Question

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Comparing Data Distributions Quick Check
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Question
The data shows the number of seconds it took two randomly selected groups to thread a needle. Compare the measures of center and variability of these data sets.

Student Group A: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
Student Group B: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20

Which of the following statements about these data sets is false?

(1 point)
Responses

The amount of variability of the time taken by Group A to thread a needle is higher than the amount of variability of the time taken by Group B.
The amount of variability of the time taken by Group A to thread a needle is higher than the amount of variability of the time taken by Group B.

The ranges of the time taken by Group A and Group B are the same.
The ranges of the time taken by Group A and Group B are the same.

The median time taken by members of Group A to thread a needle is higher than that of members of Group B.
The median time taken by members of Group A to thread a needle is higher than that of members of Group B.

The mean time taken by Group A is higher than that of Group B.
The mean time taken by Group A is higher than that of Group B.
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Answer 1

To evaluate the statements about the data sets from Group A and Group B, we first need to calculate the key measures of center and variability: the mean, median, and range for each group.

### Group A Data:
56, 14, 26, 28, 29, 45, 32, 80, 3, 10

**Calculations:**

1. **Mean**:
\[
\text{Mean} = \frac{56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10}{10} = \frac{ 56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10 }{10} = \frac{ 343 }{10} = 34.3
\]

2. **Median**:
- Sort the data: 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
- Middle values: 28 and 29
\[
\text{Median} = \frac{28 + 29}{2} = 28.5
\]

3. **Range**:
\[
\text{Range} = 80 - 3 = 77
\]

### Group B Data:
27, 24, 18, 19, 5, 16, 22, 10, 6, 20

**Calculations:**

1. **Mean**:
\[
\text{Mean} = \frac{27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20}{10} = \frac{ 27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20 }{10} = \frac{ 147 }{10} = 14.7
\]

2. **Median**:
- Sort the data: 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
- Middle values: 18 and 19
\[
\text{Median} = \frac{18 + 19}{2} = 18.5
\]

3. **Range**:
\[
\text{Range} = 27 - 5 = 22
\]

### Summary of the data:

- **Group A**:
- Mean: 34.3
- Median: 28.5
- Range: 77

- **Group B**:
- Mean: 14.7
- Median: 18.5
- Range: 22

### Evaluating the Statements:

1. **Variability**:
- Correct statement: **Group A's variability (Range = 77) is higher than Group B's variability (Range = 22).**

2. **Range**:
- False statement: The **ranges are not the same**. Group A has a range of 77 and Group B has a range of 22.

3. **Median**:
- Correct statement: The **median time taken by Group A (28.5) is higher than that of Group B (18.5)**.

4. **Mean**:
- Correct statement: The **mean time taken by Group A (34.3) is higher than that of Group B (14.7)**.

### Conclusion:
The false statement is: **The ranges of the time taken by Group A and Group B are the same.**