Math worksheet for finding the median of given number sets.
A worksheet titled "Find the Median" with six problems requiring students to order numbers and find the median by crossing out the lowest and highest values.
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Step-by-step solution for: Finding the Median worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Finding the Median worksheet
Let’s solve each problem step by step.
We are told to:
1. Order the numbers (from smallest to largest).
2. Cross out the lowest and highest numbers — but actually, for median, we don’t cross them out unless we’re doing a visual method. The real rule is:
→ If there’s an odd number of values, the median is the middle one after ordering.
→ If even, it’s the average of the two middle ones.
But looking at the worksheet instructions: “Cross out the lowest and highest numbers” — this seems like a simplified method for small sets with odd counts. Let’s check each set.
Actually, let’s just use the standard definition: order the numbers, then pick the middle one (if odd count) or average the two middle ones (if even).
Let’s go one by one.
---
Problem 1: 7, 5, 4
Order: 4, 5, 7 → 3 numbers → middle is 5 → Median = 5
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Problem 2: 1, 6, 3, 9, 2
Order: 1, 2, 3, 6, 9 → 5 numbers → middle is 3rd → 3 → Median = 3
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Problem 3: 9, 5, 4, 7
Order: 4, 5, 7, 9 → 4 numbers → even → average of 2nd and 3rd: (5 + 7)/2 = 6 → Median = 6
Wait — but the instruction says “cross out lowest and highest”. Let’s try that method too, in case that’s what they want.
For Problem 3: 4, 5, 7, 9
Cross out 4 and 9 → left with 5, 7 → now cross out? No, only two left. So maybe take average? Or perhaps the worksheet expects you to keep crossing until one remains? But with even numbers, you can’t get one left.
Looking back at the problems:
Problem 1: 3 numbers → cross out min/max → left with 1 → that’s median.
Problem 2: 5 numbers → cross out 1 and 9 → left with 2,3,6 → cross out 2 and 6 → left with 3 → median.
Problem 3: 4 numbers → cross out 4 and 9 → left with 5,7 → now what? Can’t cross both. So maybe average? Or perhaps the worksheet assumes all sets have odd numbers? But Problem 6 has 6 numbers.
Wait — let’s look at Problem 6: 1,0,0,8,2,6 → 6 numbers → even.
So probably, the “cross out” method is just a teaching aid for odd-sized lists, but for even, we need to average the two middle.
But let’s follow the standard math definition to be accurate.
I’ll solve using standard median rules.
---
Problem 4: 3, 7, 8, 2, 0
Order: 0, 2, 3, 7, 8 → 5 numbers → middle is 3rd → 3 → Median = 3
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Problem 5: 4, 1, 2
Order: 1, 2, 4 → 3 numbers → middle is 2 → Median = 2
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Problem 6: 1, 0, 0, 8, 2, 6
Order: 0, 0, 1, 2, 6, 8 → 6 numbers → even → average of 3rd and 4th: (1 + 2)/2 = 1.5 → Median = 1.5
But wait — is 1.5 acceptable? In some contexts, especially elementary school, they might expect whole numbers, but mathematically, it’s correct.
Alternatively, if they insist on “cross out lowest and highest” repeatedly:
Start: 0,0,1,2,6,8
Cross out 0 and 8 → left: 0,1,2,6
Cross out 0 and 6 → left: 1,2 → now? Average? Still 1.5.
So either way, it’s 1.5.
But let me double-check all.
---
Rechecking:
1.) 7,5,4 → sorted: 4,5,7 → median = 5 ✔
2.) 1,6,3,9,2 → sorted: 1,2,3,6,9 → median = 3 ✔
3.) 9,5,4,7 → sorted: 4,5,7,9 → median = (5+7)/2 = 6 ✔
4.) 3,7,8,2,0 → sorted: 0,2,3,7,8 → median = 3 ✔
5.) 4,1,2 → sorted: 1,2,4 → median = 2 ✔
6.) 1,0,0,8,2,6 → sorted: 0,0,1,2,6,8 → median = (1+2)/2 = 1.5 ✔
All correct.
Now, since the user did not ask for explanation, teaching, or practice, I will only provide the final answers as per format.
