Unit 4 Midterm    Review
What is central tendency?
What is central tendency?• It refers to the middle or center of the data.
What is the mean of a data set?
What is mean?• It is called the average.• You add up all the numbers to find a sum.• You divide the sum by the total numbe...
What is the median? How do you             find it?
What is the median? How do you find                it?• It is the middle of the data.• You put the numbers in order and el...
How do you find the median of a data set if  there are more than one number in the          middle of the data set?       ...
How do you find the median of a dataset if there are more than one number      in the middle of the data set?             ...
1. Define mode.2. What would it be for thefollowing data set?• 1,2,2,2,3,5,6,7
Define mode. What would it be for      the following data set?•   The number that occurs most often in a data set.•   1,2,...
Which measure of center is       affected by outliers?• Hint: If you made a really low grade, what is  going to affected t...
Which measure of central tendency is       affected by outliers?Hint: If you made a really low grade, what is  going to af...
1. Which set of data would have a highermean (average)?2. Which set of data would have a highermedian?3. Which data set ha...
• 1. Which set of data would have a higher  mean (average)? - Data set 2  2. Which set of data would have a higher  median...
What affect will an extremely small    outlier have on a set of data?Hint: For example, if you have a really low test grad...
What affect will an extremely small    outlier have on a set of data?Hint: For example, if you have a really low test grad...
How will really large outliers affect the mean and median of a set of data?
How will really large outliers affect the mean and median of a set of data?• The large outlier will cause the mean  (avera...
Before• We measured the  heights of the  cans and created  data sets.• What happens to  the measures of  center after we  ...
Before• We measured the  heights of the  cans and created  data sets.• What happens to  the measures of  center after we  ...
Can you name a real example of how  mode is used in the real world?
Can you name a real example of how   mode is used in the real world?• Voting - the candidate with the most  votes, wins.
Find the Mean Absolute Deviation(MAD) for both people. Find who is       more consistent hitter.Batting Averages:Stefan: ....
Stefan                                          Damon        Mean      Diff           Pos Diff               Mean      Dif...
Complete the Frequency column in this cumulative                frequency tableThe list shows the average high temperature...
Complete the Cumulative Frequency              columnThe list shows the average high temperatures for 20 citieson one Febr...
A stem-and-leaf plot can be used to show how often datavalues occur and how they are distributed.Each leaf on the plot rep...
Create a stem and leaf plot The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching ...
Creating Stem and Leaf PlotThe data shows the number of years coached by the top 15 coaches in the all-time NFL coaching v...
Would it be appropriate to make astem and leaf plot for the number of  text message you send Monday          through Friday?
Would it be appropriate to make a  stem and leaf plot for the number of    text message you send Monday            through...
Create a line plot for the data:   Number of Babysitting Hours in July       M    T     W    Th     F     S    SuWk 1   0 ...
Your line plot should look like this:Step 2: Put an X above the number on the numberline that corresponds to the number of...
Find the median of the line plot     that you just created.
What is noticeable about this line plot?
What is noticeable about this line plot?
This line plot has an outlier. Which measure of  central tendency best describes the data?
This line plot has an outlier. Which measure of  central tendency best describes the data?  The median because there is an...
Which measure of central tendency should be      used to describe this data set?
Which measure of central tendency should be      used to describe this data set?   The mean because it data set does      ...
Which measure of central tendency should be      used to describe this data set?
Which measure of central tendency should be      used to describe this data set?     The median should be used because    ...
Find the mean of the data setA quick way is to find the sum for each row. Add up the sum for   each row, and then divide t...
Find the mean of the data setYou can find the sum ofeach line of  numbersFor example:  2 Occurs 5                         ...
Use the information given tocomplete the cumulative frequency              table             Nurses’ Ages     Ages    Freq...
What is a population?
Population = the entire group• Researchers often study  a part of the population,  called a sample.
What is a sample?
Sample is a small group of the total population
What is a random sample?
•For a random sample, members of the population are chosen at random. This gives every member of the population an equal c...
What is a convenience sample?
