Nominal and Ordinal Data - Case Study Example

1. Nominal data is data that is in the form of distinct and discrete categories. Nominal data lacks order thus preventing them from being to arithmetic or logical operations. For example, in a population we can count the number of males and female but we cannot place them in rank order. Ordinal data are measurements of quantities that can be ranked however the intervals between the rank points may be uneven. These uneven intervals between rank points prevent ordinal data from being subject to arithmetic operations. Nevertheless, logical operations can be performed on ordinal data. For example in a race we can establish the finishing ranking of the participating athletes but the time interval between the finishing times between each athlete is not even. Interval data is data that has both order and even intervals. The equal intervals are what we refer to as a continuous scale of measurement. An example of a set of interval level data would be a collection of measurements of height. Ratio data is a special form of interval data that has a true zero point. A good example is provided by Garson (2009) “Temperature is not ratio data because zero degrees does not imply ‘no temperature’, but income is ratio data because zero dollars implies no income.” Income has a true zero point while temperature does not. 2. AGEBAND and SALNBAND: ordinal and quantitative data. AGE: interval and quantitative data. SALBEG and SALNOW: ratio and quantitative data. We are assuming that employees could work with zero salary e.g. trainees. IDNUM, SEX, ISWELSH, EDLEVEL and JOBCAT: nominal and qualitative data. 3. Variable Mean Median Mode IDNUM Not applicable Not applicable Not applicable AGEBAND Not applicable 40 – 44.99 (4) 25 - 29.99 (1) SALNBAND Not applicable 15,000 – 19,999 (2) & 20,000 – 24,999 (3) 10,000 – 14,999 (1) SALBEG 6,806 6,000 6,000 SALNOW 55,071 46,200 49,200 SEX Not applicable Not applicable Male (0) ISWELSH Not applicable Not applicable Welsh (0) EDLEVEL Not applicable Not applicable GCSE/BTEC first (1) JOBCAT Not applicable Not applicable Clerical (1) AGE 37 32 30.33 4. 5. SALNOW RANGE CATEGORY FREQUENCY CUMMULATIVE FREQ 25000 - 29999 A 21 21 30000 - 34999 B 42 63 35000 - 39999 C 80 143 40000 - 44999 D 81 224 45000 - 49999 E 70 294 50000 - 54999 F 34 328 55000 - 59999 G 28 356 60000 - 64999 H 21 377 65000 - 69999 I 11 388 70000 - 74999 J 8 396 75000 - Upwards K 78 474 6. 7. SALNOW histogram is positively skewed. 8. From the chart 5 above: Quartile 1, Q1 is approximately £36,000. MEDIAN is approximately £44,000. Quartile 3, Q3 is approximately £58,000 9. From the chart above the top 25% earners is represented by the upper quartile, i.e. Q3 therefore the range would be from £58,000 - Upwards 10. Using the values we have approximated from the chart above, the interquartile range = Q3 – Q1 = £58,000 - £36,000 = £22,000 11.   SALBEG SALNOW mean 6,806 55,071 median 6,000 46,200 Maximum 31,992 216,000 Minimum 3,600 25,200 Range 28,392 190,800 Standard deviation 3,148 27,321 SALNOW has got greater variability than SALBEG as seen from the table we have generated from Excel. This is manifested by the bigger range, greater standard deviation and larger difference between mean and median. References Garson, GD 2009, “Data Levels and Measurement”, viewed 18 June 2010, Read More