Final Answer:
1.) 5
2.) 3
3.) 6
4.) 3
5.) 2
6.) 1.5
We are told to:
1. Order the numbers (from smallest to largest).
2. Cross out the lowest and highest numbers — but actually, for median, we don’t cross them out unless we’re doing a visual method. The real rule is:
→ If there’s an odd number of values, the median is the middle one after ordering.
→ If even, it’s the average of the two middle ones.
But looking at the worksheet instructions: “Cross out the lowest and highest numbers” — this seems like a simplified method for small sets with odd counts. Let’s check each set.
Actually, let’s just use the standard definition: order the numbers, then pick the middle one (if odd count) or average the two middle ones (if even).
Let’s go one by one.
---
Problem 1: 7, 5, 4
Order: 4, 5, 7 → 3 numbers → middle is 5 → Median = 5
---
Problem 2: 1, 6, 3, 9, 2
Order: 1, 2, 3, 6, 9 → 5 numbers → middle is 3rd → 3 → Median = 3
---
Problem 3: 9, 5, 4, 7
Order: 4, 5, 7, 9 → 4 numbers → even → average of 2nd and 3rd: (5 + 7)/2 = 6 → Median = 6
Wait — but the instruction says “cross out lowest and highest”. Let’s try that method too, in case that’s what they want.
For Problem 3: 4, 5, 7, 9
Cross out 4 and 9 → left with 5, 7 → now cross out? No, only two left. So maybe take average? Or perhaps the worksheet expects you to keep crossing until one remains? But with even numbers, you can’t get one left.
Looking back at the problems:
Problem 1: 3 numbers → cross out min/max → left with 1 → that’s median.
Problem 2: 5 numbers → cross out 1 and 9 → left with 2,3,6 → cross out 2 and 6 → left with 3 → median.
Problem 3: 4 numbers → cross out 4 and 9 → left with 5,7 → now what? Can’t cross both. So maybe average? Or perhaps the worksheet assumes all sets have odd numbers? But Problem 6 has 6 numbers.
Wait — let’s look at Problem 6: 1,0,0,8,2,6 → 6 numbers → even.
So probably, the “cross out” method is just a teaching aid for odd-sized lists, but for even, we need to average the two middle.
But let’s follow the standard math definition to be accurate.
I’ll solve using standard median rules.
---
Problem 4: 3, 7, 8, 2, 0
Order: 0, 2, 3, 7, 8 → 5 numbers → middle is 3rd → 3 → Median = 3
---
Problem 5: 4, 1, 2
Order: 1, 2, 4 → 3 numbers → middle is 2 → Median = 2
---
Problem 6: 1, 0, 0, 8, 2, 6
Order: 0, 0, 1, 2, 6, 8 → 6 numbers → even → average of 3rd and 4th: (1 + 2)/2 = 1.5 → Median = 1.5
But wait — is 1.5 acceptable? In some contexts, especially elementary school, they might expect whole numbers, but mathematically, it’s correct.
Alternatively, if they insist on “cross out lowest and highest” repeatedly:
Start: 0,0,1,2,6,8
Cross out 0 and 8 → left: 0,1,2,6
Cross out 0 and 6 → left: 1,2 → now? Average? Still 1.5.
So either way, it’s 1.5.
But let me double-check all.
---
Rechecking:
1.) 7,5,4 → sorted: 4,5,7 → median = 5 ✔
2.) 1,6,3,9,2 → sorted: 1,2,3,6,9 → median = 3 ✔
3.) 9,5,4,7 → sorted: 4,5,7,9 → median = (5+7)/2 = 6 ✔
4.) 3,7,8,2,0 → sorted: 0,2,3,7,8 → median = 3 ✔
5.) 4,1,2 → sorted: 1,2,4 → median = 2 ✔
6.) 1,0,0,8,2,6 → sorted: 0,0,1,2,6,8 → median = (1+2)/2 = 1.5 ✔
All correct.
Now, since the user did not ask for explanation, teaching, or practice, I will only provide the final answers as per format.
Final Answer:
1.) 5
2.) 3
3.) 6
4.) 3
5.) 2
6.) 1.5
Parent Tip: Review the logic above to help your child master the concept of median worksheet.