Algebra 1 : Statistics and Probability

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #3 : How To Find Median

A short quiz with 5 questions is given to a class of 30 students. 7 students answered 5 questions correctly, 12 students answered 4 questions correctly, 9 students answered 3 questions correctly, and 2 students answered 2 questions correctly.

What is the median number of questions answered correctly by the students of this class?

Possible Answers:

Correct answer:

Explanation:

The median score will be located in the middle of the class's scores when arranged from lowest to highest or highest to lowest. Because there are 30 students in the class, the median score is the average of the 15th and 16th score. In this case, the 15th and 16th highest score is 4, which means that its median must be 4.

Example Question #4 : How To Find Median

For one algebra class, the scores on last week's exam were 93, 62, 79, 85, 58, and 85. Which statement about this set of values is false?

Possible Answers:

The median of this set is .

The mode of this set is .

The range of this set is .

The mean of this set is .

Correct answer:

The range of this set is .

Explanation:

The simplest of these statistical measurements is the mode, which refers to the most common value in the set. Here, all of the values are present once except for 85, which is present twice, making it our mode. The corresponding answer choice is true and is not our solution.

Next, we find the mean by adding the values and dividing by 6. The mean is indeed 77.

Let's look at the median. The two middle values of the set are 85 and 79, so the median falls directly between them, at 82.

Finally, the range is the difference between the highest value and the lowest. , so the answer choice stating that the range is 31 is our false answer.

Example Question #1 : Median

Find the median of the following set of numbers: 3, 5, 18, 6, 3. 

Possible Answers:

Correct answer:

Explanation:

The median of a set of numbers is the number that falls in the middle when the numbers are arranged from smallest to largest: 3, 3, 5, 6, 18.  The number that falls exactly in the middle of this set is 5, which is the median. 

Example Question #11 : How To Find Median

A committee of 3 members is to be selected from amongst 5 contestants.  How many ways the committee can be selected assuming the order is not important?

Possible Answers:

Correct answer:

Explanation:

This is a combination problem where the order of selection is not important (e.g., ABC is same as ACB is same as CAB).  Hence we need to eliminate any duplication due to order of selection.

 

Example Question #1632 : Algebra 1

There are 5 men and 4 women running for the following positions:

 

President, Vice President, Secretary

We must select 1 man out of 5 and 2 women out of 4.

 

Hoe many ways the three positions can be filled?

Possible Answers:

Correct answer:

Explanation:

One man can be selected out of 5 is

and 2 women can be selected out of 4 women in

ways

Having selected 3 candidates, these candidates can be assigned the three positions in 3! ways giving us the correct answer which is

 

Example Question #2 : Median

We are given the following number set:

8, 6, 10, 15, 7, 15 ,5, 14, 9, 5, 19, 18, 9, 16, 9

Find the median.

Possible Answers:

Correct answer:

Explanation:

The median is the middle number of an ordered number set. By ordered number set, I mean that the numbers are arranged from lowest to largest. In this problem, we can arrange the number set from lowest to largest so that it is rewritten as

5, 5, 6, 7, 8, 9, 9, 9, 10, 14, 15, 15, 16, 18, 19

It looks like the middle-most number is 9.  Therefore, 9 is the median.

Example Question #12 : How To Find Median

Find the median of the set .

Possible Answers:

32

36

33

32.44

Correct answer:

33

Explanation:

To find the median of the set, we put the numbers in ascending order and find the middle number.  Arranging the set in ascending order, we get .  Since the number of values is odd,  we simply take the middle number, 33. 

Example Question #4 : Median

Find the median of the set .

Possible Answers:

Correct answer:

Explanation:

The median of a set of numbers is simply the middle number in the ordered set. To find it, we can first put the set in order from least to greatest (greatest to least works just as well). The set can now be read as

Now, it is clear that the median number is 46. Don't confuse median and mean! The mean, or average value, is the result of the sum of all the values divided by the number of terms in the set.

Example Question #13 : How To Find Median

Find the median of the following numbers:

11, 13, 16, 13, 14, 19, 13, 13

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

Reorder the numbers in ascending order (from lowest to highest):

11, 13, 13, 13, 13, 14, 16, 19

Find the middle number. In this case, the middle number is the average of the 4th and 5th numbers. Because both the 4th and 5th number are 13, the answer is simply 13.

Example Question #14 : How To Find Median

Find the median of this number set:  2, 15, 4, 3, 6, 11, 8, 9, 4, 16, 13

Possible Answers:

Correct answer:

Explanation:

List the numbers in ascending order: 2,3,4,4,6,8,9,11,13,15,16

The median is the middle number, or 8.

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