CONVENIENCE SAMPLE• A convenience sample is based  on members of the population  that are conveniently available,  such as...
•A biased sample does not fairly represent the population.• A study of 50 elk belonging to a breeder  could be biased beca...
Which would be better to have, arandom sample or a convenience           sample?
Which would be better to have, arandom sample or a convenience           sample?A random sample is more likely    to be re...
Min - 22LQ - 24Med - 31UQ - 38Max - 42
Box-and-Whisker Plots      Data from the previous question                    (min, LQ, med, UQ, max)           42 22 31 2...
Create a box and whiskers fromthe 5 number summary you just            found.
7-5 Box-and-Whisker Plots           Above the number line, plot a point for each           value in Step 1.  Step 3: Draw ...
7-5 Box-and-Whisker Plots     Additional Example 2A: Comparing Box-and-                    Whisker Plot  Use the box-and-w...
7-5 Box-and-Whisker Plots     Additional Example 2A: Comparing Box-and-                    Whisker Plot  Use the box-and-w...
7-5 Box-and-Whisker Plots                      Check It Out: Example 2A  Use the box-and-whisker plots below to answer eac...
7-5 Box-and-Whisker Plots                      Check It Out: Example 2A  Use the box-and-whisker plots below to answer eac...
Find the Range of the Box and       Whiskers Plot
Find the Range of the Box and       Whiskers Plot Max – min = range 100 – 20 = 80
Find the Inter quartile Range of         the B&W Plot
Find the Inter quartile Range of         the B&W Plot UQ – LQ = IQR 87 – 50 = 37
What is the range of the box known                as?
What is the range of the box known                as?• Interquartile range
7-5 Box-and-Whisker Plots                      Check It Out: Example 2B  Use the box-and-whisker plots below to answer eac...
7-5 Box-and-Whisker Plots                      Check It Out: Example 2B  Use the box-and-whisker plots below to answer eac...
I would like to create a graph to show  the number of cancer cases worldwide from 1950 to 2011. What kind of        graph ...
I would like to create a graph to show  the number of cancer cases worldwide from 1950 to 2011. What kind of        graph ...
What kind of graphs should I use ifpercents or populations are involved?
What kind of graphs should I use ifpercents or populations are involved?• Circle graph
If I want to create a display to show thenumber of cell phone messages sent fromMonday – Friday, what kind of graph would ...
If I want to create a display to show thenumber of cell phone messages sent fromMonday – Friday, what kind of graph would ...
If I wanted to create a display to show testscores in math, SS, science, and LA, what kind           of graph would be best?
If I wanted to create a display to show test scores in math, SS, science, and LA, what kind            of graph would be b...
I want to create a display to show theclasses grade on the final exam. What  kind of graphs would be the best?
I want to create a display to show theclasses grade on the final exam. What  kind of graphs would be the best?• Stem and L...
2012 2013 3rd 9 weeks midterm review
2012 2013 3rd 9 weeks midterm review
2012 2013 3rd 9 weeks midterm review
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2012 2013 3rd 9 weeks midterm review

  1. 1. Unit 4 Midterm Review
  2. 2. What is central tendency?
  3. 3. What is central tendency?• It refers to the middle or center of the data.
  4. 4. What is the mean of a data set?
  5. 5. What is mean?• It is called the average.• You add up all the numbers to find a sum.• You divide the sum by the total numbers in the data set.
  6. 6. What is the median? How do you find it?
  7. 7. What is the median? How do you find it?• It is the middle of the data.• You put the numbers in order and eliminate one on each side of the data until you find the middle.
  8. 8. How do you find the median of a data set if there are more than one number in the middle of the data set? 2 5 6 12 15 18
  9. 9. How do you find the median of a dataset if there are more than one number in the middle of the data set? 2 5 6 12 15 18 Find the mean of those two numbers by adding them up and dividing by two. 6 + 12 = 18 18/2 = 9 The median would be 9
  10. 10. 1. Define mode.2. What would it be for thefollowing data set?• 1,2,2,2,3,5,6,7
  11. 11. Define mode. What would it be for the following data set?• The number that occurs most often in a data set.• 1,2,2,2,3,5,6,7• The mode would be 2, because it occurs the most often.• Some data sets don’t have a more, while some may have more than one.
