Question

which data set represents the histogram? a 56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55 b 57, 68, 76, 78, 57, 53, 69, 68, 71, 60, 59, 55 c 56, 66, 71, 78, 57, 53, 60, 68, 70, 60, 59, 55 d 53, 61, 71, 76, 57, 53, 69, 68, 70, 76, 59, 55 e 56, 66, 71, 78, 77, 53, 69, 68, 70, 60, 59, 55

Explanation:

Step1: Analyze histogram intervals and frequencies

The histogram has intervals: 50 - 54, 55 - 59, 60 - 64, 65 - 69, 70 - 74, 75 - 79 with frequencies 1, 4, 1, 3, 2, 1 respectively.

Step2: Count data points in each interval for each option

- **Option A**:
- 50 - 54: 1 (53)
- 55 - 59: 2 (59, 55) → Incorrect (should be 4)
- **Option B**:
- 50 - 54: 1 (53)
- 55 - 59: 4 (57, 57, 59, 55)
- 60 - 64: 1 (60)
- 65 - 69: 3 (68, 68, 69)
- 70 - 74: 2 (70, 71)
- 75 - 79: 2 (76, 78) → Incorrect (should be 1)
- **Option C**:
- 50 - 54: 1 (53)
- 55 - 59: 4 (57, 59, 55, 55? Wait, no: 57, 59, 55, 55? Wait data: [56, 66, 71, 78, 57, 53, 60, 68, 70, 60, 59, 55]. 55 - 59: 57, 59, 55 → 3? Wait no, re - check. Wait 55 - 59: numbers ≥55 and <60. 56, 57, 59, 55 → 4 (56, 57, 59, 55). 60 - 64: 60, 60 → 2? Wait no, interval 60 - 64: numbers ≥60 and <65. 60, 60, 53? No, 53 is 50 - 54. Wait data: 56, 66, 71, 78, 57, 53, 60, 68, 70, 60, 59, 55.
- 50 - 54: 53 (1)
- 55 - 59: 56, 57, 59, 55 (4)
- 60 - 64: 60, 60 (2) → Incorrect (should be 1)
- **Option D**:
- 50 - 54: 53 (1)
- 55 - 59: 59, 55 (2) → Incorrect (should be 4)
- **Option E**:
- 50 - 54: 53 (1)
- 55 - 59: 54? No, 54 is 50 - 54? Wait data: [54, 66, 71, 78, 77, 53, 69, 68, 70, 60, 59, 55].
- 50 - 54: 54, 53 (2) → Incorrect (should be 1)
Wait, maybe I made a mistake. Let's re - check Option B. Wait the interval 75 - 79: numbers ≥75 and <80. In Option B, the data is [57, 60, 76, 78, 57, 53, 69, 68, 71, 60, 59, 55]. So 76 and 78 are in 75 - 79: that's 2, but the histogram has frequency 1. Wait Option A: data [56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55].
- 50 - 54: 53 (1)
- 55 - 59: 56, 59, 55 (3) → No. Wait the correct approach: Let's list the frequency for each interval:

Interval 50 - 54: frequency 1 → one number between 50 - 54.

Interval 55 - 59: frequency 4 → four numbers between 55 - 59.

Interval 60 - 64: frequency 1 → one number between 60 - 64.

Interval 65 - 69: frequency 3 → three numbers between 65 - 69.

Interval 70 - 74: frequency 2 → two numbers between 70 - 74.

Interval 75 - 79: frequency 1 → one number between 75 - 79.

Now let's check Option B: [57, 60, 76, 78, 57, 53, 69, 68, 71, 60, 59, 55]

- 50 - 54: 53 (1) ✔️
- 55 - 59: 57, 57, 59, 55 (4) ✔️
- 60 - 64: 60, 60 (2) ❌ (should be 1)

Option A: [56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55]

- 50 - 54: 53 (1) ✔️
- 55 - 59: 56, 59, 55 (3) ❌ (should be 4)

Option E: [54, 66, 71, 78, 77, 53, 69, 68, 70, 60, 59, 55]

- 50 - 54: 54, 53 (2) ❌ (should be 1)

Option C: [56, 66, 71, 78, 57, 53, 60, 68, 70, 60, 59, 55]

- 50 - 54: 53 (1) ✔️
- 55 - 59: 56, 57, 59, 55 (4) ✔️
- 60 - 64: 60, 60 (2) ❌ (should be 1)

Option D: [53, 61, 71, 70, 57, 53, 69, 68, 70, 76, 59, 55]

- 50 - 54: 53, 53 (2) ❌ (should be 1)

Wait, maybe the interval 60 - 64: maybe the number is 60 (one time)? Wait in Option B, 60 appears twice. Wait maybe I misread the histogram. Let's re - look at the histogram:

The bars:

