Question

Find the mode, median and mean for each data set.
Minutes to Run 3 miles

30, 30.7, 35.4, 27.9, 27, 29.4, 35.2, 32, 35.9, 35.7

Answer 1

To find the mode, median, and mean for the given data set of minutes to run 3 miles, we first need to organize the data.

### Given Data:
30, 30.7, 35.4, 27.9, 27, 29.4, 35.2, 32, 35.9, 35.7

### Step 1: Sort the Data
First, let's sort the data in ascending order:

27, 27.9, 29.4, 30, 30.7, 32, 35.2, 35.4, 35.7, 35.9

### Step 2: Find the Mode
The mode is the number that appears most frequently in the data set.

In this case, all the values are unique; thus, there is no mode.

**Mode: None**

### Step 3: Find the Median
The median is the middle value of a data set when it is ordered. If the data set has an even number of observations, the median is the average of the two middle numbers.

Since there are 10 data points (even number), we find the median by averaging the 5th and 6th values in the sorted list:

5th value = 30.7
6th value = 32

Median = (30.7 + 32) / 2 = 31.35

**Median: 31.35**

### Step 4: Find the Mean
The mean is calculated by adding all the data points together and dividing by the number of data points.

Mean = (27 + 27.9 + 29.4 + 30 + 30.7 + 32 + 35.2 + 35.4 + 35.7 + 35.9) / 10

First, we calculate the sum:

Sum = 27 + 27.9 + 29.4 + 30 + 30.7 + 32 + 35.2 + 35.4 + 35.7 + 35.9 = 31.83

Mean = 31.83 / 10 = 31.83

**Mean: 31.83**

### Summary:
- **Mode:** None
- **Median:** 31.35
- **Mean:** 31.83