Exam January? 9:30 11:30

Transcription

1 UNIT STATISTICS Date Lesson TOPIC Homework Dec. 9 Dec. Dec. Jan. 9 Jan. 0 Jan Representing Data WS. Histograms WS. Measures of Central Tendenc Find the mean, median, and mode of the data sets on WS.. Check answers with TI-. Measures of Spread WS. Line of Best Fit and Correlation WS. Outliers WS. Check answers with TI-. Jan.. Review for Unit Test Unit Review WS Jan. Jan. -. TEST # Eam Review Eam Review Worksheets Eam Januar? 9:0 :0

2 MAP C Lesson. Representing Data E. In a surve of hocke fans, it is discovered that.% support the Ottawa Senators,.% support the Montreal Canadiens,.% support the Toronto Maple Leafs and.% support other teams. Represent this data in a circle graph. Team Fans (%) Central Angle Sens. Habs. Lafs. Other. E. A surve asked students what mode of transportation the normall use to get to school. The results were as follows: Bike, walk 9, bus, car 0. Represent this data in a circle graph.

3 Frequenc Mode Number Central Angle Bike Walk 9 Bus Car 0 BAR GRAPH We can use a bar graph when the data are counted. For eample, we could use a bar graph for the transportation data used above: 0 A surve asked students what mode of transportation the normall use to get to school. The results were as follows: Bike, walk 9, bus, car 0. Represent this data in a bar graph. Mode

4 Stopping Distance SCATTER PLOT A scatter plot eamines one number s relationship with another number. It is a series of points plotted from a set of ordered pairs. E. A car manufacturer has tested the stopping distance of a new model of car relative to the speed when the brakes are applied. The results are shown in the table below. Speed of car (km/h) Stopping Distance (m) a) Displa this data in a scatter plot. b) Does there appear to be a relationship between car speed and stopping distance? Eplain Speed WS.

5 Frequenc MAP C Lesson. Histograms E. A report of English marks must be prepared for the principal. One teacher has the following marks recorded. Prepare a frequenc table and present the information in a histogram., 9,, 0,,, 9,,,,,,,,,, 9,,,,,, 9, A histogram is similar to a bar graph, but it has no separation between the bars, and each bar represents an interval of measurement. A histogram should have between and 0 intervals. To determine the length of each interval, first determine the range of the data. Range = highest value of the data lowest value of the data For this data, Range = To determine the interval length, divide the range b both and 0. Your interval length should be between those values. So, the interval length for this data should be between 0. and.. 0 For this data we will choose an interval length of. Class Interval Tall Frequenc Mark

6 Frequenc E. The ages of people at a park in Arnprior one afternoon are shown below.,,, 9,,,,,, 9,,,,, 9 Construct a histogram for the data using appropriate intervals. Range: 9 = Interval length between: 9. and.. choose an interval length of. 0 Class Interval 9 Tall Frequenc Age WS.

7 MAP C Lesson. Measures of Central Tendenc The mean, median, and the mode are three measures of central tendenc. The give us information about the centre or average of a set of data. To calculate the mean, add all the data items and then divide the sum b the number of items. sum of all items Mean number of items The mean of,,,,,, and 9 is: The median is the middle item of a set of data. To calculate the median, put the data in order, then find the middle number. The median of,,,,,, 9 is The median of,,,,, 9 is The median of,,,,, 9 is The mode is the number or numbers that occur the most often. The mode of,,,,,, 9 is: The mode of,,,,,, 9 is: E. Marks on a class test are,,,,,,, 90, 9. Calculate the mean and the median. mean ( ) = bar median =

8 E. The following table shows the annual salaries earned b emploees of a small compan. Determine the mean, median, and mode. Annual Salar ($) () Frequenc (f) (f)() E. If the data are grouped into intervals, the calculated values for mean, median, and mode will onl be estimates. Calculate the mean, median, and mode of these amounts of charitable donations. Amount of Donation ($) Value to use Frequenc HW: Find the mean, median, and mode of the data sets on the grouped data sheet. Check with TI-

9 MAP C Lesson. Measures of Spread E. A class project required each student to make an Automatic Toothpick Maker. Ideall each toothpick should be cm in length. In addition to the measures of central tendenc which measures the average toothpick length, we will eamine the measures of spread which measures how much the toothpicks deviate from the average. Following are the measures of the lengths of toothpicks made b Aaron (A), Brandi (B), and Chris (C). (all measures are in cm) A:,,,,, 9 B:,,,,, 9 C:,,,,, Which student is the most reliable toothpick maker? JUSTIFY YOUR ANSWER. First we will calculate the mean and the median, A:,,,,, 9 B:,,,,, 9 C:,,,,, Mean Median Range Standard Deviation See net page for calculations Clearl the mean and the median don t tell us everthing about the data. The range is one measure of spread. The range is the difference between the highest number and the lowest number. It provides a quick glimpse as to how spread out the data is. Fill in the ranges in the above chart. In this case the range is a little misleading. The most powerful measure of spread is the standard deviation ( ). It measures how far the numbers are from the mean ( ). There are different versions of the standard deviation. The formula we will use is: ( ) ( ) ( )... ( ) n n It s much simpler than it looks. It often helps to use a chart.