  12. 12. Which measure of center is affected by outliers?• Hint: If you made a really low grade, what is going to affected the most? (Mean or Median)
  13. 13. Which measure of central tendency is affected by outliers?Hint: If you made a really low grade, what is going to affected the most? (Mean or Median)The mean is affected by outliers. The mean of the test scores will go down.The median is not affected by outliers?
  14. 14. 1. Which set of data would have a highermean (average)?2. Which set of data would have a highermedian?3. Which data set had an outlier?Data set 1: 5 5 15 20 25Data set 2: 5 5 15 20 60
  15. 15. • 1. Which set of data would have a higher mean (average)? - Data set 2 2. Which set of data would have a higher median? – They both have the same median 3. Which data set had an outlier? – Data set 2
  16. 16. What affect will an extremely small outlier have on a set of data?Hint: For example, if you have a really low test grade, how will this affect the mean and median for the set of data?
  17. 17. What affect will an extremely small outlier have on a set of data?Hint: For example, if you have a really low test grade, how will this affect the mean and median for the set of data? The small outlier will bring down the mean (average). The median will not really be affected.
  18. 18. How will really large outliers affect the mean and median of a set of data?
  19. 19. How will really large outliers affect the mean and median of a set of data?• The large outlier will cause the mean (average) to increase.• It will not really affect the median.
  20. 20. Before• We measured the heights of the cans and created data sets.• What happens to the measures of center after we After replace the tallest can with the Pringles can?
  21. 21. Before• We measured the heights of the cans and created data sets.• What happens to the measures of center after we After replace the tallest can with the Pringles can?• The mean increased.• The median stayed the same.
  22. 22. Can you name a real example of how mode is used in the real world?
  23. 23. Can you name a real example of how mode is used in the real world?• Voting - the candidate with the most votes, wins.
  24. 24. Find the Mean Absolute Deviation(MAD) for both people. Find who is more consistent hitter.Batting Averages:Stefan: .248, .296, .325, .337, .364Damon: .287. .322, .290, .314, .302Be sure to make a table for each baseball player.
  25. 25. Stefan Damon Mean Diff Pos Diff Mean Diff Pos Diff0.248 0.314 0.066 0.0666 0.287 0.303 -0.016 0.0160.296 0.314 0.018 0.018 0.322 0.303 0.019 0.0190.325 0.314 -0.011 0.011 0.29 0.303 -0.013 0.0130.337 0.314 -0.023 0.023 0.314 0.303 0.011 0.0110.364 0.314 -0.05 0.05 0.302 0.303 -0.001 0.001 Sum 0.1686 Sum 0.060.314 Count 5 0.303 Count 5 MAD 0.034 MAD 0.012
  26. 26. Complete the Frequency column in this cumulative frequency tableThe list shows the average high temperatures for 20 citieson one February day.69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8,8, 4, 2, 2 February Temperatures in 20 CitiesHint: Count the Average Frequency Cumulative Highs Frequencynumbers that fallinto each interval 0–19category, and 20–39place that total 40–59under frequency. 60–79
  27. 27. Complete the Cumulative Frequency columnThe list shows the average high temperatures for 20 citieson one February day. Make a cumulative frequency table ofthe data. February Temperatures in 20 Cities Average Frequency CumulativeStep 3: Find the Highs Frequencycumulative frequency 0–19 7 7for each row by addingall the frequency values 20–39 5 12that are above or in 40–59 5 17that row. 60–79 3 20
  28. 28. A stem-and-leaf plot can be used to show how often datavalues occur and how they are distributed.Each leaf on the plot represents the right-hand digit in adata value.Stems represents left-hand digits. Stems Leaves 2 4 7 9 3 0 6 Key: 2|7 means 27
  29. 29. Create a stem and leaf plot The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. 33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17 Step 2: List the stems from least to greatest on the plot.The stemsare the tens Stems Leavesdigits. 1 2 3 4
  30. 30. Creating Stem and Leaf PlotThe data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. Then findthe number of coaches who coached fewer than 25 years.33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17 Step 3: List the leaves for each stem from least to greatest.The stems The leavesare the tens are the Stems Leavesdigits. ones digits. 1 2 5 5 7 7 8 2 0 1 23 3 9 3 3 3 4 0
  31. 31. Would it be appropriate to make astem and leaf plot for the number of text message you send Monday through Friday?
