Question

​Find the Mean, Median, Mode and Range for the set of numbers below.
​

5, 7, 2, 7, 9, 6, 8, 4

​

​Mean =


​

​Median =


​

​Mode =


​

​Range =

Answer 1

To find the Mean, Median, Mode, and Range for the set of numbers \(5, 7, 2, 7, 9, 6, 8, 4\), we can follow these steps:

### 1. Mean
The mean is calculated as the sum of all the numbers divided by the count of the numbers.

Sum of the numbers:
\(5 + 7 + 2 + 7 + 9 + 6 + 8 + 4 = 48\)

Count of the numbers:
There are \(8\) numbers.

Mean:
\[
\text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{48}{8} = 6
\]

### 2. Median
The median is the middle value of a sorted list. First, we sort the numbers:

Sorted numbers:
\(2, 4, 5, 6, 7, 7, 8, 9\)

Since there are \(8\) (an even number of) values, the median will be the average of the two middle numbers, which are the 4th and 5th numbers (6 and 7).

Median:
\[
\text{Median} = \frac{6 + 7}{2} = \frac{13}{2} = 6.5
\]

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

In the given set \(5, 7, 2, 7, 9, 6, 8, 4\), the number \(7\) appears twice, which is more frequent than any other number.

Mode:
\[
\text{Mode} = 7
\]

### 4. Range
The range is the difference between the highest and lowest values.

Highest value: \(9\)
Lowest value: \(2\)

Range:
\[
\text{Range} = \text{Highest} - \text{Lowest} = 9 - 2 = 7
\]

### Summary
- Mean = \(6\)
- Median = \(6.5\)
- Mode = \(7\)
- Range = \(7\)