Question

Select the mean, median, mode and range of the following list of values.
​ 1,2,4,71,2,4,71,2,4,7
Averages
3.5
3.5
None
3
3
6
6
Mean




Median




Range




Mode

Answer 1

To calculate the mean, median, mode, and range of the list of values \(1, 2, 4, 71, 2, 4, 71, 2, 4, 7\), let's go through each step:

### Step 1: Mean
The mean is calculated by summing all the values and dividing by the number of values.

\[
\text{Sum} = 1 + 2 + 4 + 71 + 2 + 4 + 71 + 2 + 4 + 7 = 168
\]
\[
\text{Number of values} = 10
\]
\[
\text{Mean} = \frac{168}{10} = 16.8
\]

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

Ordered list: \(1, 2, 2, 2, 4, 4, 4, 7, 71, 71\)

The median is the average of the middle two numbers in an ordered list of an even number of observations.

\[
\text{Middle two numbers} = 4, 4
\]
\[
\text{Median} = \frac{4 + 4}{2} = 4
\]

### Step 3: Mode
The mode is the number that appears most frequently in a data set.

In this case:
- \(1\) appears 1 time,
- \(2\) appears 3 times,
- \(4\) appears 3 times,
- \(7\) appears 1 time,
- \(71\) appears 2 times.

Since \(2\) and \(4\) both appear most frequently (3 times), this dataset is bimodal.

\[
\text{Modes} = 2, 4
\]

### Step 4: Range
The range is calculated by subtracting the smallest value from the largest value.

\[
\text{Range} = 71 - 1 = 70
\]

### Summary:
- **Mean:** 16.8
- **Median:** 4
- **Mode:** 2, 4 (bimodal)
- **Range:** 70

None of the provided options (like 3, 3, 6, etc.) seem to be correct based on the calculations. The values provided do not match the actual mean, median, mode, or range of the dataset provided.