ISEE Middle Level Math : How to find median

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

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Example Questions

Example Question #764 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Find the median for this set of numbers:

\(\displaystyle 50, 58, 56, 59, 57\)

Possible Answers:

 \(\displaystyle 55\)

\(\displaystyle 58\)

\(\displaystyle 59\)

\(\displaystyle 50\)

\(\displaystyle 57\)

Correct answer:

\(\displaystyle 57\)

Explanation:

First, order the numbers from least to greatest:

\(\displaystyle 50, 56, 57, 58 ,59\)

Then, identify the middle number: \(\displaystyle 57\)

Answer: \(\displaystyle 57\)

Example Question #765 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Find the median for this set of numbers:

\(\displaystyle 29, 23, 26, 28, 21\)

Possible Answers:

\(\displaystyle 23\)

\(\displaystyle 26\)

\(\displaystyle 24\)

\(\displaystyle 28\)

\(\displaystyle 29\)

Correct answer:

\(\displaystyle 26\)

Explanation:

First order the numbers from least to greatest:

\(\displaystyle 21, 23, 26, 28, 29\)

Then, identify the middle number: \(\displaystyle 26\)

Answer: \(\displaystyle 26\)

Example Question #61 : How To Find Median

Find the median in this set of numbers:

\(\displaystyle 35, 34, 32, 36, 38\)

Possible Answers:

\(\displaystyle 6\)

 

\(\displaystyle 35\)

\(\displaystyle 34\)

\(\displaystyle 36\)

Correct answer:

\(\displaystyle 35\)

Explanation:

First, order the numbers from least to greatest:

\(\displaystyle 32,34,35,36,38\)

Identify the middle number: \(\displaystyle 35\)

Answer: \(\displaystyle 35\)

Example Question #461 : Data Analysis And Probability

Find the median for this set of numbers: 

\(\displaystyle 41, 44, 40, 46, 47\)

Possible Answers:

\(\displaystyle 49\)

\(\displaystyle 46\)

\(\displaystyle 40\)

\(\displaystyle 44\)

\(\displaystyle 45\)

Correct answer:

\(\displaystyle 44\)

Explanation:

First order the numbers from least to greatest:

\(\displaystyle 40, 41, 44, 46, 47\)

Then identify the middle number: \(\displaystyle 44\)

Answer: \(\displaystyle 44\)

Example Question #461 : Data Analysis

Find the median of the set.

\(\displaystyle 9,8,6,6,2, 3\)

Possible Answers:

\(\displaystyle 5\)

\(\displaystyle 12\)

\(\displaystyle 6\)

\(\displaystyle 8\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 6\)

Explanation:

The first step towards finding the median of the set is to reorder the numbers from smallest to largest. 

\(\displaystyle 2,3,6,6,8,9\)

The median is equal to middle number in the set. Since this set has an even number of terms, the average of the middle two numbers will be the median.

The middle two numbers are 6 and 6. Find the average.

\(\displaystyle \frac{6+6}{2}=\frac{12}{2}=6\)

The median is 6.

Example Question #62 : How To Find Median

What is the median of the set?

\(\displaystyle 4, 9, 8, 2, 5, 3, 1\)

Possible Answers:

\(\displaystyle 5\)

\(\displaystyle 7\)

\(\displaystyle 9\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 4\)

Explanation:

The median of a set is the middle number once the numbers are listed from smallest to largest. If we list this set smallest to largest, we get:

\(\displaystyle 1, 2, 3, 4, 5, 8, 9\)

 

Given that 4 is the middle number, it is the median. 

Example Question #63 : How To Find Median

What is the median of the set below?

\(\displaystyle 1, 7, 5, 6, 6.5, 3\)

Possible Answers:

\(\displaystyle 5.5\)

\(\displaystyle 5.25\)

\(\displaystyle 6\)

\(\displaystyle 5\)

Correct answer:

\(\displaystyle 5.5\)

Explanation:

The median is the middle number in a set when ordered smallest to largest. 

The set \(\displaystyle 1, 7, 5, 6, 6.5, 3\), when ordered smallest to largest is:

\(\displaystyle 1, 3, 5, 6, 6.5, 7\)

When there is an even number of items in a set, the average is taken of the middle two numbers. The middle numbers are 5 and 6. Therefore, the median is the average of these two, which is 5.5. 

Example Question #465 : Data Analysis And Probability

The substitute teacher gave her class a quiz. Initially, she believed that there were 15 students in her class who scored an average of 7 out of 10. However, she later realized that there was a 16th student in the class who simply refused to take the quiz, and thereby got a score of 0. What is the average quiz score (to the nearest hundredth), when considering this 16th student?

Possible Answers:

\(\displaystyle 7\)

\(\displaystyle 6.65\)

\(\displaystyle 6\)

\(\displaystyle 6.56\)

Correct answer:

\(\displaystyle 6.56\)

Explanation:

If 15 students got an average score of 7, and 1 student got a score of 0, the average score of the 16 students can be found with this equation:

\(\displaystyle Average = \frac{15\cdot7+0}{16}\)

\(\displaystyle Average = \frac{105}{16}\)

\(\displaystyle Average = 6.56\)

Example Question #551 : Ssat Middle Level Quantitative (Math)

In Jane's previous six basketball games, she made the following number of baskets:

\(\displaystyle 3, 7, 1, 4, 6, 7\)

What is the median number of baskets she made?

Possible Answers:

\(\displaystyle 3.5\)

\(\displaystyle 6\)

\(\displaystyle 4\)

\(\displaystyle 5\)

Correct answer:

\(\displaystyle 5\)

Explanation:

The first step to finding the median is to reorder the number of baskets that Jane scored from smallest to largest. This gives us:

\(\displaystyle 1, 3, 4, 6, 7, 7\)

The median number is the number in the middle of the set. Given that there are two middle numbers (4 and 6), the average of these numbers will be the median. 

The average of 4 and 6 is:

\(\displaystyle \frac{4+6}{2}=5\)

Example Question #465 : Data Analysis

Find the median in this set of numbers:

\(\displaystyle 75,78,71,72,79\)

Possible Answers:

\(\displaystyle 79\)

\(\displaystyle 78\)

\(\displaystyle 72\)

\(\displaystyle 75\)

\(\displaystyle 8\)

Correct answer:

\(\displaystyle 75\)

Explanation:

The median is the middle number of a data set.

Note: If there are an even number of elements in the set, then the median is the average of the middle two elements. Since this data set has five numbers, we don't have to worry about that, but finding the median of an even set is a common test question!

First order the numbers from least to greatest:

\(\displaystyle 71,72,75,78,79\)

Then simply identify the middle number: \(\displaystyle 75\)

Answer: \(\displaystyle 75\)

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