• MA.5.DP.1 Data Analysis and probability

    Collect, represent and interpret data and find the mean, mode, median or range of a data set. 



    Interpret numerical data, with whole-number values, represented with tables or line plots by determining the mean, mode, median or range. Example: Rain was collected and measured daily to the nearest inch for the past week. The recorded amounts are 1, 0, 3, 1, 0, 0 and 1. The range is 3 inches, the modes are 0 and 1 inches, and the mean value can be determined as (1+0+3+1+0+0+1)/7 , which is equivalent to 6/7 of an inch. This mean would be the same if it rained 6/7 of an inch each day.

    Benchmark Clarifications:
    Clarification 1: Instruction includes interpreting the mean in real-world problems as a leveling out, a balance point or an equal share.

    Purpose and Instructional Strategies
    The purpose of this benchmark is to interpret numerical data by using the mean, mode, median and range. This work builds on the previous understanding of mode, median, and range in Grade 4 (MA.4.DP.1.2). In Grade 6, a focus will be on comparing the advantages and disadvantages of the mean and median.

     When finding median and mode, it is important for students to organize their data, putting it in order from least to greatest.

     With the data organized, students can determine:
    o range by subtracting the least value from the greatest value in the set.
    o mode by finding the value that occurs most often.
    o median by finding the value in middle of the set.
    o mean by finding the average of the set of numbers.

    Common Misconceptions or Errors
     Students may confuse the mean and median of a data set. During instruction, teachers should provide students with examples where the median and mean of a data set are not close in value.

    Instructional Tasks
    Instructional Task 1
    Bobbie is a fifth grader who competes in the 100-meter hurdles. In her 8 track meets during the season, she recorded the following times to the nearest second.


    Part A. What is the mean time, in seconds, of Bobbie’s 100-meter hurdles?
    Part B. What is the median time, in seconds, of Bobbie’s 100-meter hurdles?
    Part C. What is the mode time, in seconds, of Bobbie’s 100-meter hurdles?
    Part D. If you were Bobbie, which of these results would you report to your friend?

    Instructional Items
    Instructional Item 1
    There was a pie-eating contest at the county fair. The line plot below shows the number of pies each of the 10 contestants ate. Use the line plot to determine the mean, mode, median and range of the data. 


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