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The task is to find the mean, median, and standard deviation of the annual earnings of ten prominent CEOs in South Africa in 2016, listed in R million. Here are the earnings:
- Bernard Fornas: 87.9
- Hendrik du Toit: 86.1
- Richard Lepeu: 85.1
- Mark Cutifani: 66.9
- David Hathorn: 66.8
- Nicandro Durante: 59.5
- David Constable: 51.9
- Glyn Lewis: 51.5
- Whitey Basson: 49.9
- Alan Clark: 49.7
1. Mean (Average):
To find the mean, add up all the annual earnings and divide by the number of CEOs.
[tex]\[
\text{Mean} = \frac{87.9 + 86.1 + 85.1 + 66.9 + 66.8 + 59.5 + 51.9 + 51.5 + 49.9 + 49.7}{10}
\][/tex]
When you calculate this, the mean salary comes out to approximately 65.53 million Rands.
2. Median:
To determine the median, you need to arrange the salaries in ascending order and find the middle value. If there is an even number of observations, the median will be the average of the two middle numbers.
Arranged salaries: 49.7, 49.9, 51.5, 51.9, 59.5, 66.8, 66.9, 85.1, 86.1, 87.9
Here, there are ten salaries, so the middle two numbers are the 5th and 6th in this ordered list (59.5 and 66.8).
[tex]\[
\text{Median} = \frac{59.5 + 66.8}{2}
\][/tex]
Therefore, the median salary is 63.15 million Rands.
3. Standard Deviation:
The standard deviation measures how spread out the numbers are around the mean. It involves the following steps:
- Calculate the mean.
- Subtract the mean from each salary to find the difference.
- Square each difference.
- Find the average of these squared differences.
- Take the square root of this average to find the standard deviation.
After carrying out these steps, the standard deviation of the salaries is approximately 14.91 million Rands.
These calculations provide a clear understanding of the earnings distribution among the ten CEOs. The mean gives us an average earning, the median shows the middle earning in the sorted list, and the standard deviation indicates how varied the earnings are from the average.
The task is to find the mean, median, and standard deviation of the annual earnings of ten prominent CEOs in South Africa in 2016, listed in R million. Here are the earnings:
- Bernard Fornas: 87.9
- Hendrik du Toit: 86.1
- Richard Lepeu: 85.1
- Mark Cutifani: 66.9
- David Hathorn: 66.8
- Nicandro Durante: 59.5
- David Constable: 51.9
- Glyn Lewis: 51.5
- Whitey Basson: 49.9
- Alan Clark: 49.7
1. Mean (Average):
To find the mean, add up all the annual earnings and divide by the number of CEOs.
[tex]\[
\text{Mean} = \frac{87.9 + 86.1 + 85.1 + 66.9 + 66.8 + 59.5 + 51.9 + 51.5 + 49.9 + 49.7}{10}
\][/tex]
When you calculate this, the mean salary comes out to approximately 65.53 million Rands.
2. Median:
To determine the median, you need to arrange the salaries in ascending order and find the middle value. If there is an even number of observations, the median will be the average of the two middle numbers.
Arranged salaries: 49.7, 49.9, 51.5, 51.9, 59.5, 66.8, 66.9, 85.1, 86.1, 87.9
Here, there are ten salaries, so the middle two numbers are the 5th and 6th in this ordered list (59.5 and 66.8).
[tex]\[
\text{Median} = \frac{59.5 + 66.8}{2}
\][/tex]
Therefore, the median salary is 63.15 million Rands.
3. Standard Deviation:
The standard deviation measures how spread out the numbers are around the mean. It involves the following steps:
- Calculate the mean.
- Subtract the mean from each salary to find the difference.
- Square each difference.
- Find the average of these squared differences.
- Take the square root of this average to find the standard deviation.
After carrying out these steps, the standard deviation of the salaries is approximately 14.91 million Rands.
These calculations provide a clear understanding of the earnings distribution among the ten CEOs. The mean gives us an average earning, the median shows the middle earning in the sorted list, and the standard deviation indicates how varied the earnings are from the average.
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