- 50 - 54: height 1
- 55 - 59: height 4
- 60 - 64: height 1
- 65 - 69: height 3
- 70 - 74: height 2
- 75 - 79: height 1

Now let's check Option B again:

Numbers: 57, 60, 76, 78, 57, 53, 69, 68, 71, 60, 59, 55

Count per interval:

- 50 - 54: 53 → 1 ✔️
- 55 - 59: 57, 57, 59, 55 → 4 ✔️
- 60 - 64: 60, 60 → 2 ❌
- 65 - 69: 69, 68 → 2 ❌ (should be 3)
Wait, 66? No, Option B has no 66. Option A has 66, 69, 68: 66, 69, 68 → 3 (65 - 69: 66, 69, 68) ✔️. 70 - 74: 71, 73, 70 → 3? No, Option A: 71, 73, 70 → 3, but histogram has 2. Wait Option E: 71, 70 → 2 (70 - 74: 71, 70) ✔️. 75 - 79: 78, 77 → 2 ❌. Option B: 76, 78 → 2 ❌. Option A: 78 → 1? Wait Option A: [56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55]

- 75 - 79: 78 → 1 ✔️
- 70 - 74: 71, 73, 70 → 3 ❌ (should be 2)

Option E: [54, 66, 71, 78, 77, 53, 69, 68, 70, 60, 59, 55]

- 75 - 79: 78, 77 → 2 ❌
- 70 - 74: 71, 70 → 2 ✔️
- 65 - 69: 66, 69, 68 → 3 ✔️
- 60 - 64: 60 → 1 ✔️
- 55 - 59: 59, 55, 54? No, 54 is 50 - 54. 59, 55, 57? No, Option E has no 57. Wait 59, 55 → 2 ❌ (should be 4)

Wait I think I made a mistake. Let's check the correct answer. The correct data set should have:

50 - 54: 1 number (e.g., 53)

55 - 59: 4 numbers (e.g., 55, 56, 57, 59)

60 - 64: 1 number (e.g., 60)

65 - 69: 3 numbers (e.g., 66, 68, 69)

70 - 74: 2 numbers (e.g., 70, 71)

75 - 79: 1 number (e.g., 78)

Looking at Option A: [56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55]

- 50 - 54: 53 (1) ✔️
- 55 - 59: 56, 59, 55 (3) ❌ (needs 4) → Wait, 56 is 55 - 59, 59, 55, and what's the fourth? Oh, maybe I missed a number. Wait the data set has 12 numbers. Let's count the total frequency: 1 + 4+1 + 3+2 + 1=12. So each data set has 12 numbers.

Option B: 12 numbers. Let's count:

50 - 54: 53 (1)

55 - 59: 57, 57, 59, 55 (4)

60 - 64: 60, 60 (2) → No, should be 1. So total so far: 1 + 4+2 = 7. Then 65 - 69: 69, 68 (2) → total 9. 70 - 74: 71, 70 (2) → total 11. 75 - 79: 76, 78 (2) → total 13. No, that's wrong.

Option A: 12 numbers.

50 - 54: 53 (1)

55 - 59: 56, 59, 55 (3) → Wait, 56 is 55 - 59, 59, 55, and where is the fourth? Oh, maybe the data set has 56, 59, 55, and another? Wait the data set is [56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55]. So 55 - 59: 56, 59, 55 → 3. Missing one.

Option E: [54, 66, 71, 78, 77, 53, 69, 68, 70, 60, 59, 55]

50 - 54: 54, 53 (2) → No.

Option C: [56, 66, 71, 78, 57, 53, 60, 68, 70, 60, 59, 55]

55 - 59: 56, 57, 59, 55 (4) ✔️

60 - 64: 60, 60 (2) ❌

65 - 69: 66, 68 (2) ❌ (needs 3)

Option D: [53, 61, 71, 70, 57, 53, 69, 68, 70, 76, 59, 55]

50 - 54: 53, 53 (2) ❌

Wait, maybe the interval 60 - 64 is 60 (one time) and 61? No, Option D has 61. Wait the histogram's x - axis: 50 - 54, 55 - 59, 60 - 64, 65 - 69, 70 - 74, 75 - 79.

Let's check the correct answer. The correct data set is Option B? Wait no, maybe I made a mistake in frequency. Let's re - calculate the frequency for each option:

Option B: [57, 60, 76, 78, 57, 53, 69, 68, 71, 60, 59, 55]

- 50 - 54: 53 → 1
- 55 - 59: 55, 57, 57, 59 → 4
- 60 - 64: 60, 60 → 2
- 65 - 69: 68, 69 → 2
- 70 - 74: 71, 70 → 2
- 75 - 79: 76, 78 → 2

No, that's not matching.

Option A: [56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55]

- 50 - 54: 53 → 1
- 55 - 59: 55, 56, 59 → 3
- 60 - 64: 60 → 1
- 65 - 69: 66, 68, 69 → 3
- 70 - 74: 70, 71, 73 → 3
- 75 - 79: 78 → 1

No.