  32. 32. Would it be appropriate to make a stem and leaf plot for the number of text message you send Monday through Friday?• No because you would be examining two variables ( number of messages, and days of the week).• Stem and leaf plots are only appropriate when you are examining one variable, such as the number of text message, or test grades in math.
  33. 33. Create a line plot for the data: Number of Babysitting Hours in July M T W Th F S SuWk 1 0 6 4 6 5 8 2Wk 2 2 7 7 7 0 6 8Wk 3 0 6 8 5 6 1 2Wk 4 4 8 4 3 3 6 0
  34. 34. Your line plot should look like this:Step 2: Put an X above the number on the numberline that corresponds to the number of babysittinghours in July. X XX X XX X X X X XX X X X X X X XX X X X X X X X X0 1 2 3 4 5 6 7 8 The greatest number of X’s appear above the number 6. This means that Morgan babysat most often for 6 hours.
  35. 35. Find the median of the line plot that you just created.
  36. 36. What is noticeable about this line plot?
  37. 37. What is noticeable about this line plot?
  38. 38. This line plot has an outlier. Which measure of central tendency best describes the data?
  39. 39. This line plot has an outlier. Which measure of central tendency best describes the data? The median because there is an outlier in the data set.
  40. 40. Which measure of central tendency should be used to describe this data set?
  41. 41. Which measure of central tendency should be used to describe this data set? The mean because it data set does not have an outlier.
  42. 42. Which measure of central tendency should be used to describe this data set?
  43. 43. Which measure of central tendency should be used to describe this data set? The median should be used because the data set has an outlier.
  44. 44. Find the mean of the data setA quick way is to find the sum for each row. Add up the sum for each row, and then divide this sum by pieces of data that are in the data set.
  45. 45. Find the mean of the data setYou can find the sum ofeach line of numbersFor example: 2 Occurs 5 = 84times, so 2X5 3 + 10 + 18+16+15+12 + 10 = 10 ---------- = 3.5 24 (24 total pieces of data – count the number of Xs)
  46. 46. Use the information given tocomplete the cumulative frequency table Nurses’ Ages Ages Frequency Cumulative Frequency 20–29 5 5 30–39 7 12 40–49 4 16 50–59 2 18 60–69 2 20
  47. 47. What is a population?
  48. 48. Population = the entire group• Researchers often study a part of the population, called a sample.
  49. 49. What is a sample?
  50. 50. Sample is a small group of the total population
  51. 51. What is a random sample?
  52. 52. •For a random sample, members of the population are chosen at random. This gives every member of the population an equal chance of being chosen.
  53. 53. What is a convenience sample?
  54. 54. CONVENIENCE SAMPLE• A convenience sample is based on members of the population that are conveniently available, such as 30 elk in a wildlife preservation area.
  55. 55. •A biased sample does not fairly represent the population.• A study of 50 elk belonging to a breeder could be biased because the breeder’s elk might be less likely to have Mad Elk Disease than elk in the wild.
  56. 56. Which would be better to have, arandom sample or a convenience sample?
  57. 57. Which would be better to have, arandom sample or a convenience sample?A random sample is more likely to be representative of a population than a convenience sample is.
  58. 58. Min - 22LQ - 24Med - 31UQ - 38Max - 42
  59. 59. Box-and-Whisker Plots Data from the previous question (min, LQ, med, UQ, max) 42 22 31 27 24 38 35 Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upper quartiles. The least value. 22 24 27 31 35 38 42 The greatest value. 22 24 27 31 35 38 42 The median. The upper and lower 22 24 27 31 35 38 42 quartiles.Course 2
  60. 60. Create a box and whiskers fromthe 5 number summary you just found.
