Business Maths & Stats
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BMS11: Business Maths & Statistics
a) The statistical summary table from Part A returned the following results from the salary observations in the Environmental Policy survey:
Salary Summary | | |
| Male | Female |
Mean | $ 53,695 | $ 58,643 |
Median | $ 50,050 | $ 58,100 |
Stdeviation | $ 10,201 | $ 13,731 |
Minimum | $ 37,700 | $ 31,000 |
Maximum | $ 78,000 | $ 81,400 |
Range | $ 40,300 | $ 50,400 |
1st Quartile | $ 45,400 | $ 49,600 |
3rd Quartile | $ 62,100 | $ 62,000 |
Inter-quartile range | $ 16,700 | $ 12,400 |
80th Percentile | $ 62,760 | $ 69,760 |
Coefficient of variation | 19.00% | 23.41% |
| | |
Average salary is higher for female respondents based on the mean of $58,643 against $53,695 for males. As this data is ordered/ranked XXX a more appropriate measurement of the centre of the distribution is obtained from the median. Again, this is higher for females, but of more interest is the relationship between mean and median. The female observations have very similar measures of central location, indicating that the distribution is symmetric. If this lack of parity in the male data were greater it would indicate that there are either extreme observations in the data set or there is a substantial skew in the data.
In addition to identifying the central location, we need to consider how typical that average value is of the set of measurements, and consider the variability, or spread of observations around the average. In these two sets, the range of the female data is greater as demonstrated by both the Range calculation (determined by deducting the lowest observation (MIN) from the largest observation (MAX) and the variance (average of squared deviations from mean to measure dispersion).
The distribution of data sets display...
a) The statistical summary table from Part A returned the following results from the salary observations in the Environmental Policy survey:
Salary Summary | | |
| Male | Female |
Mean | $ 53,695 | $ 58,643 |
Median | $ 50,050 | $ 58,100 |
Stdeviation | $ 10,201 | $ 13,731 |
Minimum | $ 37,700 | $ 31,000 |
Maximum | $ 78,000 | $ 81,400 |
Range | $ 40,300 | $ 50,400 |
1st Quartile | $ 45,400 | $ 49,600 |
3rd Quartile | $ 62,100 | $ 62,000 |
Inter-quartile range | $ 16,700 | $ 12,400 |
80th Percentile | $ 62,760 | $ 69,760 |
Coefficient of variation | 19.00% | 23.41% |
| | |
Average salary is higher for female respondents based on the mean of $58,643 against $53,695 for males. As this data is ordered/ranked XXX a more appropriate measurement of the centre of the distribution is obtained from the median. Again, this is higher for females, but of more interest is the relationship between mean and median. The female observations have very similar measures of central location, indicating that the distribution is symmetric. If this lack of parity in the male data were greater it would indicate that there are either extreme observations in the data set or there is a substantial skew in the data.
In addition to identifying the central location, we need to consider how typical that average value is of the set of measurements, and consider the variability, or spread of observations around the average. In these two sets, the range of the female data is greater as demonstrated by both the Range calculation (determined by deducting the lowest observation (MIN) from the largest observation (MAX) and the variance (average of squared deviations from mean to measure dispersion).
The distribution of data sets display...