This handy Spectrum Math Grade 7 Answer Key Chapter 6 Lesson 6.3 Reviewing Measures of Center provides detailed answers for the workbook questions
Spectrum Math Grade 7 Chapter 6 Lesson 6.3 Reviewing Measures of Center Answers Key
The mean is the average of a set of numbers. It is found by adding the set of numbers and then dividing by the number of addends.
The median is the middle number of a set of numbers that is ordered from least to greatest. When there is an even amount of numbers, it is the mean of the two middle numbers.
The mode is the number that appears most often in a set of numbers. There is no mode if all numbers appear the same number of times.
The range is the difference between the greatest and least numbers in the set.
Find the mean, median, mode, and range of the following set of numbers.
34, 32, 39, 33, 37, 36, 39, 38
mean: 34 + 32 + 39 + 33 + 37 + 36 + 39 + 38 = \(\frac{288}{8}\) = 36
Arrange the numbers from least to greatest to find median, mode, and range.
32, 33, 34, 36, 37, 38, 39, 39
median: \(\frac{36+37}{2}\) = 36.5
mode: 39
range: 39 – 32 = 7
Find the mean, median, mode, and range of the following sets of numbers.
Question 1.
a. 8, 6, 9, 11, 12, 4, 9, 10, 9, 2
mean: ______________
median: _____________
mode: _____________
range: _____________
Answer:
mean: 8
median: 9
mode: 9
range: 10
Explanation:
Given set of data is: 8, 6, 9, 11, 12, 4, 9, 10, 9, 2
We know that,
The mean is the average of a set of numbers.
It is found by adding the set of numbers and then dividing by the number of addends.
8 + 6 + 9 + 11 + 12 + 4 + 9 + 10 + 9 + 2 = \(\frac{80}{10}\) = 8
We know that,
The median is the middle number of a set of numbers that is ordered from least to greatest.
When there is an even amount of numbers, it is the mean of the two middle numbers.
Arrange the numbers from least to greatest to find median.
2, 4, 6, 8, 9, 9, 9, 10, 11, 12 = \(\frac{9 + 9}{2}\) = \(\frac{18}{2}\) = 9
We know that,
The mode is the number that appears most often in a set of numbers.
Arrange the numbers from least to greatest to find mode.
2, 4, 6, 8, 9, 9, 9, 10, 11, 12 = 9
We know that,
The range is the difference between the greatest and least numbers in the set.
Arrange the numbers from least to greatest to find range.
2, 4, 6, 8, 9, 9, 9, 10, 11, 12 = 12 – 2 = 10
b. 40.7, 23.1, 18.5, 43.6, 52.1, 50.9, 44.8, 23.1
mean: ______________
median: _____________
mode: _____________
range: _____________
Answer:
mean: 37.1
median: 42.15
mode: 23.1
range: 33.6
Explanation:
Given set of data is: 40.7, 23.1, 18.5, 43.6, 52.1, 50.9, 44.8, 23.1
We know that,
The mean is the average of a set of numbers.
It is found by adding the set of numbers and then dividing by the number of addends.
40.7 + 23.1 + 18.5 + 43.6 + 52.1 + 50.9 + 44.8 + 23.1 = \(\frac{296.8}{8}\) = 37.1
We know that,
The median is the middle number of a set of numbers that is ordered from least to greatest.
When there is an even amount of numbers, it is the mean of the two middle numbers.
Arrange the numbers from least to greatest to find median.
18.5 + 23.1 + 23.1 + 40.7 + 43.6 + 44.8 + 50.9 + 52.1 = \(\frac{40.7 + 43.6}{2}\) = \(\frac{84.3}{2}\) = 42.15
We know that,
The mode is the number that appears most often in a set of numbers.
Arrange the numbers from least to greatest to find mode.
18.5, 23.1, 23.1, 40.7,43.6, 44.8, 50.9, 52.1 = 23.1
We know that,
The range is the difference between the greatest and least numbers in the set.
Arrange the numbers from least to greatest to find range.
18.5, 23.1, 23.1, 40.7,43.6, 44.8, 50.9, 52.1 = 52.1 – 18.5 = 33.6
Question 2.
a. 152, 136, 171, 208, 193, 163, 124, 212, 216, 171
mean: ______________
median: _____________
mode: _____________
range: _____________
Answer:
mean: 174.6
median: 171
mode: 171
range: 92
Explanation:
Given set of data is: 152, 136, 171, 208, 193, 163, 124, 212, 216, 171
We know that,
The mean is the average of a set of numbers.
It is found by adding the set of numbers and then dividing by the number of addends.
152 + 136 + 171 + 208 + 193 + 163 + 124 + 212 + 216 + 171 = \(\frac{1746}{10}\) = 174.6
We know that,,
The median is the middle number of a set of numbers that is ordered from least to greatest.
When there is an even amount of numbers, it is the mean of the two middle numbers.
Arrange the numbers from least to greatest to find median.
124, 136, 152, 163, 171, 171, 193, 208, 212, 216 = \(\frac{171 + 171}{10}\) = \(\frac{342}{2}\) = 171
We know that,
The mode is the number that appears most often in a set of numbers.
Arrange the numbers from least to greatest to find mode.
124, 136, 152, 163, 171, 171, 193, 208, 212, 216 = 171
We know that,
The range is the difference between the greatest and least numbers in the set.
Arrange the numbers from least to greatest to find range.
124, 136, 152, 163, 171, 171, 193, 208, 212, 216 = 216 – 124 = 92
b. 349, 562.5, 612, 349, 187, 612, 530, 716.5, 349, 902
mean: ______________
median: _____________
mode: _____________
range: _____________
Answer:
mean: 516.9
median: 546.25
mode: 349
range: 715
Explanation:
Given set of data is: 349, 562.5, 612, 349, 187, 612, 530, 716.5, 349, 902
We know that,
The mean is the average of a set of numbers.
It is found by adding the set of numbers and then dividing by the number of addends.
349 + 562.5 + 612 + 349 + 187 + 612 + 530 + 716.5 + 349 + 902 = \(\frac{5169}{10}\) = 516.9
We know that,
The median is the middle number of a set of numbers that is ordered from least to greatest.
When there is an even amount of numbers, it is the mean of the two middle numbers.
Arrange the numbers from least to greatest to find median.
187, 349, 349, 349, 530, 562.5, 612, 612, 716.5, 902 = \(\frac{1092.5}{2}\) = 546.25
We know that,
The mode is the number that appears most often in a set of numbers.
Arrange the numbers from least to greatest to find mode.
187, 349, 349, 349, 530, 562.5, 612, 612, 716.5, 902 = 349
We know that,
The range is the difference between the greatest and least numbers in the set.
Arrange the numbers from least to greatest to find range.
187, 349, 349, 349, 530, 562.5, 612, 612, 716.5, 902 = 902 – 187 = 715