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Statistics       Data6543210
What is an average? An average is a measure of the "middle" value of a                   set of data.Mode, Mean, and Media...
WALT……understand  what the Mode isand how to identify it in data.
Definition of Mode• The “mode” for a set of data is the number (or item)               that occurs most frequently.• Somet...
How to find the Mode.   Mode is the most common number   Put the numbers in order   Choose the number that appears the ...
Find the mode in this data setClass high jump heights (in metres)1.05, 1.10, 1.05, .95, .85,1.05, 1.10,                1.2...
Mode of non-numerical dataRed, green, blue, red, blue, yellow, red, pink, green, white.Red, red, red, blue, blue, green, g...
What is the mode in this data?                            Icecream10 9 8 7 6 5 4                                          ...
Bar graph dataMode = Neopolitan
Bimodal and trimodal                 BimodalData Set = 2, 5, 2, 3, 5, 4, 72, 2, 3, 4, 5, 5, 7Modes = 2 and 5              ...
ExampleData Set= 3, 5, 6, 4, 7, 8, 9, 2, 1, 0What is the mode?0,1,2,3,4,5,6,7,8,9Is the mode = 0?Mode = no mode
When might the Mode be used?    The mode can be useful for dealing with    categorical data. For example, if a sandwich s...
Averages   What other ways can we calculate    the average of a set of data?   We can use the Mean to give us an    aver...
WALT…understand what the Mean is and how        to identify it in data.
Definition of the Mean   The „Mean‟ is the „Average‟ value of numerical    data.   The Mean (or average) is found by add...
Example   Class shoe sizes: 3, 5, 5, 6, 4, 3, 2, 1, 5, 6   Add up the numbers:   3 + 5 + 5 + 6 + 4 + 3 + 2 + 1 + 5 + 6 ...
Find the Mean        Class high jump heights (in metres)1.05, 1.10, 1.05, .95, .85,1.05, 1.10, 1.20, .95, 1.2             ...
Population of NZ Cities1600000140000012000001000000 800000 600000 400000                                       Population ...
Work it out   Mode = most common – 390,000 is the mode of    the population of the NZ Cities on the graph.   Mean = the ...
When to use the mean…   The mean can give a good average value when    the data is fairly evenly distributed as in the hi...
However   It is not always suitable to use the    mean to get an average of data    when there is a huge variation in    ...
Example          Population of NZ Cities1600000140000012000001000000 800000 600000 400000                             Popu...
What is an average?                    , . An average is a measure of the "middle" value of a                   set of dat...
RecapDefinition of Mode –The “Mode” for a set of data is thenumber (or item) that occurs mostfrequently.Definition of Mean...
Example.  Class high jump heights (in metres)1.05, 1.10, 1.05, .95, .85,1.05, 1.05,1. 20, .95, .50, .80, .65, 1.05, 1.10,....
AnswersMode = 1.05 and 1.10Mean = 1.00
WALT…..understand what the Median is and     how to identify it in data.
Definition of Median   The Median is the middle value when    numbers are put in order.   To find the Median, place the ...
Find the median…Room 19 test scores56%, 48%, 76%, 78%, 85%, 77%, 91%, 77%, 73%, 88%, 69%, 67%, 58%, 64%, 88%, 89%, 87%,83%...
Find the mode           How many children in your family?121086                                               Quantity420 ...
Find the Mean                          ..             How many children in your family?1210    8    6                     ...
To find the mean…(10 x 2) + (10 x 3) + (5 x 4) + (3 x 5)+ (1 x 6) = 9191 ÷ 29 = 3.13 rounded to 3Mean = 3
Find the. median       .         How many children in your family?1210    8    6                                         ...
To find the median… Put the numbers in order…2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3,3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5,...
Range   Range is the gap from the biggest to    smallest value.   Put the numbers in order   Take the smallest number a...
