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Magazine Chapter 2: Q47. (page 66)
A surveyor measures the depth of a river at three different points and obtains depths of 4.7 meters, 8.5 meters, and 6.3 meters.
a. Use properties of addition to find the sum of the surveyor鈥檚 measurements.
b. Analyze: What is the mean depth?
Short Answer
(a) The sum of surveyor鈥檚 measurements is meters.
(b) The mean depth is 6.5 meters.
Step by step solution
Step 1 . What are real numbers?
Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.
Step 2 . Associative Property of Addition of Real Numbers:
Suppose a, b, and c is three real numbers.
Associative property of Addition: (a + b) + c = a + (b + c)
If you are adding three real numbers, the sum is always the same regardless of their grouping.
Example: (11+12) + 13 = 11 + (12+13) = 36
Use properties of addition to find the sum of the surveyor’s measurements.
The depth of a river at three different points and obtains depths of 4.7 meters, 8.5 meters, and 6.3 meters.
Hence sum of depth will bemeters
Associative property of Addition states, if you are adding three real numbers, the sum is always the same regardless of their grouping.
Associative property of Addition: (a + b) + c = a + (b + c)
According to the above property, we can evaluate the expression:
Hence sum of surveyor鈥檚 measurements is meters.
Step 1 . What is the meaning mean of data set?
In mathematics, the average of a number of observations is called mean of the data set.
Step 2 . How to find the mean of a data set
The mean is the same as the average value of a data set and is found using a calculation. Add up all of the numbers and divide by the number of numbers in the data set.
How to Find the Mean
By adding all data values to get the sum, and then count the number of values in your data set. At last divide the sum by the count.
We can write: Mean =
Step 3 . Find the mean depth.
In the question given:
The sum of surveyor鈥檚 measurements meters and number of measurement is 3.
The mean depth is the sum of surveyor鈥檚 measurements divided by the number of measurement taken by the surveyor. Therefore,
Thus, the mean depth is 6.5 meters.
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