Let's solve each of the problems step by step. Since I can't see the image directly, I will assume that the problems are as listed in your text and proceed accordingly.
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Problem 1: Find the second quartile for the data shown below.
Data: 32, 42, 61, 45, 55, 53, 54
#### Step 1: Order the data
Arrange the numbers in ascending order:
32, 42, 45, 53, 54, 55, 61
#### Step 2: Find the second quartile (Q2)
The second quartile is the
median of the data set.
Since there are 7 values (odd number), the median is the middle value.
Position = (n + 1)/2 = (7 + 1)/2 = 4th value
So, Q2 =
53
✔ Answer: 53
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Problem 2: Find the first quartile for the data shown below.
Data: 2, 5, 4, 1, 5, 8, 3, 5, 1, 9, 10
#### Step 1: Order the data
1, 1, 2, 3, 4, 5, 5, 5, 8, 9, 10
There are 11 values.
#### Step 2: Find the first quartile (Q1)
Q1 is the median of the
lower half of the data (not including the overall median if odd).
- Median (Q2) is the 6th value:
5
- Lower half: 1, 1, 2, 3, 4 → 5 values
Median of lower half = 3rd value =
2
✔ Answer: 2
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Problem 3: Find the third quartile for the data shown below.
Data: 12, 24, 52, 50, 32, 32, 43
#### Step 1: Order the data
12, 24, 32, 32, 43, 50, 52
7 values → median is 4th value = 32
#### Step 2: Find Q3 (third quartile)
Upper half: 43, 50, 52
Median of upper half =
50
✔ Answer: 50
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Problem 4: Find the mode for the data shown below.
Data: 98, 79, 71, 79, 78, 79, 80, 79, 79, 78
#### Step 1: Count frequency
- 71: 1
- 78: 2
- 79: 5
- 80: 1
- 98: 1
Most frequent =
79 (appears 5 times)
✔ Answer: 79
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Problem 5: Find the range for the data shown below.
Data: 30, 48, 55, 45, 15, 25, 25
#### Step 1: Find max and min
Max = 55
Min = 15
Range = Max - Min = 55 - 15 =
40
✔ Answer: 40
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Problem 6: Find the interquartile range for the data shown below.
Data: 40, 45, 32, 48, 42, 46, 41
#### Step 1: Order the data
32, 40, 41, 42, 45, 46, 48
7 values → median (Q2) = 4th value =
42
Lower half: 32, 40, 41 → median =
40 → Q1 = 40
Upper half: 45, 46, 48 → median =
46 → Q3 = 46
Interquartile Range (IQR) = Q3 - Q1 = 46 - 40 =
6
✔ Answer: 6
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✔ Final Answers:
1.
53
2.
2
3.
50
4.
79
5.
40
6.
6
Let me know if you'd like a visual explanation or box plots!
Parent Tip: Review the logic above to help your child master the concept of iqr worksheet.
