ISEE Middle Level Math : Data Analysis and Probability

Study concepts, example questions & explanations for ISEE Middle Level Math

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Example Questions

Example Question #101 : How To Find Median

Use the following data set to answer the question:

\(\displaystyle 4, 6, 3, 2, 1, 7, 8, 4, 7, 2, 5\)

 

Find the median.

Possible Answers:

\(\displaystyle 7\)

\(\displaystyle 8\)

\(\displaystyle 5\)

\(\displaystyle 6\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 4\)

Explanation:

To find the median of a data set, we will first arrange the numbers within the set in ascending order.  Then, we will find the number in the middle of the set.

So, given the set

\(\displaystyle 4, 6, 3, 2, 1, 7, 8, 4, 7, 2, 5\)

we will arrange the numbers in ascending order.  To do that, we will arrange them from smallest to largest.  So, we get

\(\displaystyle 1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8\)

Now, we will locate the number in the middle of the set.

\(\displaystyle 1, 2, 2, 3, 4,{\color{Red} 4}, 5, 6, 7, 7, 8\)

We can see that it is 4.

 

Therefore, the median of the data set is 4.

Example Question #102 : Median

Use the following data set to answer the question:

\(\displaystyle 4, 2, 7, 6, 5, 6, 7, 8, 6, 1, 6\)

Find the median.

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 7\)

\(\displaystyle 6\)

\(\displaystyle 1\)

\(\displaystyle 2\)

Correct answer:

\(\displaystyle 6\)

Explanation:

To find the median of a data set, we will first arrange the numbers within the set in ascending order, then we will locate the number in the middle of the set.

So, given the set

\(\displaystyle 4, 2, 7, 6, 5, 6, 7, 8, 6, 1, 6\)

we will arrange them in ascending order.  To do that, we will arrange them from smallest to largest.  So, we get

\(\displaystyle 1, 2, 4, 5, 6, 6, 6, 6, 7, 7, 8\)

Now, we will locate the number in the middle of the set.  So,

\(\displaystyle 1, 2, 4, 5, 6,{\color{Red} 6}, 6, 6, 7, 7, 8\)

We can see that it is 6.

 

Therefore, the median of the data set is 6.

Example Question #103 : Median

A Math class took an exam.  Here are the scores of 11 students:

\(\displaystyle 98, 87, 76, 89, 80, 95, 89, 87, 90, 77, 87\)

Find the median score.

Possible Answers:

\(\displaystyle 87\)

\(\displaystyle 90\)

\(\displaystyle 85\)

\(\displaystyle 88\)

\(\displaystyle 89\)

Correct answer:

\(\displaystyle 87\)

Explanation:

To find the median score, we will first arrange the scores in ascending order.  Then, we will find the score in the middle of the set.

So, given the set of scores

\(\displaystyle 98, 87, 76, 89, 80, 95, 89, 87, 90, 77, 87\)

We will arrange the scores in ascending order.  To do that, we will arrange them from smallest to largest.  So, we get

\(\displaystyle 76, 77, 80, 87, 87, 87, 89, 89, 90, 95, 98\) 

Now, we will find the score in the middle of the set.

\(\displaystyle 76, 77, 80, 87, 87,{\color{Red} 87}, 89, 89, 90, 95, 98\)

 

Therefore, the median score is 87.

Example Question #104 : Median

A class takes an exam.  Here are the scores of the 7 students who took the exam:

\(\displaystyle 89, 95, 90, 93, 85, 90, 86\)

Find the median score.

Possible Answers:

\(\displaystyle 85\)

\(\displaystyle 90\)

\(\displaystyle 95\)

\(\displaystyle 89\)

\(\displaystyle 86\)

Correct answer:

\(\displaystyle 90\)

Explanation:

To find the median score, we will first arrange the numbers in ascending order.  Then, we will find the number in the middle of the set. 

So, given the set

\(\displaystyle 89, 95, 90, 93, 85, 90, 86\)

We will arrange the scores in ascending order.  To do this, we will arrange them from smallest to largest.  So, we get

\(\displaystyle 85, 86, 89, 90, 90, 93, 95\)

Now, we will find the number in the middle of the set.

\(\displaystyle 85, 86, 89, {\color{Red} 90}, 90, 93, 95\)

We can see that it is 90.

Therefore, the median score is 90.

Example Question #105 : How To Find Median

A Science class takes an exam.  Here are the results from 11 random students:

\(\displaystyle 76, 82, 90, 85, 91, 75, 83, 88, 92, 88, 75\)

 

Find the median score.

