# GED Math : Statistics

## Example Questions

### Example Question #1901 : Ged Math

In order for Joseph to pass his math class, he must have an average test score of . On his past four math tests he received the following scores: . What must he score on his fifth and final test in order to pass the class?

Explanation:

Recall how to find the average of a set of numbers:

We can then set up the following equation. Let  be the score of the fifth test.

Solve for .

Joseph must score a  on his next test to pass the class.

### Example Question #31 : Mean

Peter ran each day during a five-day period. The number of miles he ran on each day was as follows:

Monday: One mile.

Tuesday: One and one half miles.

Wednesday: One mile.

Thursday: Two miles.

Friday: One half mile.

Give the average number of feet Peter ran per day over the five-day period in question.

Explanation:

The average distance Peter ran over five days is the sum of the distances he ran divided by five, so first, add the distances:

Rewrite the expressions in terms of halves, and add numerators:

Peter ran a total of six miles. Since we are asked for an answer in feet, first, multiply this by 5,280 feet per mile:

feet.

Now, divide by 5:

feet per day, the correct response.

### Example Question #32 : Mean

What is the mean of this set of data?

Explanation:

To find the mean, you must first add up all of the numbers in the set, then divide the total by how many numbers you have.

Let's start by adding up all the whole set.

Not counting the total, we see that we have  numbers in our set. We will divide  by  in order to get the mean.

### Example Question #33 : Mean

What is the mean for this set of data?

Explanation:

To find the mean, we must add up all of the numbers in our set, then divide our total by how many numbers we have.

Let's first add up the set. Remember to include the negative when adding.

If we count all of our numbers, not including the total, we can see that we have  numbers. Now we shall divide  from .

### Example Question #34 : Mean

What is the mean of this set of data?

Explanation:

To find the mean, we must first add up all of the numbers in our set, then divide the total by the number of numbers in our set.

Let's first add up all of our numbers.

Not including the total, we can see that we have  numbers in our set. We will divide  by  in order to get the mean.

### Example Question #40 : Mean

What is the mean for this set of data?

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  by  with , and  with  in order to have  as the denominator. Make sure to multiply the numerator too!

Since we have  fractions, we will divide  by . This is the same as saying we are multiplying it by .

### Example Question #1 : Median

Find the median of the following set of numbers:

This set of numbers does not have a median.

Explanation:

The median of a set of numbers is the number that is in the middle of the set when the numbers are written in increasing order (from smallest to largest).

When a list of numbers includes an even quantity, like the list in this question, you need to find the mean (average) of the two numbers in the middle.

The steps to find the median of this number set are below:

1. Rewrite the list of numbers so that the numbers are written in increasing order

2. Identify the number(s) in the middle of the set

3. Since there are two numbers in the middle of the set, find the average of the two numbers

### Example Question #1 : Median

Given the data set , which of the following quantities are equal to each other/one another?

I: The mean

II: The median

III: The mode

I and II only

II and III only

I,  II, and III

I and III only

II and III only

Explanation:

The median of a data set with an odd number of elements is the middle value when the set is arranged in ascending order; the middle value of this nine-element set is the fifth value, 5.

The mode of a data set is the most frequently occurring element. Here, only 5 appears multiple times, so it is the mode.

The mean of a data set is the sum of its elements divided by the number of elements, which here is 9:

The mean and the mode are equal, but the mean is different. The correct answer is "II and III only".

### Example Question #1 : Median

Which of the following elements can be added to the data set

so that its median remains unchanged?

I:

II:

III:

II and III only

I, II, and III

I and III only

I and II only

I, II, and III

Explanation:

The median of a data set with an even number of elements is the mean of the two elements that are in the middle when the elements are arranged in ascending order, such as this one. The middle elements of this ten-element set are both 5, so this is the median.

The median of a data set with an odd number of elements is the element that is in the middle when the elements are arranged in ascending order.

If 0 is added to the set, it becomes

.

If 5 is added, it becomes

.

If 100 is added, it becomes

.

In all cases, the middle element is 5, so the median remains 5. The correct choice is "I, II, and III".

### Example Question #2 : Median

Veronica went to the mall and bought several gifts for her sister's birthday. The prices of the items were the following:

$8,$10, $6,$7, $10,$2, $5,$3, $4 What is the median price of the gifts? Possible Answers:$2

$8$10

$6$4.50

$6 Explanation: To find the median, first reorder the prices in ascending order:$2,  $3,$4, $5,$6, $7,$8, $10,$10
Here, the middle number in this set of nine prices is the 5th number, which is $6.$2,  $3,$4, $5,$6, $7,$8, $10,$10