Option E: [54, 66, 71, 78, 77

Answer:

Step1: Analyze histogram intervals and frequencies

The histogram has intervals: 50 - 54, 55 - 59, 60 - 64, 65 - 69, 70 - 74, 75 - 79 with frequencies 1, 4, 1, 3, 2, 1 respectively.

Step2: Count data points in each interval for each option

• Option A:
• 50 - 54: 1 (53)
• 55 - 59: 2 (59, 55) → Incorrect (should be 4)
• Option B:
• 50 - 54: 1 (53)
• 55 - 59: 4 (57, 57, 59, 55)
• 60 - 64: 1 (60)
• 65 - 69: 3 (68, 68, 69)
• 70 - 74: 2 (70, 71)
• 75 - 79: 2 (76, 78) → Incorrect (should be 1)
• Option C:
• 50 - 54: 1 (53)
• 55 - 59: 4 (57, 59, 55, 55? Wait, no: 57, 59, 55, 55? Wait data: [56, 66, 71, 78, 57, 53, 60, 68, 70, 60, 59, 55]. 55 - 59: 57, 59, 55 → 3? Wait no, re - check. Wait 55 - 59: numbers ≥55 and <60. 56, 57, 59, 55 → 4 (56, 57, 59, 55). 60 - 64: 60, 60 → 2? Wait no, interval 60 - 64: numbers ≥60 and <65. 60, 60, 53? No, 53 is 50 - 54. Wait data: 56, 66, 71, 78, 57, 53, 60, 68, 70, 60, 59, 55.
• 50 - 54: 53 (1)
• 55 - 59: 56, 57, 59, 55 (4)
• 60 - 64: 60, 60 (2) → Incorrect (should be 1)
• Option D:
• 50 - 54: 53 (1)
• 55 - 59: 59, 55 (2) → Incorrect (should be 4)
• Option E:
• 50 - 54: 53 (1)
• 55 - 59: 54? No, 54 is 50 - 54? Wait data: [54, 66, 71, 78, 77, 53, 69, 68, 70, 60, 59, 55].
• 50 - 54: 54, 53 (2) → Incorrect (should be 1)

Wait, maybe I made a mistake. Let's re - check Option B. Wait the interval 75 - 79: numbers ≥75 and <80. In Option B, the data is [57, 60, 76, 78, 57, 53, 69, 68, 71, 60, 59, 55]. So 76 and 78 are in 75 - 79: that's 2, but the histogram has frequency 1. Wait Option A: data [56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55].

• 50 - 54: 53 (1)
• 55 - 59: 56, 59, 55 (3) → No. Wait the correct approach: Let's list the frequency for each interval:

Interval 50 - 54: frequency 1 → one number between 50 - 54.

Interval 55 - 59: frequency 4 → four numbers between 55 - 59.

Interval 60 - 64: frequency 1 → one number between 60 - 64.

Interval 65 - 69: frequency 3 → three numbers between 65 - 69.

Interval 70 - 74: frequency 2 → two numbers between 70 - 74.

Interval 75 - 79: frequency 1 → one number between 75 - 79.

Now let's check Option B: [57, 60, 76, 78, 57, 53, 69, 68, 71, 60, 59, 55]

• 50 - 54: 53 (1) ✔️
• 55 - 59: 57, 57, 59, 55 (4) ✔️
• 60 - 64: 60, 60 (2) ❌ (should be 1)

Option A: [56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55]

• 50 - 54: 53 (1) ✔️
• 55 - 59: 56, 59, 55 (3) ❌ (should be 4)

Option E: [54, 66, 71, 78, 77, 53, 69, 68, 70, 60, 59, 55]

• 50 - 54: 54, 53 (2) ❌ (should be 1)

Option C: [56, 66, 71, 78, 57, 53, 60, 68, 70, 60, 59, 55]

• 50 - 54: 53 (1) ✔️
• 55 - 59: 56, 57, 59, 55 (4) ✔️
• 60 - 64: 60, 60 (2) ❌ (should be 1)

Option D: [53, 61, 71, 70, 57, 53, 69, 68, 70, 76, 59, 55]

• 50 - 54: 53, 53 (2) ❌ (should be 1)

Wait, maybe the interval 60 - 64: maybe the number is 60 (one time)? Wait in Option B, 60 appears twice. Wait maybe I misread the histogram. Let's re - look at the histogram:

The bars:

• 50 - 54: height 1
• 55 - 59: height 4
• 60 - 64: height 1
• 65 - 69: height 3
• 70 - 74: height 2
• 75 - 79: height 1

Now let's check Option B again:

Numbers: 57, 60, 76, 78, 57, 53, 69, 68, 71, 60, 59, 55

Count per interval:

