Statistics Class 3

transcript

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)

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

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

List the lower values

Add in the upper limit values

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

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

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

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

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

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

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

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

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

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

0.10.15

0.20.25

0.30.35

Female Pulse Rates

Pulse Rate

Cumulative Histogram

69 or less

79 or less

89 or less

99 or less

109 or less

119 or less

129 or less

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

IQ Scores

IQ Score

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

Weights of Pennies

Weight of Penny

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

Statistics Class 3

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