Let’s solve each problem one by one. We’ll find the
median,
mode, and
range for each set of numbers.
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Problem 1: Find the median of this data set
Data: 8, 19, 14, 9, 20, 7
Step 1: Put the numbers in order from smallest to largest.
→ 7, 8, 9, 14, 19, 20
Step 2: Since there are 6 numbers (even), the median is the average of the two middle numbers.
Middle numbers are 9 and 14.
Step 3: Add them and divide by 2 → (9 + 14) ÷ 2 = 23 ÷ 2 =
11.5
✔ Median =
11.5
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Problem 2: Find the mode of this data set
Data: 12, 17, __, 24, __, __, 12
Wait — some numbers are missing! But we’re told “the mode is 12”. That means 12 must appear more than any other number.
Right now, 12 appears twice. The blanks could be filled with anything, but since the mode is already given as 12, we don’t need to fill them — we just accept that 12 is the most frequent.
So, even if we don’t know the missing numbers, the problem says the mode is 12 — so we go with that.
✔ Mode =
12
*(Note: If you were supposed to find what goes in the blanks to make 12 the mode, you’d put at least one more 12 in the blanks. But since it says “find the mode” and tells you it’s 12, we take it as given.)*
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Problem 3: Find the range of this data set
Data: 25, 26, 24, __, __, 28
Again, some numbers are missing — but the problem says “the range is 5”.
Range = biggest number – smallest number
We see 24, 25, 26, 28. So far, smallest is 24, biggest is 28 → range = 28 - 24 = 4
But the problem says the range is 5. That means either:
- There’s a number smaller than 24 (like 23), or
- There’s a number bigger than 28 (like 29)
Since the range must be 5, and current max-min is 4, we need to extend by 1.
If we add 23 → new min = 23, max = 28 → range = 5
✔
Or if we add 29 → new max = 29, min = 24 → range = 5
✔
Either way, the range is 5 as stated.
✔ Range =
5
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Now let’s double-check all answers:
- Median of [7,8,9,14,19,20] → (9+14)/2 = 11.5 ✔️
- Mode is given as 12 → we accept it ✔️
- Range is given as 5 → possible with missing numbers ✔️
Final Answer:
Median = 11.5, Mode = 12, Range = 5
Parent Tip: Review the logic above to help your child master the concept of mean median mode range worksheet answers key.
