Let's solve this step by step.
### Step 1: Determine the sixth number
Given:
- The mean value of six numbers is 50.
- Five of the numbers are 44, 50, 56, 48, and 40.
To find the sixth number, follow these steps:
1. Calculate the total sum needed for six numbers to have a mean of 50.
- [tex]\(\text{Total Sum} = \text{Mean} \times \text{Number of Values} = 50 \times 6 = 300\)[/tex]
2. Calculate the sum of the given five numbers:
- [tex]\(44 + 50 + 56 + 48 + 40 = 238\)[/tex]
3. Determine the sixth number by subtracting the sum of the five numbers from the total sum:
- [tex]\(\text{Sixth Number} = 300 - 238 = 62\)[/tex]
So, the sixth number is 62.
### Step 2: Calculate the mean and median of all six numbers
Now we have the six numbers: 44, 50, 56, 48, 40, and 62.
#### Mean
1. Add all the numbers together:
- [tex]\(44 + 50 + 56 + 48 + 40 + 62 = 300\)[/tex]
2. Divide the sum by the number of values (6):
- [tex]\(\text{Mean} = \frac{300}{6} = 50.0\)[/tex]
So, the mean of these numbers is 50.0.
#### Median
1. Arrange the numbers in ascending order:
- 40, 44, 48, 50, 56, 62
2. Since we have an even number of values (6), the median is the average of the two middle numbers. The middle numbers are the 3rd and 4th values in the sorted list:
- The two middle numbers are 48 and 50.
3. Calculate the median:
- [tex]\(\text{Median} = \frac{48 + 50}{2} = 49.0\)[/tex]
So, the median of these numbers is 49.0.
### Summary
- The sixth number is 62.
- The mean of all six numbers is 50.0.
- The median of all six numbers is 49.0.
