Chapter 2 section 1 through 5Presentation Transcript
Chapter 2D E S C R I P T I V E S TA T I S T I C S SECTIONS 1 - 5
2.1 Descriptive StatisticsGoals: Be able to display data graphically and interpret graphs correctly. Calculate and interpret measures of the center, location and spread of data.
2.3 Line Graph Line graphs represent each piece of data by a point on a graph. Categories are shown on the horizontal axis and the associated frequencies or data values are shown on the vertical axis. The points are then connected to allow us to look for trends. Line graphs are generally used for quantitative data and work particularly well for showing how things change over time.
2.3 Line Graph
2.3 Line Graph Height Comparison for Girls and Boys to Age Four (Line Graph) 42 40 38 36Hieght (inches) 34 Girls Boys 32 30 28 26 24 0 1 2 3 4 5 Age (years)
2.3 Line Graph Height Comparison for Girls and Boys to Age Four (line graph) 45 40 35 30Hieght (inches) 25 Girls Boys 20 15 10 5 0 0 1 2 3 4 5 Age (years)
EXAMPLE number of year dolphinsThe following dataset shows the 1996 1827number of dolphinssited in Santa 1997 7290Barbara Channelfrom 1996 to 2001. 1998 4941Create a line graphusing the following 1999 6154data 2000 5011 2001 7768
2.3 Bar Graph Bar Graphs are similar to line graphs but categories can be shown on either the vertical or horizontal axis and the frequencies or values are represented by rectangles (or rectangular boxes) instead of points. On a bar graph the bars generally do not touch. Bar graphs work particularly well for showing frequencies or relative frequencies of qualitative or quantitative discrete catagories.
2.3 Bar Graph How often do you wear a seat belt when riding in a car driven by someone else?30002500200015001000 500 0 Never Rarely Sometimes Most of the Always time
2.3 Bar Graph How often do you wear a seat belt when riding in a car driven by someone else? AlwaysMost of the time Sometimes Rarely Never 0 500 1000 1500 2000 2500 3000
2.3 Bar GraphHow often do you wear a seat belt when riding in a car driven by someone else?300025002000 1500 1000 500 0
EXAMPLE color frequencyCreate a bar graph RED 44using the followingdata ORANGE 14 YELLOW 12 GREEN 30 BLUE 66 PURPLE 34
2.4 Histograms A histogram is similar to a bar graph but is used to represent quantitative categories. Categories should be placed along the horizontal axis. The bars in a histogram always touch.
EXAMPLE 1. What is the most frequent number of carsA car salesman sold in a week?records the numberof sales made perweek for the past 2. What is the highest number of cars soldyear and constructs in a week.the followinghistogram. Answereach question using 3. For how many weeks were two cars sold?the histogram. 4. Determine the percentage of the time that 6 cars were sold.
2.4 Histograms Car Sales 14 12 10frequency 8 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10 cars sold in one week
Number of Cars FrequencyEXAMPLE Sold per week 60-69 2The followingfrequency table 70-79 3represents the IQ 80-89 13scores of a random 90-99 42sample of seventh-grade students. IQ 100-109 58scores are measured 110-119 40to the nearest whole 120-129 31number. Construct ahistogram 130-139 8representing this 140-149 2data. 150-159 1
2.5 Measures of Location The median of a data set is the value that falls in the center of the data set when arranged in ascending order. If there are an even number of values the median will be the average of the two central values. The median can also be thought of as the second quartile of the data set. The first quartile and the third quartile can be found by dividing the data into two sets consisting of the numbers above and below the median and finding the central values of each of theses new sets. The median of the lower half of the data set is the first quartile and the median of the upper half is the third quartile.
EXAMPLEFind the 1. 4.5, 10, 1, 1, 9, 14, 4, 8.5, 6, 1, 9minimum, maximum, median, firstquartile, and third 2. 49.2, 53.3, 55.9, 48. 1, 43.2, 49.6, 47.7, 52.3quartile of each dataset.
2.5 Box Plot A box plot is a graphical representation of a quantitative data set that tells us about the location of the data. It gives a visual summary of the minimum value, first quartile, median, third quartile, and maximum value of the data. The graph is shown in relation to one axis representing the values of the data. A box is drawn extending from Q1 to Q3 with a vertical bar dividing it at the median. Whiskers, horizontal lines, are drawn extending from the sides of the box to the minimum and maximum values.
EXAMPLE#2.13.20 A survey was conducted of 130 purchasers of new BMW 3 series cars, 130 purchasers of BMW 5 series cars, and 130 purchasers of BMW 7 series cars. In it, people were asked the age they were when they purchased their car. The following box plots display the results.
HOMEWORK2.13 #s 4a, b, c, 7, 10, 12, 13a, b, d, e, f, also construct a linegraph for the data from Publisher A and Publisher B, 16a parti and iii, 16b, 21, 29, 30, 31