10 Set A 9 Sum ( ) = Set B 9 Sum ( ) = Set C Sum ( ) =

11 E. Determine the mean, median, and standard deviation of each of the following data sets using the TI-. For long and tedious calculations, it is helpful to use technolog. a) Mark Frequenc = = median = b) Mark Frequenc = = median = c) Mark Frequenc = = median = WS.

12 Attendance MAP C Lesson. Line of Best Fit and the Correlation Coefficient E. The data shown in the graph below represents the attendance at the Arnprior Packers first games of the season Line of Best Fit Draw the line. Choose two points on the line. Use these points to calculate the slope (m) of the line. Estimate or find the -intercept (b) Write the equation of the line in the form = m + b. Use the equation to make predictions. 9 0 Game a) Draw the line of best fit and determine its equation. b) Use the equation to predict the attendance in game 0. c) Use the equation to predict when the attendance will be 0 people.

13 MAP C Correlation The correlation between two variables can be classified as STRONG, WEAK, or NONE and as either POSITIVE or NEGATIVE. a b c d a 0 Scatter Plot STRONG, WEAK, NONE POSITIVE OR NEGATIVE r = b 0 Scatter Plot 9 0 STRONG, WEAK, NONE POSITIVE OR NEGATIVE r = c 9 Scatter Plot 9 STRONG, WEAK, NONE POSITIVE OR NEGATIVE r = d 9 Scatter Plot STRONG, WEAK, NONE POSITIVE OR NEGATIVE r = The correlation coefficient, r, is a number used to describe the amount of correlation between two variables. The value of the correlation coefficient must be between - (STRONG NEGATIVE) and + (STRONG POSITIVE). The value for r can be found on the TI- b going STAT, CALC,. LINREG.

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15 E. For data sets A, B, and C, draw a scatter plot, describe the correlation, estimate the correlation coefficient and then find the line of best fit correct to decimal places. Set A 0 0 Set B Set C 0 9 A B C predicted r: predicted r: predicted r: actual r: actual r: actual r: predicted LBF: predicted LBF: predicted LBF:

16 The table below shows games plaed for Daniel Alfredsson and Jason Spezza. L L L Year Alfie Spezza a) State the LoBF for Alfie. b) State r, the correlation coefficient for Alfie s games plaed. c) State the LoBF for Spezza. d) State r, the correlation coefficient for Spezza s games plaed. WS.

17 MAP C Lesson. Outliers An outlier is an observation that lies outside the overall pattern of a distribution. Usuall, the presence of an outlier indicates some sort of problem. This can be a case which does not fit the model under stud, or an error in measurement. E. Given the following data for a compan s monthl revenues, Compan Revenues 9 Month Revenue a) Make a scatter plot. b) Determine the equation for the line of best fit and graph the line. c) Calculate the correlation coefficient (r) LoBF: 9 0 r = d) Predict the revenues for month 0. e) Wh might ou not be ver confident in this prediction? Outlier = 0000 f) Now consider the data with the outlier removed LoBF: r = 9 0 g) Now predict the compan s revenues for ear 0.

18 Outliers can also occur when comparing relationships between two sets of data. Outliers of this tpe can easil be identified on a scatter plot. Tpicall, we believe that outliers represent a random error that we would like to be able to control. Unfortunatel, there is no widel accepted method to remove outliers automaticall, thus what we are left with is to identif an outliers b eamining a scatterplot of each important correlation. Needless to sa, outliers ma not onl artificiall increase the value of a correlation coefficient, but the can also decrease the value of a "legitimate" correlation. Outlier A value that "lies outside" (is much smaller or larger than) most of the other values in a set of data. For eample in the scores,,,,9,,,, both and are "outliers". WS.

19 Calculating Mean, Median and Standard Deviation for a Sample with TI- Step : Press [STAT] [ ] for STAT Edit Enter the data into one of the lists Step : Press [STAT] Press right arrow ke [ ] to highlight CALC Press [ENTER] or [] for -Var Stats Enter the name of the list containing our data Press [ nd ] [] for L, [ nd ] [] for L... Press [ENTER] On TI- screen choose: = (Sample mean or average) Med =... (Sample median) = (Sample standard deviation)