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 #394 : Data Analysis

On the last day of school, Adam asked each of his classmates how many days of school they missed for the entire school year.  He created a stem-and-leaf plot with the information.

0 | 0 0 2 4 5 6 8

1 | 0 0 1 2

2 | 3

4 | 7

What is the median number of school days missed by Adam's classmates?

Possible Answers:

\dpi{100} 4\(\displaystyle \dpi{100} 4\)

\dpi{100} 8\(\displaystyle \dpi{100} 8\)

\dpi{100} 5\(\displaystyle \dpi{100} 5\)

\dpi{100} 10\(\displaystyle \dpi{100} 10\)

Correct answer:

\dpi{100} 8\(\displaystyle \dpi{100} 8\)

Explanation:

In a stem-and-leaf plot, each number on the right side of the vertical lines is a piece of data.  For instance, the "4 | 7" means one student missed 47 days(!) of school.  Each number on the left of the line represents the ten's digit, and each number on the right of the line represents the one's digit.

We can find the total number of classmates by counting the numbers on the right side of the vertical lines, which in this case is 13.

The median of a group of data represents the physical middle of the data. 

If there is an even number of pieces of data, you take the middle two pieces of data, add them up, and divide by two for the median.

If there is an odd number of pieces of data (such as here), one number represents the median.  Since we have 13 pieces of data, the 7th value is the median, because we would have 6 pieces smaller or equal to it, and 6 pieces greater than or equal to it.

The seventh piece of data here is the 8, which is "0 | 8".  Since the ten's digit is 0, that means that the median number of days missed is 8.

Example Question #1 : How To Find Median

Find the median of this set of numbers: 89, 75, 111, 94, 36, 89, 81.

Possible Answers:

\(\displaystyle 89\)

\(\displaystyle 94\)

\(\displaystyle 36\)

\(\displaystyle 111\)

\(\displaystyle 75\)

Correct answer:

\(\displaystyle 89\)

Explanation:

Place the numbers in order from least to greatest:

36, 75, 81, 89, 89, 94, 111

Identify the middle number in the set. The answer is \(\displaystyle 89.\)

Example Question #2 : How To Find Median

Find the median in this set of numbers:

3021, 3211, 3120, 3102, 3012, 3201, 3210, 3112, 3011

 

 

Possible Answers:

\(\displaystyle 200\)

\(\displaystyle 3112\)

\(\displaystyle 3111\)

\(\displaystyle 3210\)

Correct answer:

\(\displaystyle 3112\)

Explanation:

First, order the numbers from least to greatest:

\(\displaystyle 3011,3012,3021,3102,3112,3120,3201,3210,3211\)

Then, identify the middle number: \(\displaystyle 3112.\)

Answer: The median is 3112.

Example Question #1 : How To Find Median

Subtract the median from the mode in this set of numbers:

241, 244, 422, 424, 422, 214, 412

Possible Answers:

\(\displaystyle 412\)

\(\displaystyle 432\)

\(\displaystyle 20\)

\(\displaystyle -10\)

\(\displaystyle 10\)

Correct answer:

\(\displaystyle 10\)

Explanation:

First, order the numbers from least to greatest:

\(\displaystyle 214, 241, 244, 412, 422, 422, 424\)

Identify the mode (most frequently appearing number): \(\displaystyle 422.\)

Identify the median (middle number): \(\displaystyle 412.\)

Finally, subtract the median from the mode: \(\displaystyle 422-412=10.\)

The answer is 10.

Example Question #3 : How To Find Median

Find the median in this set of numbers:

1144, 1187, 1198, 1034, 1073, 1187, 1081

Possible Answers:

\(\displaystyle 1034\)

\(\displaystyle 1198\)

\(\displaystyle 1144\)

\(\displaystyle 1081\)

Correct answer:

\(\displaystyle 1144\)

Explanation:

First, order the numbers from least to greatest.

\(\displaystyle 1034, 1073, 1081, 1144, 1187, 1187, 1198\)

Identify the middle number in the set.

Answer: The median is 1144.

Example Question #4 : How To Find Median

Find the median in this set of numbers:

2521, 2512, 2525, 2552, 2551, 2525, 2515

Possible Answers:

\(\displaystyle 2528\)

\(\displaystyle 2552\)

\(\displaystyle 2525\)

\(\displaystyle 2521\)

 

Correct answer:

\(\displaystyle 2525\)

Explanation:

First, order the numbers from least to greatest:

\(\displaystyle 2512, 2515, 2521, 2525, 2525, 2551, 2552\)

Identify the middle number: 2525

Answer: The median is 2525.

Example Question #5 : How To Find Median

Find the median in this set of numbers:

9881, 9889, 9818, 9981, 9891, 9918, 9989, 9889, 9198

Possible Answers:

\(\displaystyle 9989\)

\(\displaystyle 9889\)

\(\displaystyle 9898\)

\(\displaystyle 9899\)

Correct answer:

\(\displaystyle 9889\)

Explanation:

First, order the numbers from least to greatest:

\(\displaystyle 9198, 9818, 9881, 9889, 9889, 9891, 9918, 9981, 9989\)

Identify the middle number: \(\displaystyle 9889\)

Answer: The median is 9889.

Example Question #6 : How To Find Median

Find the median in this set of numbers:

3343, 4434, 4334, 3343, 4343, 3434, 3334

Possible Answers:

\(\displaystyle 3834\)

\(\displaystyle 3343\)

\(\displaystyle 3434\)

\(\displaystyle 3795\)

Correct answer:

\(\displaystyle 3434\)

Explanation:

First order the numbers from least to greatest:

\(\displaystyle 3334, 3343, 3343, 3434, 4334, 4343, 4434\)

Then, identify the middle number: 3434.

Answer: The median is 3434.

Example Question #7 : How To Find Median

Find the median in this set of numbers:

6363, 6336, 6366, 6633, 6333, 6363, 6663

Possible Answers:

\(\displaystyle 6366\)

\(\displaystyle 6636\)

\(\displaystyle 6336\)

\(\displaystyle 6363\)

\(\displaystyle 6633\)

Correct answer:

\(\displaystyle 6363\)

Explanation:

First, order the numbers from least to greatest:

\(\displaystyle 6333, 6336,6363,6363, 6366, 6633, 6663\)

Then, identify the middle number: \(\displaystyle 6363\)

Answer: the median is \(\displaystyle 6363\)

Example Question #8 : How To Find Median

Find the median in this set of numbers:

9080, 9008, 9800, 9099, 9009, 9090, 9008

Possible Answers:

\(\displaystyle 9099\)

\(\displaystyle 9080\)

\(\displaystyle 9008\)

\(\displaystyle 9009\)

Correct answer:

\(\displaystyle 9080\)

Explanation:

First, order the numbers from least to greatest:

\(\displaystyle 9008, 9008, 9009, 9080, 9090, 9099, 9800\)

Then, identify the middle number: \(\displaystyle 9080\).

Answer: The median in 9080.

 

 

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