The report analyses the numeric nature of the salaries of UK graduate students who are in their first year of full time paid work (2004). The report aims to compare the salaries between the genders. Descriptive statistics is used to perform the analysis. The source data are taken from the Office for National Statistics website.
Statistics is an important field of Mathematics as it is used to interpret, investigate and analyse the real world situations using scientific methods. Descriptive statistics is the primary step of analysing a data set with the help of the parameters like measures of central tendency and variation. Pictorial representations are also a part of descriptive statistics. Here we analyse the given data using the important measures of central tendency and variation.
Relative Frequencies and Relative Cumulative frequencies
The data given is of grouped data with unequal class interval widths and two open ended intervals. There are ten intervals of data and individual relative frequencies are given for male and female. It is better to construct an “Above” cumulative frequency because we cannot assume the upper limit but we can assume the lower limit as zero. The cumulative frequencies for both male and female approximately remains same up to the class “Above 15” but gets more difference after that. It shows that the distribution of female students is higher in lower salary levels than the males.
Measures of Central Tendency
The important measures of Central tendency are Mean and Median. Mean is the average of the data and Median is the mid-value specifying the position. Formula: (Weisstein, Eric W).The drawback for calculating mean of open ended interval is that we cannot get the accurate mid-point for the interval 50+. Median eliminates this difficulty as it is robust against the extreme values. The average salary for Male students is 24.9(£000) whereas that of female students is 22.34(£000). The Male students get more salary on average than the female students. The Median salary for male students is 20.147(£000) and the median salary for female students is 21.389(£000). As median splits the data set into two equal halves, half of the male students get less than 20.147(£000) and other half get more than this. In case of females half of the students get less than 21.389(£000) and other half get more than 21.389(£000). Here we can take Median as the appropriate measure of central tendency as mean is affected by the extreme value of the last class interval.
MEASURES OF VARIATION
The suitable measure of variation to be interpreted is standard deviation. It describes the average spread of individual data from the mean. (Weisstein, Eric W). Standard deviation for male students is 85.812 and that of females is 76.381. This shows that female student’s salary spread is less than that of males. The variance can be interpreted but the difficulty is that it is square of standard deviation and hence the units are of square units. This difficulty is avoided in standard deviation. Also measure of spread gives more detail about the individual data than the measures of central tendency.
The male students on average earn more than the female students in the first year of their full time paid work but the spread is higher than that of female students. The median also states that female students get salary more evenly than the male students.