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Common Core: 6th Grade Math : Find mean

Study concepts, example questions & explanations for Common Core: 6th Grade Math

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All Common Core: 6th Grade Math Resources

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Example Questions

Example Question #1 : Find Mean

In a group of 4 books, the average number of pages is is 10. Juan adds a book with 20 pages to the group. What is the new average number of pages?

Possible Answers:

$\displaystyle 10$

$\displaystyle 12$

$\displaystyle 30$

$\displaystyle 20$

$\displaystyle 15$

Correct answer:

$\displaystyle 12$

Explanation:

If the average of 4 books was 10, then the total number of pages was $4\times10 =40$ $\displaystyle 4\times10 =40$. Adding in the 20 new pages, but now dividing by 5 you get $\displaystyle 60/5 = 12$.

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Example Question #1 : Find Mean

Give the mean of the data set (nearest tenth, if applicable):

$\left \{ 56,78,98,85,77,73 \right \}$ $\displaystyle \left \{ 56,78,98,85,77,73 \right \}$

Possible Answers:

77.8 $\displaystyle 77.8$

76.5 $\displaystyle 76.5$

75.7 $\displaystyle 75.7$

79.6 $\displaystyle 79.6$

77.3 $\displaystyle 77.3$

Correct answer:

77.8 $\displaystyle 77.8$

Explanation:

Add the six elements and divide the sum by 6:

$\displaystyle 56 + 78 + 98 + 85 +77 + 73 = 467$

$467 \div 6 \approx 77.8$ $\displaystyle 467 \div 6 \approx 77.8$

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Example Question #2 : Find Mean

Find the mean of this set of numbers:

54, 41, 99, 120, 66.

Possible Answers:

$\displaystyle 79$

$\displaystyle 99$

$\displaystyle 80$

$\displaystyle 76$

Correct answer:

$\displaystyle 76$

Explanation:

Firrst, add the numbers:

$\displaystyle 54+41+99+120+66=380$

Then, divide by the amount of numbers in the set:

$380\div 5=76$ $\displaystyle 380\div 5=76$

Answer: The mean is 76.

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Example Question #3 : Find Mean

Give the mean of the following eight scores:

$\left \{ 61, 67, 80, 72, 76, 73, 90, 68 \right \}$ $\displaystyle \left \{ 61, 67, 80, 72, 76, 73, 90, 68 \right \}$

Possible Answers:

72.875 $\displaystyle 72.875$

73.375 $\displaystyle 73.375$

72.5 $\displaystyle 72.5$

$\displaystyle 73$

75.5 $\displaystyle 75.5$

Correct answer:

73.375 $\displaystyle 73.375$

Explanation:

Divide the sum of the scores by eight:

$\frac{ 61+ 67+80+72+76+73+90+ 68}{8} = \frac{ 587}{8} = 73.375$ $\displaystyle \frac{ 61+ 67+80+72+76+73+90+ 68}{8} = \frac{ 587}{8} = 73.375$

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Example Question #1 : Data Analysis

Give the mean of the following nine scores:

$\left \{ 61, 67, 80, 72, 76, 73, 90, 68, 70 \right \}$ $\displaystyle \left \{ 61, 67, 80, 72, 76, 73, 90, 68, 70 \right \}$

Possible Answers:

75.5 $\displaystyle 75.5$

$\displaystyle 72$

$\displaystyle 73$

$\displaystyle 68$

72.5 $\displaystyle 72.5$

Correct answer:

$\displaystyle 73$

Explanation:

Divide the sum of the scores by nine:

$\frac{ 61 + 67+ 80+ 72+ 76+73+90+68+70}{9} = \frac{ 657}{9} = 73$ $\displaystyle \frac{ 61 + 67+ 80+ 72+ 76+73+90+68+70}{9} = \frac{ 657}{9} = 73$

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Example Question #2 : Data Analysis

The average age of 4 people is 12. What will be the sum of their ages in 3 years?

Possible Answers:

$\displaystyle 12$

$\displaystyle 56$

$\displaystyle 60$

$\displaystyle 15$

$\displaystyle 24$

Correct answer:

$\displaystyle 60$

Explanation:

The current sum of their ages is $12\times 4=48$ $\displaystyle 12\times 4=48$. Since all 4 people will gain 3 years in age, we have to add 12 to the current sum.

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Example Question #2 : Find Mean

Give the mean of the following data set:

$\left \{1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 9, 10 \right \}$ $\displaystyle \left \{1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 9, 10 \right \}$

Possible Answers:

$\displaystyle 5$

5.0625 $\displaystyle 5.0625$

5.375 $\displaystyle 5.375$

$\displaystyle 6$

5.5 $\displaystyle 5.5$

Correct answer:

5.0625 $\displaystyle 5.0625$

Explanation:

Since there are 16 elements, divide their sum by 16 to get the mean:

$(1+ 2+ 3+ 3+ 4+ 4+ 4+ 5+ 5+ 6+ 6+ 6+ 6+ 7+ 9+ 10) \div 16 = 81 \div 16 = 5.0625$ $\displaystyle (1+ 2+ 3+ 3+ 4+ 4+ 4+ 5+ 5+ 6+ 6+ 6+ 6+ 7+ 9+ 10) \div 16 = 81 \div 16 = 5.0625$

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Example Question #1 : Find Mean

Find the average of this set of numbers:

521, 834, 754, 902, 899

Possible Answers:

782 $\displaystyle 782$

600 $\displaystyle 600$

378 $\displaystyle 378$

754 $\displaystyle 754$

Correct answer:

782 $\displaystyle 782$

Explanation:

First, add all the numbers in this set:

$\displaystyle 521+834+754+902+899=3910$

Divide, 3910 by the total amount of numbers in the set:

$3910\div 5=782$ $\displaystyle 3910\div 5=782$

Answer: The average is 782.

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Example Question #4 : Find Mean

Find the mean in this set of numbers:

5570, 4886, 5226, 4120, 6561, 4120, 6008

Possible Answers:

2440 $\displaystyle 2440$

5213 $\displaystyle 5213$

5226 $\displaystyle 5226$

4120 $\displaystyle 4120$

Correct answer:

5213 $\displaystyle 5213$

Explanation:

First, add all the numbers in this set:

$\displaystyle 5570+4886+5226+4120+6561+4120+6008=36491$

Then, divide that amount by the total number in the set:

$36491\div 7=5213$ $\displaystyle 36491\div 7=5213$

Answer: The mean is 5213.

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Example Question #3 : Find Mean

Find the average of this set of numbers:

2521, 2512, 2525, 2552, 2551, 2525, 2517

Possible Answers:

2552 $\displaystyle 2552$

2525 $\displaystyle 2525$

$\displaystyle 40$

2529 $\displaystyle 2529$

Correct answer:

2529 $\displaystyle 2529$

Explanation:

First, add all the numbers in this set:

$\displaystyle 2521+ 2512+2525+2552+2551+2525+2517=17703$

Then, divide by the amount of numbers in the set:

$17703\div 7=2529$ $\displaystyle 17703\div 7=2529$

Answer: The average is 2529. $\displaystyle 2529.$

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Common Core: 6th Grade Math : Find mean

Study concepts, example questions & explanations for Common Core: 6th Grade Math

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #1 : Find Mean

Example Question #1 : Find Mean

Example Question #2 : Find Mean

Example Question #3 : Find Mean

Example Question #1 : Data Analysis

Example Question #2 : Data Analysis

Example Question #2 : Find Mean

Example Question #1 : Find Mean

Example Question #4 : Find Mean

Example Question #3 : Find Mean

All Common Core: 6th Grade Math Resources

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