
109 or less
119 or less
129 or less
05
1015202530354045
Cumulative Frequency Distribution of the Pulse Rates of Females
This data because of its shape is said to have a normal distribution.
50-69 70-89 90-109 110-129 130-1490
100
200
300
400
500
600
IQ Scores
IQ Score
Freq
uenc
y
Histograms
2.40-2.49
2.50-2.59
2.60-2.69
2.70-2.79
2.80-2.89
2.90-2.99
3.00-3.09
3.10-3.19
0
5
10
15
20
25
30
Weights of Pennies
Weight of Penny
Freq
uenc
y
Statistical Graphs
obama-needs-charts-and-graphs
Homework
2-2: 1-4, 5-17 odd . 2-3: 1-4, 5-19 odd.
Read 2-4