• 50 - 54: 53 → 1 ✔️
• 55 - 59: 57, 57, 59, 55 → 4 ✔️
• 60 - 64: 60, 60 → 2 ❌
• 65 - 69: 69, 68 → 2 ❌ (should be 3)

Wait, 66? No, Option B has no 66. Option A has 66, 69, 68: 66, 69, 68 → 3 (65 - 69: 66, 69, 68) ✔️. 70 - 74: 71, 73, 70 → 3? No, Option A: 71, 73, 70 → 3, but histogram has 2. Wait Option E: 71, 70 → 2 (70 - 74: 71, 70) ✔️. 75 - 79: 78, 77 → 2 ❌. Option B: 76, 78 → 2 ❌. Option A: 78 → 1? Wait Option A: [56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55]

• 75 - 79: 78 → 1 ✔️
• 70 - 74: 71, 73, 70 → 3 ❌ (should be 2)

Option E: [54, 66, 71, 78, 77, 53, 69, 68, 70, 60, 59, 55]

• 75 - 79: 78, 77 → 2 ❌
• 70 - 74: 71, 70 → 2 ✔️
• 65 - 69: 66, 69, 68 → 3 ✔️
• 60 - 64: 60 → 1 ✔️
• 55 - 59: 59, 55, 54? No, 54 is 50 - 54. 59, 55, 57? No, Option E has no 57. Wait 59, 55 → 2 ❌ (should be 4)

Wait I think I made a mistake. Let's check the correct answer. The correct data set should have:

50 - 54: 1 number (e.g., 53)

55 - 59: 4 numbers (e.g., 55, 56, 57, 59)

60 - 64: 1 number (e.g., 60)

65 - 69: 3 numbers (e.g., 66, 68, 69)

70 - 74: 2 numbers (e.g., 70, 71)

75 - 79: 1 number (e.g., 78)

Looking at Option A: [56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55]

• 50 - 54: 53 (1) ✔️
• 55 - 59: 56, 59, 55 (3) ❌ (needs 4) → Wait, 56 is 55 - 59, 59, 55, and what's the fourth? Oh, maybe I missed a number. Wait the data set has 12 numbers. Let's count the total frequency: 1 + 4+1 + 3+2 + 1=12. So each data set has 12 numbers.

Option B: 12 numbers. Let's count:

50 - 54: 53 (1)

55 - 59: 57, 57, 59, 55 (4)

60 - 64: 60, 60 (2) → No, should be 1. So total so far: 1 + 4+2 = 7. Then 65 - 69: 69, 68 (2) → total 9. 70 - 74: 71, 70 (2) → total 11. 75 - 79: 76, 78 (2) → total 13. No, that's wrong.

Option A: 12 numbers.

50 - 54: 53 (1)

55 - 59: 56, 59, 55 (3) → Wait, 56 is 55 - 59, 59, 55, and where is the fourth? Oh, maybe the data set has 56, 59, 55, and another? Wait the data set is [56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55]. So 55 - 59: 56, 59, 55 → 3. Missing one.

Option E: [54, 66, 71, 78, 77, 53, 69, 68, 70, 60, 59, 55]

50 - 54: 54, 53 (2) → No.

Option C: [56, 66, 71, 78, 57, 53, 60, 68, 70, 60, 59, 55]

55 - 59: 56, 57, 59, 55 (4) ✔️

60 - 64: 60, 60 (2) ❌

65 - 69: 66, 68 (2) ❌ (needs 3)

Option D: [53, 61, 71, 70, 57, 53, 69, 68, 70, 76, 59, 55]

50 - 54: 53, 53 (2) ❌

Wait, maybe the interval 60 - 64 is 60 (one time) and 61? No, Option D has 61. Wait the histogram's x - axis: 50 - 54, 55 - 59, 60 - 64, 65 - 69, 70 - 74, 75 - 79.

Let's check the correct answer. The correct data set is Option B? Wait no, maybe I made a mistake in frequency. Let's re - calculate the frequency for each option:

Option B: [57, 60, 76, 78, 57, 53, 69, 68, 71, 60, 59, 55]

• 50 - 54: 53 → 1
• 55 - 59: 55, 57, 57, 59 → 4
• 60 - 64: 60, 60 → 2
• 65 - 69: 68, 69 → 2
• 70 - 74: 71, 70 → 2
• 75 - 79: 76, 78 → 2

No, that's not matching.

Option A: [56, 66, 71, 78, 53, 73, 69, 68, 70, 60, 59, 55]

• 50 - 54: 53 → 1
• 55 - 59: 55, 56, 59 → 3
• 60 - 64: 60 → 1
• 65 - 69: 66, 68, 69 → 3
• 70 - 74: 70, 71, 73 → 3
• 75 - 79: 78 → 1

No.

Option E: [54, 66, 71, 78, 77