Statistics Class 3. Jan 30, 2012

Transcription

1 Statistics Class 3 Jan 30, 2012

2 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, Is $ 29, 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 ranbom sample? Simple random Sample? Explain.

3 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

4 Frequency Distributions Class midpoints are the values in the middle of the classes. Class width is the difference between two consecutive lower class limits.

5 Procedure for constructing a frequency Distribution. 1. Determine the number of classes. 2. Calculate the class width 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.

6 Example 1 Frequency table by hand

7 Example 1 Frequency table by hand Lets Have 7 classes. 2. Find the width.

8 Example 1 Frequency table by hand Lets Have 7 classes. 2. Find the width = 64 64/7=9.14

9 List the min data value or convenient data value

10 60 List the lower values

11 60 70 List the lower values

12 Add in the upper limit values

13 Tally Ho!

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15 Tally Ho!

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17 Tally Ho!

18 Pulse Rate Freq Make it look nice

19 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%

20 Pulse Rate Relative Frequency / / / / / / /40 Change into a relative frequency

21 Pulse Rate Relative Frequency /40= /40= /40= /40= /40= /40= /40=0.025 Change into a relative frequency

22 Pulse Rate Relative Frequency Change into a relative frequency

23 Pulse Rate Freq Change into cumulative frequency

24 Pulse Rate Cumulative Freq Change into cumulative frequency

25 Pulse Rate Cumulative Freq 69 or less or less 12+14=26 89 or less =37 99 or less = or less = or less = or less =40 Change into cumulative frequency

26 Pulse Rate Cumulative Freq

27 Frequency Distribution Do # 17 on page 54

28 Now go to my website and use the data provided to use open office to construct a Frequency Table

29 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.

30 Relative Frequency Histogram A relative frequency histogram is the same as a histogram with relative frequencies instead of frequencies.

31 This data because of its shape is said to have a normal distribution.

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33 Measure of center A measure of center is a value at the center or middle of a data set. The mean of a set of data is the measure of center found by adding the data values and dividing the total by the number of data values. =average(data)

34 Calculate the mean of some data

35 Calculate the mean of some data x= 3052/40=76.3

36 Median The median of a data set is the measure of center that is the middle value when the data values are arranged in increasing (decreasing) order. So take order it

37 Median Select the middle values Even number of data values average the middle two. (72+76)/2=148/2=74 open office: median(data)

38 Mode The mode of a data set is the data value that occurs with greatest frequency. When two data values occur with the same greatest frequency, each one is a mode and the data set is bimodal. No repeated data value, then there is no mode. Find the mode of our previous data

39 Mode The mode of a data set is the data value that occurs with greatest frequency. When two data values occur with the same greatest frequency, each one is a mode and the data set is bimodal. No repeated data value, then there is no mode. Find the mode of our previous data Mode is 72, in open office use mode(data).

40 Midrange The midrange of a data set is the value midway between the maximum and minimum values midrange=(maximum data value + minimum data value)/2 From our previous data set the max was 124 and the min was 60 so... midrange= ( )/2=62.

41 Mean from a frequency distribution

42 Pulse Rate Freq Total 40

43 Pulse Rate Freq Midpoint Total 40

44 Pulse Rate Freq f Midpoint x x*f Total 40

45 Pulse Rate Freq f Midpoint x x*f Total

46 Pulse Rate Freq f Midpoint x x*f Totals Mean 3070/

47 Homework 2-2: 1, 3, 17, : 3, 9, : 1, 3, 7, 17, 29.