Source: Wiggins, G., & McTighe, J. Understanding by Design.
Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
Title: Statistics & Probability Subject/Course: PreAlgebra Topic: Measures of Central Tendency Grade(s): 7 Designer(s):
Lillian
Laster 

Stage
1 – Desired Results 

Established
Goal(s) Students will demonstrate understanding
of data analysis by posing questions, collecting data, analyzing the data
using measures of central tendency and variation, and using the data to
answer the questions posed. QCC: 42 Strand: Statistics
& Probability Topic: Measures of Central
Tendency and Spread Standard: Uses
mean, median, and mode to describe central tendencies of a data set, and uses
range to describe spread of the data. 

Understanding(s)
Students
will understand that... 1. In statistics there are three measures that tell how the data cluster near the center of the data. These averages (mean, median, mode) are called measures of central tendency. 2. Average and arithmetic mean are equivalent. 3. For sets of data with no very high or low numbers, mean may be a better description. 4. For sets of data with a couple of points much higher or lower than most of the others, median may be a better description. 5. For sets of data with many identical data points, mode may be a better description. U 
Essential
Question(s) 1. If you were to pick a number that best describes all
the data in a set, what number would you pick? 2. How is the mean (average) affect when all the data are
close to each other, or when one piece of data is much bigger or much smaller
than the rest? 3. How is the median (middle) determined when there is an
even number of numbers in a set of data? 4. How can the measures of central tendency be used to
describe tendencies and make predictions? Q 

Students will know... 1. Average and arithmetic mean are equivalent. 2.
Mean is found by adding all the values in a set and
dividing by the number of values. 3.
Median is the number that falls exactly in the middle
of a set of data when the data are arranged in order from least to greatest. 4.
Mode is the value that occurs the most often in a set
of data. 5.
Range is the difference between the greatest and
least numbers in a set of data. K 
Students will be able to... 1. State
measures which describe central tendency of a set of numbers. 2. To define
data and range of a set of data. To
find the range. 3. To define
arithmetic mean of a set of data. To
compute the mean. 4. To find
the median of a set of data. 5. To find
the mode(s) of a set of data. 6.
Produce sets of numbers whose statistical measures
are specified. 7.
To organize, plot and analyze statistical data. 

Stage
2 – Assessment Evidence 


Performance
Task(s) Summary in G.R.A.S.P.S. form 1.
Divide
class into groups of 4 and 5
students. 2. Ask each group to list each
member’s favorite number between 120 also show data using a stemandleaf
plot. 3. Have each group write the
definition of range in their own words and determine the range for their set
of date. Compare range for all
groups. 4. Have each group write the
definition of median in their own words and determine the median of their set
of data. Compare medians for all
groups. 5. Have each group write the
definition of mode in their own words and determine the mode of their set of
data. Compare modes for all groups. 6. Have each group write the
definition of mean in their own words and determine the mean of their set of
data. Compare means for all groups. 7. Class extension
exercise: Have each group determine
if any central tendency is affected if the teacher’s favorite number is added
to their group’s data. T 

Key Criteria: Students will participate in verbal responses and
questioning. Each cooperative group
will show and summarize all work.
Teacher observation 

Other
Evidence Learning activity, quiz 

Stage
3 – Learning Plan 
Learning
Activities Consider the W.H.E.R.E.T.O. elements. 
Your local newspaper has reported standardized test scores for
seventhgraders. Your class had the following
raw scores on the test: 95, 101, 82,
150, 178, 164, 103, 181, 97, 154, 144, 130, 133,159, 177, 99, 124, 127,
151. ·
Make a stemandleaf plot from the data. ·
Solve for all measures (range, mean, median, mode) of
the nineteen scores. The newspaper realizes that a score was omitted. The score was 149. ·
Which of the measures of central tendency, mean,
median, or mode, changes the most as a result of the last score? Extension: If you
happen to know that your score was 150, compare how well you did to
other testtakers by finding your percentile ranking. Note: Students should be able to arrange the
data in order from least to greatest.
Find the total number of scores: n=20. Find how many scores are less than or equal to their score
(150); 13 of the 20 scores are less than or equal to 150. Find out what percent 13 is of 20: 65%.
Therefore, their score of 150 is in the 65^{th}
percentile. Their score is at least
as good as the scores of 65% of their classmates. 