Sure! Let's go through the question step-by-step in a detailed manner:
### 1. Calculate the Sum
The sum of the numbers in the dataset can be found by adding all the numbers together.
[tex]\[ \text{Sum} = 78 + 6 + 4 + 64 \][/tex]
Adding them step by step:
[tex]\[ 78 + 6 = 84 \][/tex]
[tex]\[ 84 + 4 = 88 \][/tex]
[tex]\[ 88 + 64 = 152 \][/tex]
So, the total sum of the numbers is [tex]\( 152 \)[/tex].
### 2. Find the Maximum Value
The maximum value in the dataset is the largest number among the given numbers.
We compare all the numbers:
[tex]\[ 78, 6, 4, 64 \][/tex]
Clearly, 78 is the largest number.
So, the maximum value is [tex]\( 78 \)[/tex].
### 3. Calculate the Mean
The mean (or average) is calculated by dividing the sum of the numbers by the number of values in the dataset.
Given that we already calculated the sum as [tex]\( 152 \)[/tex] and there are 4 numbers in the dataset:
[tex]\[ \text{Mean} = \frac{\text{Sum}}{\text{Number of Values}} = \frac{152}{4} \][/tex]
Dividing:
[tex]\[ \frac{152}{4} = 38 \][/tex]
So, the mean of the numbers is [tex]\( 38.0 \)[/tex].
### Summary of Results
- Sum: [tex]\( 152 \)[/tex]
- Maximum Value: [tex]\( 78 \)[/tex]
- Mean: [tex]\( 38.0 \)[/tex]
These are the three key results based on the given dataset.