Possible Answers:

\(\displaystyle 88\)

\(\displaystyle 85\)

\(\displaystyle 76\)

\(\displaystyle 92\)

\(\displaystyle 75\)

Correct answer:

\(\displaystyle 85\)

Explanation:

To find the median score, we will arrange the scores in ascending order, then we will find the number in the middle.  So, in the data set

\(\displaystyle 76, 82, 90, 85, 91, 75, 83, 88, 92, 88, 75\)

Now, we will arrange them in ascending (from smallest to largest) order.  We get

\(\displaystyle 75, 75, 76, 82, 83, 85, 88, 88, 90, 91, 92\)

And the number in the middle

\(\displaystyle 75, 75, 76, 82, 83, {\color{Red} 85}, 88, 88, 90, 91, 92\)

 

Therefore, the median score is 85.

Example Question #811 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Identify the median of the numbers:  \(\displaystyle [9,10,11,0,12,36,57]\)

Possible Answers:

\(\displaystyle 13\)

\(\displaystyle 0\)

\(\displaystyle 12\)

\(\displaystyle 20\)

\(\displaystyle 11\)

Correct answer:

\(\displaystyle 11\)

Explanation:

The median of an odd set of numbers is the central number of a chronologically ordered data set from least to greatest.

Rearrange the numbers from least to greatest.

\(\displaystyle [0,9,10,11,12,35,57]\)

The central number is 11.

The answer is: \(\displaystyle 11\)

Example Question #106 : Median

Use the following data set to answer the question:

\(\displaystyle 7, 5, 11, 8, 4, 14, 9, 4, 7, 11, 5\)

Find the median.

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle 6\)

\(\displaystyle 11\)

\(\displaystyle 7\)

\(\displaystyle 5\)

Correct answer:

\(\displaystyle 7\)

Explanation:

To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will find the number in the middle of the set. 

So, given the data set

\(\displaystyle 7, 5, 11, 8, 4, 14, 9, 4, 7, 11, 5\)

we will arrange them in ascending order (from smallest to largest).  We get

\(\displaystyle 4, 4, 5, 5, 7, 7, 8, 9, 11, 11, 14\)

Now, we will find the number in the middle of the set.  So, 

\(\displaystyle 4, 4, 5, 5, 7, {\color{Red} 7}, 8, 9, 11, 11, 14\)

We can see that it is 7.

Therefore, the median of the data set is 7.

Example Question #1 : How To Find The Probability Of An Outcome

There are 32 marbles in a bag: 7 are Red, 11 are Blue, 8 are Purple and 6 are Green. If I pick one marble out of the bag, which color would it most likely be?

Possible Answers:

\(\displaystyle Blue\)

\(\displaystyle Red\)

\(\displaystyle Purple\)

\(\displaystyle Green\)

Correct answer:

\(\displaystyle Blue\)

Explanation:

Find the color with the largest number of marbles in the bag.

Answer: There are more blue marbles in the bag, therefore it would be more likely to pick a blue marble.

Example Question #2 : How To Find The Probability Of An Outcome

The red queens are removed from a standard deck of fifty-two cards. What is the probability that a card randomly drawn from that modified deck will be a face card (jack, queen, king)?

Possible Answers:

\(\displaystyle \frac{6}{25}\)

\(\displaystyle \frac{5}{26}\)

\(\displaystyle \frac{1}{5}\)

\(\displaystyle \frac{1}{3}\)

\(\displaystyle \frac{1}{4}\)

Correct answer:

\(\displaystyle \frac{1}{5}\)

Explanation:

There are four cards of each rank in a standard deck; since three ranks - jacks, queens, kings - are considered face cards, this makes twelve face cards out of the fifty-two. But two of those face cards - two red queens - have been removed, so now there are ten face cards out of fifty. This makes the probability of a randomly drawn card being a face card

\(\displaystyle \frac{10}{50} = \frac{1}{5}\).

Example Question #3 : How To Find The Probability Of An Outcome

Jamie rolled a normal 6-sided die. What is the probability of rolling a number greater than 4?

Possible Answers:

\(\displaystyle 1/2\)

\(\displaystyle 1/6\)

\(\displaystyle 1/3\)

\(\displaystyle 1/4\)

Correct answer:

\(\displaystyle 1/3\)

Explanation:

Probability is determined by dividing the number of incidences of a specific outcome (in this case rolling greater than 4, or rolling a 5 or 6) by the total number of outcomes (there are 6 sides to the die).

\(\displaystyle P=\frac{2}{6}=\frac{1}{3}\)

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