# High School Math : Basic Statistics

## Example Questions

### Example Question #13 : Data Properties

Harry's final grade in Algebra is based on the average of four tests and one final.  The final is worth twice as much as the other tests. What is the minimum score he must get on the final to get an A in the course if his other test scores are ?

Explanation:

Let the final test score.

The average is given by .

Solve by cross multiplying to get .

Then subtract from both sides to get

### Example Question #21 : Data Properties

Each student's grade in Becky's math class is determined using a weighted average. Exams comprise 50% of the grade, quizzes comprise 20%, and homework comprises the final 30%. Becky has an 87% average on tests, 82% on quizzes, and 97% on homework. What is her overall grade?

Explanation:

First, convert the weighted percents to decimals.

Next, multiply each score by the weight.

Finally, sum all of the weighted scores.

### Example Question #421 : Algebra Ii

Find the mean and median of the following data set:

Mean:

Median:

Mean:

Median:

Mean:

Median:

Mean:

Median:

Mean:

Median:

Mean:

Median:

Explanation:

The mean is the sum of the numbers divided by their count:

To find the median, order the set from smallest to largest:

When there are two numbers in the middle, find the average of those numbers:

### Example Question #23 : Data Properties

Albert's biology grade is based on the average of three test scores and a final.  The final is worth twice a regular test.  What is the minimum grade he must get on the final to get an A in the course if his other test scores were ?

Explanation:

The average is the sum of the data divided by the total number of data points.

Let final score.

Simplify so the equation to solve becomes .

Cross multiplying we get .

Then subtract from both sides and divide by to get .

### Example Question #1 : How To Find The Percentiles For A Data Set

The 70th and 80th percentiles of a set of scores are 78 and 86, respectively; the interquartile range of the scores is 41. Which of these scores is more likely than the others to be at the 25th percentile?

Explanation:

The interquartile range of a set of scores is the difference between the third and first quartile - that is, the difference between the 75th and 25th percentiles. The 75th percentile is between 78 and 86, so, if 41 is subtracted from those numbers, the upper and lower bounds of the 25th percentile can be found.

Of our choices, only 40 falls in this range.

### Example Question #1 : Independent And Dependent Events

What is the probability of getting a sum of when rolling two six-sided fair dice?

Explanation:

The sample space, or total possible outcomes, when rolling two six-sided dice is .

Ways to get what you want:

So there are ways to get a .

So the probability becomes

### Example Question #431 : Algebra Ii

is the median of the overall data set.   is the median of the lower half of the data set.   is the median of the upper half of the data set.

Find the interquartile range  for the following data set:

Explanation:

First, put the data set in order from smallest to largest:

which is the middle number in the data set.

which is the average of the two middle numbers of the lower half of the data set.

which is the average of the two middle numbers of the upper half of the data set.

Thus the interquartile range is

Note, the range of the data set is given by the largest number minus the smallest number, or

### Example Question #1 : Understanding Variance

A bird watcher observed how many birds came to her bird feeder for four days.  These were the results:

Day 1: 15

Day 2: 12

Day 3: 10

Day 4: 13

What is the variance of the number of birds that visited the bird feeder over the four days?

Explanation:

Variation measures the average difference between values within a group.  The process is not complicated but there are four steps that can take time.  First, find the mean of the values.  Second, subtract the mean from the first value and square the result.  Do this for all remaining values.  Third, add these results together.  Fourth, divide this value by the number of values in the group minus one (in this case, there are four days).

1:

2:

3:

4:

Note that to find the standard deviation, we would simply take one additional step of finding the square root of the variance.

### Example Question #2 : Understanding Variance

Alice recorded the outside temperature at noon each day for one week. These were the results.

Monday: 78

Tuesday: 85

Wednesday: 82

Thursday: 84

Friday: 82

Saturday: 79

Sunday: 80

What is the variance of the temperatures?

Explanation:

There are four steps to finding the variance of values within a group.  First, find the mean of the values.  Second, subtract the mean from the first value and square the result.  Do this for all remaining values.  Third, add these results together.  Fourth, divide the result  by the number of values in the group minus one (in this case, there are seven days, so you must divide by six).

### Example Question #3 : Understanding Variance

The standard deviation of a population is 7.5.  What is the variance of the population?