Explanation:
To find the quartiles, we follow these steps for each data set:
1.
Sort the numbers in ascending order (from smallest to largest).
2. Find the
median (second quartile, Q2) — this splits the data into two halves.
3. The
first quartile (Q1) is the median of the *lower half* (not including Q2 if the total number of data points is odd).
4. The
third quartile (Q3) is the median of the *upper half* (again, not including Q2 if odd count).
Let’s go one problem at a time.
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Problem 1: 4, 6, 5, 6, 2, 7, 6, 8
→ Sort: 2, 4, 5, 6, 6, 6, 7, 8
Count = 8 (even)
Median (Q2) = average of 4th and 5th values = (6 + 6)/2 = 6
Lower half: first 4 numbers → 2, 4, 5, 6 → median = (4 + 5)/2 = 4.5 → Q1
Upper half: last 4 numbers → 6, 6, 7, 8 → median = (6 + 7)/2 = 6.5 → Q3
✔ Q1 = 4.5, Q2 = 6, Q3 = 6.5
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Problem 2: 17, 14, 20, 29, 12, 24, 10, 19
→ Sort: 10, 12, 14, 17, 19, 20, 24, 29
Count = 8 (even)
Q2 = (17 + 19)/2 = 18
Lower half: 10, 12, 14, 17 → median = (12 + 14)/2 = 13 → Q1
Upper half: 19, 20, 24, 29 → median = (20 + 24)/2 = 22 → Q3
✔ Q1 = 13, Q2 = 18, Q3 = 22
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Problem 3: 68, 88, 44, 68, 50, 68, 37, 50
→ Sort: 37, 44, 50, 50, 68, 68, 68, 88
Count = 8
Q2 = (50 + 68)/2 = 59
Lower half: 37, 44, 50, 50 → median = (44 + 50)/2 = 47 → Q1
Upper half: 68, 68, 68, 88 → median = (68 + 68)/2 = 68 → Q3
✔ Q1 = 47, Q2 = 59, Q3 = 68
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Problem 4: 52, 60, 24, 36, 48, 52, 72
→ Sort: 24, 36, 48, 52, 52, 60, 72
Count = 7 (odd)
Median (Q2) = middle value = 4th = 52
Lower half (first 3): 24, 36, 48 → median = 36 → Q1
Upper half (last 3): 52, 60, 72 → median = 60 → Q3
✔ Q1 = 36, Q2 = 52, Q3 = 60
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Problem 5: 102, 78, 312, 170, 250, 40, 52, 38, 125
→ Sort: 38, 40, 52, 78, 102, 125, 170, 250, 312
Count = 9 (odd)
Q2 = middle value = 5th = 102
Lower half: first 4 → 38, 40, 52, 78 → median = (40 + 52)/2 = 46 → Q1
Upper half: last 4 → 125, 170, 250, 312 → median = (170 + 250)/2 = 210 → Q3
✔ Q1 = 46, Q2 = 102, Q3 = 210
Let me double-check each:
1) Sorted: 2,4,5,6,6,6,7,8 → Q1 = (4+5)/2=4.5 ✔️
2) 10,12,14,17,19,20,24,29 → Q1=13, Q2=18, Q3=22 ✔️
3) 37,44,50,50,68,68,68,88 → Q1=47, Q2=59, Q3=68 ✔️
4) 24,36,48,52,52,60,72 → Q1=36, Q2=52, Q3=60 ✔️
5) 38,40,52,78,102,125,170,250,312 → Q1=46, Q2=102, Q3=210 ✔️
All correct.
Final Answer:
1) First quartile = 4.5, Second quartile = 6, Third quartile = 6.5
2) First quartile = 13, Second quartile = 18, Third quartile = 22
3) First quartile = 47, Second quartile = 59, Third quartile = 68
4) First quartile = 36, Second quartile = 52, Third quartile = 60
5) First quartile = 46, Second quartile = 102, Third quartile = 210
Parent Tip: Review the logic above to help your child master the concept of quartile worksheet.
