Question

Find the mean median mode and range of five, six, six, seven, seven, seven, eight, eight, eight, eight

Answer 1

To find the mean, median, mode, and range of the dataset {5, 6, 6, 7, 7, 7, 8, 8, 8, 8}, we follow these steps:

1. **Mean**: The mean is the average of the numbers.

\[
\text{Mean} = \frac{\sum \text{all data points}}{\text{number of data points}}
\]

Sum of all data points:

\[
5 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 8 + 8 = 70
\]

Number of data points:

\[
10
\]

So, the mean is:

\[
\text{Mean} = \frac{70}{10} = 7
\]

2. **Median**: The median is the middle value of the dataset when it is ordered. Since the dataset has an even number of elements (10), the median will be the average of the 5th and 6th values.

Ordered dataset:

\{5, 6, 6, 7, 7, 7, 8, 8, 8, 8\}.

The 5th and 6th values are both 7.

\[
\text{Median} = \frac{7+7}{2} = \frac{14}{2} = 7
\]

3. **Mode**: The mode is the number that appears most frequently in the dataset.

Here, the value 8 appears four times, which is more frequent than any other number.

So, the mode is:

\[
\text{Mode} = 8
\]

4. **Range**: The range is the difference between the highest and lowest values in the dataset.

Highest value:

\[
8
\]

Lowest value:

\[
5
\]

So, the range is:

\[
\text{Range} = 8 - 5 = 3
\]

To summarize:

- Mean = 7
- Median = 7
- Mode = 8
- Range = 3