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 ______.

Answer 1

To find the mean, median, and modes of the data set \( 91, 93, 89, 97, 89, 98, 94, 93 \), we can follow these steps:

### Step 1: Calculate the Mean
The mean is calculated by summing all the numbers and dividing by the total count of numbers.

\[
\text{Mean} = \frac{91 + 93 + 89 + 97 + 89 + 98 + 94 + 93}{8}
\]
Calculating the sum:
\[
91 + 93 + 89 + 97 + 89 + 98 + 94 + 93 = 91 + 93 = 184
\]
\[
184 + 89 = 273
\]
\[
273 + 97 = 370
\]
\[
370 + 89 = 459
\]
\[
459 + 98 = 557
\]
\[
557 + 94 = 651
\]
\[
651 + 93 = 744
\]

Now divide by 8:
\[
\text{Mean} = \frac{744}{8} = 93
\]

### Step 2: Calculate the Median
To find the median, we first need to sort the data in ascending order:
\[
89, 89, 91, 93, 93, 94, 97, 98
\]

Since there are 8 numbers (an even number), the median is the average of the two middle numbers (4th and 5th):
The two middle numbers are \(93\) and \(93\):
\[
\text{Median} = \frac{93 + 93}{2} = \frac{186}{2} = 93
\]

### Step 3: Identify the Modes
The mode is the number that appears most frequently in the data set. In our sorted data:
\[
89, 89, 91, 93, 93, 94, 97, 98
\]
We can see:
- \(89\) occurs 2 times.
- \(93\) occurs 2 times.

Since both modes occur with the highest frequency, we can report them as:
- The first mode is \(89\).
- The second mode is \(93\).

### Summary of Results
- The mean is **93**.
- The median is **93**.
- The first mode in the data set is **89**.
- The second mode in the data set is **93**.