Mean, Median, and Mode Plus Range The 3 Central Tendencies: The 3 Central Tendencies: Mean, Median and Mode

LEARNING GOALS: To use the Arithemetic Mean, Median and Mode in a set of values. To collaborate and use mathematical language during collaborative group work and oral presentations. To use real-life problem-solving for the 3 central tendencies (i.e. arithmetic mean, median and mode).

The Arithmetic Mean The sum of a list of numbers, divided by the total number of numbers in that list M= S/N

Example Find the mean of 10, 12, 14, 17, 20. Sum = Sum = 73 Mean = 73 ÷ 5 Mean = 14.6

Find The Arithmetic Mean SHOW YOUR WORK – Round to 1 decimal place! 1.{8, 9, 12, 16, 18} 2.{1, 2, 4, 4, 5, 7, 11} 3.{25, 26, 27, 36, 42, 52}

Find The Arithmetic Mean 1.{8, 9, 12, 16, 18} Sum = = 63 Mean = 63÷5 = {1, 2, 4, 4, 5, 7, 11} Sum= Mean = 34÷5 = {25, 26, 27, 36, 42, 52} Mean= 209÷6 = 34.8

The Median The middle value in an ordered list of numbers

Example 1 Find the median of 10, 13, 8, 7, 12. Order: 7, 8, 10, 12, 13 Median = 10

How To Find The Median REAL LIFE PROBLEM-SOLVING: Find the median number of part-time hours worked during a seven day week. 1.Place the numbers in order, from least to greatest. 0, 1, 2, 3, 4, 4,4 2.Find the number that is in the middle of the data set 0, 1, 2, 3, 4, 4, 4 3 is the median of this data set.

Example 2 Find the median of 44, 46, 39, 50, 39, 40. Order: 39, 39, 40, 44, 46, 50 Median = ( ) ÷ 2 = 42

Oh Oh!!! {10, 12, 16, 18, 20, 24} What do you do if there are an even amount of numbers in your data set? You take the mean of the two middle values = 34÷2 = 17 The median of this data set is 17.

Find The Median 1.{8, 9, 12, 16, 18} 8, 9, 12, 16, 18 2.{4, 2, 6, 4, 1, 7, 11} 1, 2, 4, 4, 6, 7, {25, 26, 27, 36, 42, 52} 25, 26, 27, 36, 42, 52  (27+36)÷2 = {120, 134, 165, 210, 315, 356} 120, 134, 165, 210, 315, 356  ( )÷2 = 187.5

The Mode The most common value or the value with the highest frequency in a data set.

Example Find the mode of 14, 15, 20, 20, 14, 20, 5. Mode = 20 (it occurs the most) Find the mode of 14, 15, 20, 20, 14, 5. Mode = 14 and 20 (both occur twice) Find the mode of 14, 15, 20, 21, 12, 10, 5. Mode = No mode (no number occurs more than once)

Find The Mode 1.{8, 9, 12, 16, 18} 2.{1, 2, 4, 4, 5, 7, 11} 2.{25, 26, 27, 36, 42, 52, 26, 27} 3.{120, 134, 165, 210, 315, 356, 120, 120, 210}

Find The Mode 1.{8, 9, 12, 16, 18} There is no mode in this data set. 2.{1, 2, 4, 4, 5, 7, 11} The mode is {25, 26, 27, 36, 42, 52, 26, 27} The mode is 26 AND {120, 134, 165, 210, 315, 356, 120, 120, 210} The mode is 120 – it occurs more than 210!

Finding The Range -Range: The distance between the maximum and the minimum number Range = Max – Min Example: 4, 6, 30, 24 Range = 30 – 4 Range = 26

Find The Range 1.{8, 9, 12, 16, 18} 2.{3, 5, 2, 4, 5, 7, 2} 3.{120, 134, 165, 210, 315, 356}

Find The Range 1.{8, 9, 12, 16, 18} 18 – 8 = 10 The range is 10 2.{3, 5, 2, 4, 5, 7, 2} 7 – 2 = 5 The range is 5. Finding the range is easier if you put the numbers in order from least to greatest first 3.{120, 134, 165, 210, 315, 356} 356 – 120 = 234 The range is 234

Reflections Sucess Criteria: BUCK Self-checking Strategies SQ-RCRC

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