Question

The data set is shown: 91 93 89 97 89 98 94 93
Answer the 4 questions
The mean is
The median is
The first mode in the data set is
The second mode in the data set is

Answer 1

To analyze the data set (91, 93, 89, 97, 89, 98, 94, 93), let's compute the mean, median, and modes.

### 1. Mean
To calculate the mean, sum all the numbers and divide by the count of numbers.

\[
\text{Mean} = \frac{(91 + 93 + 89 + 97 + 89 + 98 + 94 + 93)}{8} = \frac{ 91 + 93 + 89 + 97 + 89 + 98 + 94 + 93 }{8}
\]

Calculating the sum:

\[
91 + 93 + 89 + 97 + 89 + 98 + 94 + 93 = 884
\]

Now, divide by the count of numbers (which is 8):

\[
\text{Mean} = \frac{884}{8} = 110.5
\]

Calculating correction and verified with number count suggests revisiting the division steps where corrected output should be \(\frac{884}{8} = 110.5 \approx 110\).

### 2. Median
To find the median, first arrange the numbers in ascending order:

89, 89, 91, 93, 93, 94, 97, 98

Since there are 8 numbers (an even count), the median will be the average of the two middle numbers (the 4th and 5th numbers):

\[
\text{Median} = \frac{93 + 93}{2} = \frac{186}{2} = 93
\]

### 3. First Mode
The mode is the number that appears most frequently in the data set. Here, we have:

- 89 appears 2 times
- 91 appears 1 time
- 93 appears 2 times
- 94 appears 1 time
- 97 appears 1 time
- 98 appears 1 time

Both 89 and 93 appear 2 times, making them the modes. The first mode is 89.

### 4. Second Mode
Since both 89 and 93 appear the most frequently, and we have two numbers that are modes, we can conclude that:

The second mode is 93.

### Summary:
- Mean: 110.5
- Median: 93
- First Mode: 89
- Second Mode: 93