Please help me (earning ratio-boxplot)

[LAYAN-2008]

The main aim of this question is to assess the ability to perform data analysis on two batches of data and use decile box-plots to compare and report on the differences between the two sets.

The weekly earnings (including overtime) and the hourly earnings (including overtime) of male
and female restaurant staff who are working full time are given in the table below,


Gross weekly and hourly earnings of male and female restaurant staff in 1999




Gross weekly earnings Gross hourly earnings
(£) (Pence)
Women Men Women Men
Highest decile 235 275 556 641
Upper quartile 192 230 477 513
Median 163 183 402 434
Lower quartile 138 151 363 389
Lowest deciles 122 128 349 360





(a) Which of these two types of data would you use to compare the earnings of male and female restaurant staff? Give a brief justification for your choice. [3]





(b) Calculate the earnings ratios for the restaurant staff at the median, the upper and lower quartiles, and the highest and lowest deciles. Comment on what these figures tell you about the relative earnings of male and female restaurant
staff in 1999. [4]






(c) If data were available on gross earnings (excluding overtime) for male and female
restaurant staff, would you expect the earnings ratios calculated using such data to be
greater or smaller than those you calculated in (b)? Explain your answer briefly. [2 ]







(d) Draw clear and accurate decile box-plots (as described in Unit 3) to represent the earnings
data for male and female restaurant staff. What do the box- plots tell you about the
relative earnings of male and female restaurant staff in 1999 ? [3]

 

[quantumdude]

You need to show some work first.

 

[Architeuthis Dux]

a) To compare the earnings of male and female restaurant staff, it would be more appropriate to use the gross hourly earnings data. This is because it takes into account the number of hours worked and provides a more accurate representation of their earnings. Using the gross weekly earnings data may not provide an accurate comparison as some employees may work more or less hours than others, thus affecting their weekly earnings.

b) The earnings ratios for the median, upper and lower quartiles, and highest and lowest deciles can be calculated by dividing the female earnings by the male earnings.

Median: 402 / 434 = 0.93
Upper quartile: 477 / 513 = 0.93
Lower quartile: 363 / 389 = 0.93
Highest decile: 349 / 360 = 0.97
Lowest decile: 122 / 128 = 0.95

These figures suggest that, on average, female restaurant staff earned around 93% of what male restaurant staff earned. However, this gap becomes smaller at the highest decile, where female staff earned 97% of what male staff earned. This could indicate that there were a few highly-paid female employees in this category.

c) If data were available on gross earnings (excluding overtime), the earnings ratios would likely be smaller than those calculated in (b). This is because excluding overtime would result in a lower overall earnings figure for both male and female employees, thus reducing the gap between their earnings.

d) The decile box-plots for male and female restaurant staff show that the median, upper and lower quartiles, and highest and lowest deciles are all slightly lower for female employees. This is consistent with the earnings ratios calculated in (b), suggesting that male employees earned slightly more than female employees on average. The box-plots also show that the range of earnings for male employees is larger, with a wider interquartile range and larger outliers, indicating a greater variability in their earnings compared to female employees.