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\( 4,5,5,5,6,9,9,18,20 \) The median is equal to the mode.

Ask by Valdez Little. in the United States
Mar 09,2025

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Tutor-Verified Answer

Answer

The median is 6 and the mode is 5, so they are not equal.

Solution

1. Arrange the numbers (already in increasing order): \[ 4, \; 5, \; 5, \; 5, \; 6, \; 9, \; 9, \; 18, \; 20 \] 2. Find the median (the middle number in an odd-numbered list): With 9 numbers, the median is the 5th number. \[ \text{Median} = 6 \] 3. Find the mode (the number that appears most frequently): The number \(5\) appears 3 times, which is more frequent than any other number. \[ \text{Mode} = 5 \] 4. Compare the median and the mode: \[ 6 \neq 5 \] Thus, the median is not equal to the mode.

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To determine the median, we first arrange the numbers in order (which they already are). The median is the middle value. Since there are 9 numbers, the median is the 5th number, which is 6. Next, the mode is the number that appears most frequently in the set, which is 5 (it appears three times). However, since the median (6) is not equal to the mode (5), the statement is incorrect. Also, a fun fact here: in many datasets, it's rare for the median and mode to be equal, especially in skewed distributions! It usually only happens in specific cases, such as in evenly spaced numbers! One common mistake when calculating the median or mode is forgetting to arrange the numbers first or miscounting the occurrences of numbers when searching for the mode. Always double-check both your arrangement and counts for accuracy!

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