Lesson Example Discussion Quiz: Class Homework |
Example |
Title: One Variable Data |
Grade: 1300-a Lesson: S4-L1 |
Explanation: The best way to understand SAT-2 is by looking at some examples. Take turns and read each example for easy understanding. |
Examples:
Dataset A consists of the heights of 58 buildings and has a mean of 26 meters.
Dataset B consists of the heights of 40 buildings and has a mean of 59 meters.
Dataset C consists of the heights of 98 buildings from datasets A and B.
What is the mean, in meters, of dataset C?
Step 1a
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Data set A: 75 buildings |
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Explanation: Here, we discuss A, B, and C buildings. |
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Step 1b
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To find the mean of data set C, we essentially need to find the average height considering the contribution of each building from sets A and B. \$"M"_"c" = ("N"_"a" times "M"_"a" + "N"_"b" times "M"_"b")/("N"_"a" + "N"_"b")\$ |
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Explanation: To calculate the mean of data set C, we factor in the contribution of buildings from sets A and B, representing this mean as a weighted average of the means of sets A and B, where \$"N"_"a"\$ and \$"N"_"b"\$ are the number of buildings in each set. |
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Step 1c
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Total height of C = Total height of A + Total height of B = 1508 meters + 2360 meters = 3868 meters Total number of buildings in C = number of buildings in A + number of buildings in B = 58 + 40 = 98 \$("Mean height of C") = ("Total height of C")/("Total number of buildings in C")\$ \$(3868 "meters")/ 98 = 39.47 "meters"\$ |
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Explanation: Therefore, the mean height of dataset C is 39.47 meters. |
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