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Statistics Class 3 Jan 30, 2012
Group Quiz 2 1. 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 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 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
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
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
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%
Frequency Distributions IQ Scores from 1000 adults were randomly selected. The results are summarized below. Notice the frequencies start low, increase then decrease.
Histograms A 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.
Relative Frequency Histogram A relative frequency histogram is the same as a histogram with relative frequencies instead of frequencies.
This data because of its shape is said to have a normal distribution.
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
