Question

Find the mean, median, and modes of the data set: 91, 93, 89, 97, 89, 98, 94, 93.(2 points)
The mean is
.
The median is
.
The first mode in the data set is
.
The second mode in the data set is
.
Sorry, that’s only partially correct

To find the mean, add the values of the dataset up and divide by the total number of values.
Remaining Attempts : 1
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Answer 1

Let's calculate the mean, median, and modes for the data set: 91, 93, 89, 97, 89, 98, 94, 93.

### Step 1: Calculate the Mean
1. **Sum the values**:
\( 91 + 93 + 89 + 97 + 89 + 98 + 94 + 93 = 884 \)

2. **Count the number of values**:
There are 8 values in the dataset.

3. **Calculate the mean**:
\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{884}{8} = 110.5
\]

### Step 2: Calculate the Median
1. **Sort the data**:
89, 89, 91, 93, 93, 94, 97, 98

2. **Find the median**:
Since there are 8 values (an even number), the median is the average of the 4th and 5th numbers.
- 4th number: 93
- 5th number: 93

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

### Step 3: Calculate the Modes
1. **Identify the frequency of each number**:
- 89 appears 2 times
- 91 appears 1 time
- 93 appears 2 times
- 94 appears 1 time
- 97 appears 1 time
- 98 appears 1 time

2. **Modes**:
The values that appear most frequently are 89 and 93. Since both appear 2 times, they are both modes.

### Final Answers
- The mean is **110.5**.
- The median is **93**.
- The first mode in the data set is **89**.
- The second mode in the data set is **93**.

**So the revised answers are:**
- Mean: 110.5
- Median: 93
- First mode: 89
- Second mode: 93