### All Algebra II Resources

## Example Questions

### Example Question #1 : Frequency Distributions

The number of runs scored per game by a little league baseball team is represented by the following frequency distribution:

Number of Runs Scored | Frequency |

0 | 5 |

1 | 2 |

2 | 7 |

3 | 9 |

4 | 3 |

5 | 0 |

6 | 4 |

7 | 2 |

8 | 2 |

9 | 1 |

Using this frequency table, select the correct answer of *m**ean* runs scored by the little league team (rounded to the nearest hundredth).

**Possible Answers:**

There's not enough information present to determine the mean.

**Correct answer:**

Number of Runs Scored | Frequency |

0 | 5 |

1 | 2 |

2 | 7 |

3 | 9 |

4 | 3 |

5 | 0 |

6 | 4 |

7 | 2 |

8 | 2 |

9 | 1 |

To determine the mean, first the data set should be re-written in sequential order:

The formula to determine mean is:

The mean is approximately 3.37 runs scored per game.

### Example Question #2 : Frequency Distributions

Thousands of people in the United States were surveyed about their grandparents. This frequency table shows their answer to the question "how many of your grandparents were born outside of the US?

Of the people who had at least one grandparent born outisde of the US, what percent had exactly 3 non-US born grandparents?

**Possible Answers:**

**Correct answer:**

Adding up the total number of grandparents that were born outside the U.S. is our first step in solving this problem.

There are

people who said they had at least 1 grandparent born outside of the US. Of those, only 976 had exactly 3.

So

or is the answer.

### Example Question #3 : Frequency Distributions

Thousands of people in the United States were surveyed about their grandparents. This frequency table shows their answer to the question "how many of your grandparents were born outside of the US?"

Is this data normally distributed?

**Possible Answers:**

Yes

Partly

No

Need more information

**Correct answer:**

No

No - normally distributed data has a low frequency of responses at the high and low ends. Also, the majority of the data is in the middle.

In this data set, the majority of people said "0," and the fewest people said "3" which is near the middle of the data. If this data was normally distributed we would have a higher frequency between 1 and 3 and much lower values for 0 and 4.

### Example Question #4 : Frequency Distributions

What is the correct frequency distribution for this data set?

1 3 5 2 5 2 4 1 5

2 4 1 2 3 5 5 2 3

3 1 4 4 6 2 3 2 4

**Possible Answers:**

**Correct answer:**

Count the number of times each number appears in the data set.

The number 1 appears 4 times, so the first line is .

Then number 2 appears 7 times, so the next line is .

Continuing in this fashion we see that the numbers 3, 4, and 5 appears 5 times and 6 appears once.

Therefore combining these together we get the following answer:

### Example Question #5 : Frequency Distributions

What is the mean of the data in this frequency table?

# Frequency

1 3

2 4

3 0

4 2

**Possible Answers:**

**Correct answer:**

The frequency table represents the data set:

1, 1, 1, 2, 2, 2, 2, 4, 4.

The sum is 19 and there are 9 data points, so the mean is

.

### Example Question #6 : Frequency Distributions

What is the median of the data in this frequency table?

# Frequency

1 3

2 4

3 0

4 2

**Possible Answers:**

**Correct answer:**

The frequency table represents the data set:

1, 1, 1, 2, 2, 2, 2, 4, 4.

The median is 2 because 4 data points appear before and after the center 2.

### Example Question #7 : Frequency Distributions

Which frequency table has a median of 5? (The first column represents the data points, the second column the frequency)

**Possible Answers:**

**Correct answer:**

The correct frequency table represents the data set 3, 4, 5, 5, 6, 6, 8.

Since there are 7 data points our median will be the 4th spot which makes the value 5. It occures at the 4th spot because at that spot half the data points are below it while the other half are above it.

The center number of that data set is 5 as required.

### Example Question #1 : Quartiles

Determine the first quartile and third quartile from the following list:

**Possible Answers:**

**Correct answer:**

To find the first and third quartile of the data set we first need to find the median of the data set. The median is the middle entry of the data set when entries are in ascending order therefore, the median is 10.

To find the first quartile, we need to break our data set into a subset that is between the first entry and the median. This set is:

Because the first quartile is the median of this subset we get the first quartile to equal 3.

The third quartile is found by taking the subset that is the median to the last entry of the data set. This subset is:

Because the third quartile is the median of the new subset we get the third quartile to equal 25.

### Example Question #2 : Quartiles

Identify the first and third quartiles for the following set of numbers.

{11, 14, 9, 2, 27, 26, 5, 8, 19, 10, 12, 6}

**Possible Answers:**

**Correct answer:**

{11, 14, 9, 2, 27, 26, 5, 8, 19, 10, 12, 6}

First, arrange the values in numerical order.

{2, 5, 6, 8, 9, 10, 11, 12, 14, 19, 26, 27}

Quartiles are the values that divide a set into four equal parts. Since this set has twelve values, "cut" the data after the 3rd and 9th value to find the 1st and 3rd quartile, respectively.

{2, 5, 6,**|** 8, 9, 10, 11, 12, 14,**|** 19, 26, 27}

The quartile will be the average of the values on either side of the "cut."

**First Quartile = (6+8)/2=7**

**Third Quartile = (14+19)/2=16.5**

### Example Question #3 : Quartiles

Salespeople who land in the top quartile of average customer satisfaction ratings at the end of the year receive a bonus. Among the set of average ratings below, what is the cutoff for receiving the bonus?

{98, 55, 67, 88, 85, 91, 83, 65, 77, 83}

**Possible Answers:**

**Correct answer:**

{98, 55, 67, 88, 85, 91, 83, 65, 77, 83}

Rearrange the values in order.

{55, 65, 67, 77, 83, 83, 85, 88, 91, 98}

To get quartiles, "cut" the data into four.

{55, 65, 6**|**7, 77, 83,**|** 83, 85, 8**|**8, 91, 98}

As you can see, the third "cut" is right at 88. Which means **88** is the cutoff for the top quartile based on this set of data.

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