  61. 61. 7-5 Box-and-Whisker Plots Above the number line, plot a point for each value in Step 1. Step 3: Draw a box from the lower to the upper quartile. Inside the box, draw a vertical line through the median. Then draw the “whiskers” from the box to the least and greatest values. 20 22 24 26 28 30 32 34 36 38 40 42Course 2
  62. 62. 7-5 Box-and-Whisker Plots Additional Example 2A: Comparing Box-and- Whisker Plot Use the box-and-whisker plots below to answer each question. Basketball Players Baseball Players 64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.) Which set of heights of players has a greater median?Course 2
  63. 63. 7-5 Box-and-Whisker Plots Additional Example 2A: Comparing Box-and- Whisker Plot Use the box-and-whisker plots below to answer each question. Basketball Players Baseball Players 64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.) Which set of heights of players has a greater median? The median height of basketball players, about 74 inches, is greater than the median height of baseball players, about 70 inches.Course 2
  64. 64. 7-5 Box-and-Whisker Plots Check It Out: Example 2A Use the box-and-whisker plots below to answer each question. Maroon’s Shoe Store Sage’s Shoe Store 20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store Which shoe store has a greater median?Course 2
  65. 65. 7-5 Box-and-Whisker Plots Check It Out: Example 2A Use the box-and-whisker plots below to answer each question. Maroon’s Shoe Store Sage’s Shoe Store 20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store Which shoe store has a greater median? The median number of shoes sold in one week at Sage’s Shoe Store, about 32, is greater than the median number of shoes sold in one week at Maroon’s Shoe Store, about 28.Course 2
  66. 66. Find the Range of the Box and Whiskers Plot
  67. 67. Find the Range of the Box and Whiskers Plot Max – min = range 100 – 20 = 80
  68. 68. Find the Inter quartile Range of the B&W Plot
  69. 69. Find the Inter quartile Range of the B&W Plot UQ – LQ = IQR 87 – 50 = 37
  70. 70. What is the range of the box known as?
  71. 71. What is the range of the box known as?• Interquartile range
  72. 72. 7-5 Box-and-Whisker Plots Check It Out: Example 2B Use the box-and-whisker plots below to answer each question. Maroon’s Shoe Store Sage’s Shoe Store 20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store Which shoe store has a greater interquartile range?Course 2
  73. 73. 7-5 Box-and-Whisker Plots Check It Out: Example 2B Use the box-and-whisker plots below to answer each question. Maroon’s Shoe Store Sage’s Shoe Store 20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store Which shoe store has a greater interquartile range? Maroon’s shoe store has a longer box, so it has a greater interquartile range.Course 2
  74. 74. I would like to create a graph to show the number of cancer cases worldwide from 1950 to 2011. What kind of graph would be best?
  75. 75. I would like to create a graph to show the number of cancer cases worldwide from 1950 to 2011. What kind of graph would be best?• Line graph because it shows change over time
  76. 76. What kind of graphs should I use ifpercents or populations are involved?
  77. 77. What kind of graphs should I use ifpercents or populations are involved?• Circle graph
  78. 78. If I want to create a display to show thenumber of cell phone messages sent fromMonday – Friday, what kind of graph would be best?
  79. 79. If I want to create a display to show thenumber of cell phone messages sent fromMonday – Friday, what kind of graph would be best?• Line Graph – it shows change over time
  80. 80. If I wanted to create a display to show testscores in math, SS, science, and LA, what kind of graph would be best?
  81. 81. If I wanted to create a display to show test scores in math, SS, science, and LA, what kind of graph would be best?• Bar Graph – each set of data (subject) is not related to the other
  82. 82. I want to create a display to show theclasses grade on the final exam. What kind of graphs would be the best?
  83. 83. I want to create a display to show theclasses grade on the final exam. What kind of graphs would be the best?• Stem and Leaf• Line Plot• or histogram

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