When should you use the      Mean, Mode, or Median?   Use the mean for data which is fairly    evenly distributed.   Use...
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  1. 1. Statistics Data6543210
  2. 2. What is an average? An average is a measure of the "middle" value of a set of data.Mode, Mean, and Median, are all types of averages.They can be used to help summarise a group of data.
  3. 3. WALT……understand what the Mode isand how to identify it in data.
  4. 4. Definition of Mode• The “mode” for a set of data is the number (or item) that occurs most frequently.• Sometimes data can have more than one mode. This happens when two or more numbers (or items)occur an equal number of times in the data. • A data set with two modes is called bimodal. • A data set with 3 modes is called Trimodal• It is also possible to have a set of data with no mode.
  5. 5. How to find the Mode. Mode is the most common number Put the numbers in order Choose the number that appears the most frequently.Class shoe sizes: 3, 5, 5, 6, 4, 3, 2, 1, 5, 6Put in order: 1, 2, 3, 3, 4, 5, 5, 5, 6, 6The class modal shoe size is 5.
  6. 6. Find the mode in this data setClass high jump heights (in metres)1.05, 1.10, 1.05, .95, .85,1.05, 1.10, 1.20, .95, 1.25, 1.30, .75, .80, .90,.75, .80, .85, .90, .95,.95, 1.05,1.05, 1.05, 1.10, 1.10, 1.20, 1.25, 1.30 The mode is 1.05m
  7. 7. Mode of non-numerical dataRed, green, blue, red, blue, yellow, red, pink, green, white.Red, red, red, blue, blue, green, green, yellow, pink, white.Mode = red
  8. 8. What is the mode in this data? Icecream10 9 8 7 6 5 4 Icecream 3 2 1 0 strawberry vanilla chocolate neopolitan
  9. 9. Bar graph dataMode = Neopolitan
  10. 10. Bimodal and trimodal BimodalData Set = 2, 5, 2, 3, 5, 4, 72, 2, 3, 4, 5, 5, 7Modes = 2 and 5 TrimodalData Set = 2, 5, 2, 7, 5, 4, 72, 2, 4, 5, 5, 7, 7Modes = 2, 5, and 7
  11. 11. ExampleData Set= 3, 5, 6, 4, 7, 8, 9, 2, 1, 0What is the mode?0,1,2,3,4,5,6,7,8,9Is the mode = 0?Mode = no mode
  12. 12. When might the Mode be used? The mode can be useful for dealing with categorical data. For example, if a sandwich shop sells 10 different types of sandwiches, the mode would represent the most popular sandwich. The mode can be useful for summarising survey data. The mode can be useful for election votes.
  13. 13. Averages What other ways can we calculate the average of a set of data? We can use the Mean to give us an average of numerical data.
  14. 14. WALT…understand what the Mean is and how to identify it in data.
  15. 15. Definition of the Mean The „Mean‟ is the „Average‟ value of numerical data. The Mean (or average) is found by adding all scores together and dividing by the number of scores.
  16. 16. Example Class shoe sizes: 3, 5, 5, 6, 4, 3, 2, 1, 5, 6 Add up the numbers: 3 + 5 + 5 + 6 + 4 + 3 + 2 + 1 + 5 + 6 = 40 Divide by how many numbers: 40 ÷ 10 = 4 The class mean shoe size is 4
  17. 17. Find the Mean Class high jump heights (in metres)1.05, 1.10, 1.05, .95, .85,1.05, 1.10, 1.20, .95, 1.2 5, 1.30, .75, .80, .90, 1.05 + 1.10 + 1.05 +.95 + .85 +1.05 + 1.10 + 1.20 + .95 + 1.25 + 1.30 + .75 + .80 + .90 = 14.3mMean = 14.3 divided by the number of people that jumped (14) 14.3 ÷ 14 = 1.02m
  18. 18. Population of NZ Cities1600000140000012000001000000 800000 600000 400000 Population 200000 0 What is the mode? What is the mean?
