GED Math - Calculations

Given the data set $\left { 2, 3, 5, 6, 6, 6, 7, 7\right }$ , which of the following quantities are equal to each other/one another?

I: The mean

II: The median

III: The mode

II and III only

I and II only

I and III only

I, II, and III

Explanation

Since this data set is arranged in ascending order and has an even number of elements, the median of the data set is the arithmetic mean of its middle two elements. Both elements are 6, so this is the median.

6 is the mode, since it occurs most frequently.

The mean is the sum of the elements divided by the number of elements, which is 8:

$\frac{2+3+ 5 + 6 + 6 + 6 + 7 +7}{8} =\frac{42}{8 } = 5.25$

The median and the mode are equal to each other, but not to the mean, so the correct answer is "II and III only".

Given the data set $\left { 2, 3, 5, 6, 6, 6, 7, 7\right }$ , which of the following quantities are equal to each other/one another?

I: The mean

II: The median

III: The mode

II and III only

I and II only

I and III only

I, II, and III

Explanation

6 is the mode, since it occurs most frequently.

The mean is the sum of the elements divided by the number of elements, which is 8:

$\frac{2+3+ 5 + 6 + 6 + 6 + 7 +7}{8} =\frac{42}{8 } = 5.25$

The median and the mode are equal to each other, but not to the mean, so the correct answer is "II and III only".

John would like to have a 90 average for math for this semester. John received a 78, 89, 100 on three of his tests. What is the lowest grade he could receive on his last test in order for him to get a 90 average for the semester?

Explanation

In order for John to maintain a 90 average for the marking period, his total for four tests must be 360.

$\frac{360}{4} = 90$ or $90 \times 4 = 360$

If you add up the scores that he already received, he already has 267 points.

If you take the total of 267, which is the total amount of points for the three tests already taken and subtract it from the 360 points which is the total amount of points needed for a 90 average, he would need to get a 93 on his last test.

What is the mean for this set of data?

$\frac{2}{3}$ , $\frac{7}{8}$ , $\frac{6}{12}$

$\frac{49}{72}$

$\frac{72}{49}$

$\frac{49}{24}$

$\frac{24}{49}$

$\frac{24}{72}$

Explanation

In order to find the mean, we must first add up all of the numbers in the set, then divide the total number by how many numbers we have.

If you have a calculator, then adding these fractions should be easy. If you don't have a calculator, then we will add them up by hand.

Right now we can't add our fractions together, as they have no common denominator. We must convert all of these fractions to have the same denominator and then we can add them.

is a number that can have , , and in it, so we will use this number as our denominator. So we will multiply $\frac{2}{3}$ by , $\frac{7}{8}$ with , and $\frac{6}{12}$ with in order to have as the denominator. Make sure to multiply the numerator too!

$(\frac{2}{3})8+(\frac{7}{8})3+(\frac{6}{12})2$

$\frac{16}{24}+\frac{21}{24}+\frac{12}{24}=\frac{49}{24}$

Since we have fractions, we will divide $\frac{49}{24}$ by . This is the same as saying we are multiplying it by $\frac{1}{3}$ .

$\frac{\frac{49}{24}}{3}=\frac{49}{72}$

Our answer is $\frac{49}{72}$

What is the mean for this set of data?

$\frac{2}{3}$ , $\frac{7}{8}$ , $\frac{6}{12}$

$\frac{49}{72}$

$\frac{72}{49}$

$\frac{49}{24}$

$\frac{24}{49}$

$\frac{24}{72}$

Explanation

In order to find the mean, we must first add up all of the numbers in the set, then divide the total number by how many numbers we have.

If you have a calculator, then adding these fractions should be easy. If you don't have a calculator, then we will add them up by hand.

Right now we can't add our fractions together, as they have no common denominator. We must convert all of these fractions to have the same denominator and then we can add them.

$(\frac{2}{3})8+(\frac{7}{8})3+(\frac{6}{12})2$

$\frac{16}{24}+\frac{21}{24}+\frac{12}{24}=\frac{49}{24}$

Since we have fractions, we will divide $\frac{49}{24}$ by . This is the same as saying we are multiplying it by $\frac{1}{3}$ .

$\frac{\frac{49}{24}}{3}=\frac{49}{72}$

Our answer is $\frac{49}{72}$