To determine which company has higher salaries, you can use the mean, median, or mode as measures of center. Let's calculate each of these measures for the given data:
Company A salaries: 45,000, 55,000, 53,000, 51,000, 49,000, and 42,000.
Mean (Average):
To calculate the mean, sum up all the salaries and divide by the total number of salaries.
Mean of Company A salaries = (45,000 + 55,000 + 53,000 + 51,000 + 49,000 + 42,000) / 6 = 295,000 / 6 = 49,167
Median:
To find the median, you arrange the salaries in ascending order and find the middle value. If there is an even number of values, you take the average of the two middle values.
Arranging the Company A salaries in ascending order: 42,000, 45,000, 49,000, 51,000, 53,000, 55,000
Median of Company A salaries = (49,000 + 51,000) / 2 = 50,000
Mode:
The mode represents the value(s) that appear most frequently in the dataset.
In Company A salaries, all the values occur only once, so there is no mode.
Now let's calculate the same measures for Company B salaries:
Company B salaries: 54,000, 39,000, 51,000, 52,000, 44,000, and 48,000.
Mean of Company B salaries = (54,000 + 39,000 + 51,000 + 52,000 + 44,000 + 48,000) / 6 = 288,000 / 6 = 48,000
Arranging the Company B salaries in ascending order: 39,000, 44,000, 48,000, 51,000, 52,000, 54,000
Median of Company B salaries = (48,000 + 51,000) / 2 = 49,500
Mode of Company B salaries = There are no repeating values, so there is no mode.
To summarize:
- Mean of Company A salaries: $49,167
- Median of Company A salaries: $50,000
- Mode of Company A salaries: No mode
- Mean of Company B salaries: $48,000
- Median of Company B salaries: $49,500
- Mode of Company B salaries: No mode
Based on these measures of center, we can see that the mean and median salaries of Company A are slightly higher than those of Company B. However, since there is no mode in either dataset, we cannot consider the mode as a determining factor in this case.