  19. 19. Work it out Mode = most common – 390,000 is the mode of the population of the NZ Cities on the graph. Mean = the average population of the NZ cities on the graph –200,000 + 60,000 + 390,000 + 390,000 + 125,000+ 1355,000 = 2520,000Mean = 2520,000 ÷ 6 = 420,000
  20. 20. When to use the mean… The mean can give a good average value when the data is fairly evenly distributed as in the high jump heights. Class high jump heights (in metres) 1.05 + 1.10 + 1.05 +.95 + .85 +1.05 + 1.10 + 1.20 + .95 + 1.25 + 1.30 + .75 + .80 + .90 = 14.3mMean = 14.3 divided by the number of people that jumped (14) 14.3 ÷ 14 = 1.02m
  21. 21. However It is not always suitable to use the mean to get an average of data when there is a huge variation in data.
  22. 22. Example Population of NZ Cities1600000140000012000001000000 800000 600000 400000 Population 200000 0
  23. 23. What is an average? , . An average is a measure of the "middle" value of a set of data.Mode, Mean, and Median, are all types of averages.They can be used to help summarise a group of data.
  24. 24. RecapDefinition of Mode –The “Mode” for a set of data is thenumber (or item) that occurs mostfrequently.Definition of Mean –The “Mean” is the „Average‟ value ofnumerical data.
  25. 25. Example. Class high jump heights (in metres)1.05, 1.10, 1.05, .95, .85,1.05, 1.05,1. 20, .95, .50, .80, .65, 1.05, 1.10,.95.95, 1.25, 1.30, .75, .80, .90, 1.00, 1.1 0, 1.15, 1.25, 1.10, 1.10, 1.15 What is the mode? What is the mean?
  26. 26. AnswersMode = 1.05 and 1.10Mean = 1.00
  27. 27. WALT…..understand what the Median is and how to identify it in data.
  28. 28. Definition of Median The Median is the middle value when numbers are put in order. To find the Median, place the numbers in numerical order and find the middle number. If the total number of values in the sample is even, the median is calculated by finding the mean of the two values in the middle.
  29. 29. Find the median…Room 19 test scores56%, 48%, 76%, 78%, 85%, 77%, 91%, 77%, 73%, 88%, 69%, 67%, 58%, 64%, 88%, 89%, 87%,83%, 73%, 74%, 92%, 69%, 80%, 80%, 75%, 72%.In order –48%, 56%, 58%, 64%, 67%, 69%, 69%, 72%, 73%, 73%, 74%, 75%, 76%, 77%, 77%, 78%, 80%,80%, 83%, 85%, 87%, 88%, 88%, 89%, 91%, 92%,
  30. 30. Find the mode How many children in your family?121086 Quantity420 Two Three Four Five Six
  31. 31. Find the Mean .. How many children in your family?1210 8 6 Quantity 4 2 0 Two Three Four Five Six
  32. 32. To find the mean…(10 x 2) + (10 x 3) + (5 x 4) + (3 x 5)+ (1 x 6) = 9191 ÷ 29 = 3.13 rounded to 3Mean = 3
  33. 33. Find the. median . How many children in your family?1210 8 6 Quantity 4 2 0 Two Three Four Five Six
  34. 34. To find the median… Put the numbers in order…2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3,3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6.The Median = 3
  35. 35. Range Range is the gap from the biggest to smallest value. Put the numbers in order Take the smallest number away from the largest.Class shoe sizes: 3, 5, 5, 6, 4, 3, 2, 1, 5, 6Put in order: 1, 2, 3, 3, 4, 5, 5, 5, 6, 6Subtract smallest from largest: 6 – 1 = 5Range: 5
  36. 36. When should you use the Mean, Mode, or Median? Use the mean for data which is fairly evenly distributed. Use the median for data which has extreme differences in scores. Use the mode in categorical data where the original scores are known.
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