Measures of Central Tendencies Mean Median Mode Range Car $5 Doll $12 Game $7 Jump Ropes $3 Mean - The sum of a set of numbers divided by the number of elements in the set (also referred to as average) Median - The middle number (or the average of the two middle numbers, when necessary) in a set of numbers that are arranged from least to greatest Mode - The number that occurs most often in a set of data (there may be one, more that one, or no mode) Range - The difference between the maximum and minimum in a set of data Football $8 Presented by: CATHY JONES Secondary Math Instruction Specialist Center for Mathematics and Science Education Arkansas NASA Education Resource Center 346 N. West Avenue, Room 202 Fayetteville, Arkansas 72701 (479) 575-3875 (479) 575-5680 (FAX) e-mail: cej001@uark.edu Website: http://www.uark.edu/~k12info/ Wiki: www.cmasemath.pbwiki.com Top $1

MATHEMATICS FRAMEWORK ARKANSAS MATHEMATICS FRAMEWORK Standard 14: Data Representation Students shall formulate questions that can be addressed with data and collect, organize and display Standard 15: Data Analysis Students shall select and use appropriate statistical methods to analyze data. Look at the Leveling the Bars task. Make a connection to the math framework. Have them identify what SLE’s have been addressed. Hand out Framework match up and discuss SLEs that go along with this lesson. Standard 14: Data Representation Students shall formulate questions that can be addressed with data and collect, organize and display Grade 5 DAP.14.5.1: Develop appropriate questions for surveys DAP.14.5.2: Collect numerical and categorical data using surveys, observations and experiments that would result in bar graphs, line graphs, line plots and stem-and-leaf plots DAP.14.5.3: Construct and interpret frequency tables, charts, line plots, stem-and-leaf plots and bar graphs Grade 6 DAP.14.6.1: Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population DAP.14.6.2: Collect data and select appropriate graphical representations to display the data including Venn diagrams DAP.14.6.3: Construct and interpret graphs, using correct scale, including line graphs and double-bar graphs Standard 15: Data Analysis Students shall select and use appropriate statistical methods to analyze data. DAP.15.5.1: Interpret graphs such as line graphs, double bar graphs, and circle graphs DAP.15.5.2: Determine, with and without appropriate technology, the range, mean, median and mode (whole number data sets) and explain what each indicates about the set of data DAP.15.6.1: Interpret graphs such as double line graphs and circle graphs DAP.15.6.2: Compare and interpret information provided by measures of central tendencies (mean, median and mode) and measures of spread (range) Standard 16: Inferences and Predictions Students shall develop and evaluate inferences and predictions that are based on data. DAP.16.5.1: Make predictions and justify conclusions based on data DAP.16.6.1: Use observations about differences in data to make justifiable inferences Standard 16: Inferences and Predictions Students shall develop and evaluate inferences and predictions that are based on data.

Measures of Central Tendencies Mean Median Mode Range Define these mathematical terms. Mean - The sum of a set of numbers divided by the number of elements in the set (also referred to as average) Median - The middle number (or the average of the two middle numbers, when necessary) in a set of numbers that are arranged from least to greatest Mode - The number that occurs most often in a set of data (there may be one, more that one, or no mode) Range - The difference between the maximum and minimum in a set of data

Using linker cubes, make a bar graph to represent the price of the toys below. Car $5 Doll $12 Game $7 Football $8 Jump Ropes $3 Opening Activity: Have students represent the data from this activity in a meaningful way using the linker cubes. Have them represent each toy using a different color cubes. When you advance the slide, a graph of the data is shown. Do not advance until students work on their own! Top $1

Leveling the Bars Doll $12 Football $8 Game $7 Car $5 Jump Ropes $3 Top $1 Opening Activity: Have students represent the data from this activity in a meaningful way. When you advance the slide, a graph of the data is shown. Do not advance until students work on their own!

Mean Leveling Calculation Doll $12 Football $8 Game $7 Car $5 Jump Ropes $3 Have participants read P. 313-314 in Van de Walle “A Leveling Concept of the Mean”. Note: This slide has animation that will perform a mean leveling for the participants to observe. Top $1

How do we find Median? Median: The middle value in an ordered set of data, or the mean of the two middle numbers Doll $12 Football $8 Jump Ropes $3 Car $5 Game $7 Read the definition of Median. Put special emphasis on the definition as being an ordered set of data. What is meant by an ordered set? The key to finding the median of a data set, is to put the data in order. Once the data is ordered, then the median can be found by identifying the middle term. Refer to page 312 in Van de Walle Top $1

How do we create an ordered set? Doll $12 Football $8 Jump Ropes $3 Car $5 Game $7 Top $1 Part of the animation.

How do we find Median? Median: The middle value in an ordered set of data, or the mean of the two middle numbers Median = ? Doll $12 6 Game $7 Football $8 Car $5 How do we find the middle term? The median is the middle value. When you click to advance, there will be a box that appears around the 2 middle terms. This poses an interesting problem where there is no middle value, but there are 2 different values. How do we find the median? The median is found by calculating the mean of the 2 middle values. The median is therefore equal to ($5 + $7)/2 = $6. Refer to page 312 in Van de Walle Jump Ropes $3 Top $1

Mode What is the mode? NO MODE $5 Doll $12 Football $8 Game $7 Marbles The teachers should recognize that this data set does not have a mode. Have them decide on ways to create a mode or multiple modes. If they would like to make $5 the mode, then they will need to add another item that costs $5. They may have a difficult time with adding data to this set, but the goal is to see how they could change the data to create one of the measures of central tendency. Marbles $5 Car $5 Jump Ropes $3 Top $1

Range What is the range? The difference in the highest and the lowest values. Doll $12 Football $8 Game $7 Car $5 Jump Ropes $3 Top $1

Difference (Range) = 11 Range What is the range? The difference in the highest and the lowest values. Doll $12 Difference (Range) = 11 Top $1

6 5 65 fall Name:______________________________ The class logged the temperature for 12 days in the fall and again later in the spring. They posted the temperatures on these line plots. What was the range of the temperatures on each of the plots? Range for Fall: ____________ Range for Spring: _____________ Was there a greater range in the fall or spring? ____________ The class logged the temperature for 12 days in the fall and posted the temperatures on this line plot. What was the mean of the temperatures? __________ 6 5 65 fall