Mode and Median as Measures of Center
Clarifying the Learning
You will learn that the median is a measure of center that is equal to the middle data value in a set with an odd number of data values arranged from lowest to highest (or highest to lowest) or the number halfway between two middle data values in a set with an even number of data values arranged from lowest to highest (or highest to lowest).
You will also learn that the mode is a measure of center that is equal to the data value that occurs the most in a data set. You will also learn a data set can have more than one mode and that a data set in which every data value occurs exactly once has no mode.
How can we use the median to describe a typical data value within a data set?
Content Standards and Objectives:
After completing this lesson, you should be able to understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.(M.6.SP.2)(CCSS.MATH.CONTENT.6.SP.A.2)
you should recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.(M.6.SP.3)(CCSS.MATH.CONTENT.6.SP.A.3)
You should also be able to summarize numerical data sets in relation to their context, such as by:(M.6.SP.5)(CCSS.MATH.CONTENT.6.SP.B.5)
- reporting the number of observations.(CCSS.MATH.CONTENT.6.SP.B.5A)
- describing the nature of the attribute under investigation, including how it was measured and its units of measurement.(CCSS.MATH.CONTENT.6.SP.B.5B)
- giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. (CCSS.MATH.CONTENT.6.SP.B.5C)
- relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. (CCSS.MATH.CONTENT.6.SP.B.5D)
Standards for Mathematical Practices:
- Make sense of problems and persevere in solving them
- You will determine medians of sets of data displayed in various forms.
- Reason abstractly and quantitatively
- You reason quantitatively when determining the medians of a sets of data displayed in various forms.
- Construct viable arguments and critique the reasoning of others
- You will explain how to determine the median or mode of a set of data displayed in various forms.
- Attend to precision
- You will determine how many modes a data set has and find the mode(s) accordingly. You will also determine exact values of medians of sets of data.
Upon mastering this objective, you should be able to conduct the tasks in the video below: