Question

Determine which data set has a greater mean and a greater median.
  
Student A
Student B
32
33
34
35
36
37
32
33
34
35
36
37
Text Messages per Day
Text Messages per Day
Question content area bottom
Part 1
Which data set has a greater​ mean?
Student Upper B
Student Upper B
Student Upper A
Student Upper A
Part 2
Which data set has a greater​ median?

Answer 1

To determine which data set has a greater mean and median, we'll first calculate both for each student.

### Data for Student A:
- Text messages: 32, 33, 34, 35, 36, 37

### Data for Student B:
- Text messages: 32, 33, 34, 35, 36, 37

#### Calculation of the Mean:

**Mean for both students:**
Mean = (Sum of all values) / (Number of values)

- For Student A:
\[
\text{Mean}_A = \frac{32 + 33 + 34 + 35 + 36 + 37}{6} = \frac{207}{6} = 34.5
\]

- For Student B:
\[
\text{Mean}_B = \frac{32 + 33 + 34 + 35 + 36 + 37}{6} = \frac{207}{6} = 34.5
\]

**Mean Comparison:**
- Mean_A = 34.5
- Mean_B = 34.5

Both students have the same mean.

#### Calculation of the Median:

**Median calculation:**
To find the median, we need to arrange the data in order and find the middle value. Since both data sets are identical and consist of the same six numbers:

- For Student A:
- Ordered values: 32, 33, 34, 35, 36, 37
- Median = (34 + 35) / 2 = 34.5 (as there are an even number of values)

- For Student B:
- Ordered values: 32, 33, 34, 35, 36, 37
- Median = (34 + 35) / 2 = 34.5

**Median Comparison:**
- Median_A = 34.5
- Median_B = 34.5

Both students have the same median.

### Conclusion:
- **Part 1:** Which data set has a greater mean? **Neither, they are the same (34.5).**
- **Part 2:** Which data set has a greater median? **Neither, they are the same (34.5).**

Both the mean and median for Student A and Student B are equal.