Statistics concepts and applications

¶ … codes were labeled thus for data analysis. Thus the category of participants who found my work to be highly interesting was coded 1, those who found it somewhat interesting were coded 2; those who found it tedious / boring, I coded 3; whilst those who found it highly disinteresting, I coded 4. I should have coded those whose data was missing (e.g. illegible, absent, or had not responded). 1,673 out of 2,715 participants had failed to complete their surveys (there was partially or utterly incomplete missing data). This made for 61.6% of the survey. The cases that I could, ultimately, rely on were 1,042.

Absolute frequency denotes the number of percentage of those who had responded. For instance 650 participants had responded that they were highly interested. This tells us that my presentation (assuming it was that) must have been highly interesting, or I am popular, or perhaps the participants were in some way or other influenced to vote on my behalf, for almost half of the population had found me highly interesting, altogether the overwhelming majority were at least positively inclined towards my presentation whilst only 89 participants ranged to being somewhat bored to being utterly bored. I might conclude that my presentation was successful. The relative frequency is my converting the absolute frequency into an approximate percentage. So, for instance, I calculate the 650 respondents of Code 1 from the total 2715 (650 / 2,715) or gain my relative frequency. The adjusted frequency allows me to compare the response across the various spectrums (to compare the response of the whole). So, for instance, I see that the majority of participants (62.4%) were highly interested in my work, whilst the lowest group of all (2.7%) loathed it. The cumulative frequency is the number of individuals as you move up the scale. For instance 62.4% of participants (i.e. 650 individuals) responded that they were highly interested, by the time you progress to the category of those who were disinterested you receive 100% cumulative frequency.

2.

Age

frequency

16

1

17

2

18

1

19

2

20

2

(b) the genders are equally balanced in their preference for coke (n=7)

2. Mean: all the scores were added and then divided by the number of scores (i.e. 30 in this case).

Standard error: The sample is never a perfectly accurate reflection of the population. There will always be some error between sample and population and the S.E. measures the average difference that should be expected between one and the other. In this case, the S.E. is low.

Median: List the score in order lowest to highest; the median is the middle score in the list (the 50th percentile). Here 16 is the median.

Mode: the most frequently reported score. # 16.

Sample variance: A sample is always biased to its population (different than it) in some way. Sample variance is measuring the extent to which it differs. In this case it verges 6.21% away from norm.

Sample deviation: The square root of the variance.

Kurtosis: describes the peakedness or the density of the distribution, in this case the average size of the sodas that peak around 0.15

Skewness: to which extent -- if any -- data skews (leans) in any particular direction. Here: 0.30

Range: the distance between the largest score in the distribution and the smallest. (I.e. subtracting lowest score from highest).

Minimum: the smallest number

Maximum: the largest number

Sum: the total of all combined

Count: non-negative integers that are considered from counting rather than ranking (i.e. those discounting repetitive). In this case, 8 such digits.

Confidence level: The amount of confidence that I have about this data- that it closely approximates actual sample is quite high (95.9%)

3. The age range of 45-54 had the highest amount of women (54%) using the low-cholesterol diet followed by 55 and over (49%), then 35-44 age range (46%) least in the 1-24 age range (29%). It seems that preference for this diet peaks amongst females in the late middle years. With men, there is a slightly different shift with the majority (35%) actually preferring this diet in their older years and regressing as they decrease in age, with a major shift occurring between the 13% in the age interval 16-24 and the 25% of the age interval 25-34. Of the difference between the sexes, women by far (54% at its peak) are more interested in the diet than men. As comparison between the ages, the diet seems most popular from 45 years onwards (43%); somewhat popular between the ages 25-34 and 35-44 (34% and 37% respectively) and least popular in the youngest age interval (21%). Apparently, its popularity increases with age. In short, I would market that specific diet to the late middle-age / elderly individual, targeting preferentially females.

5. Nominal and ordinal scales are typically used in cross-tabulation analysis, although interval and ratio could be used too. (All would be interpreted as nominal).

6. I think that data analysis and interpretation, although heavily used in the managerial / business sciences are not exclusively business-oriented since they are employed across the board in all sciences from the social and behavioral fields to journalism for instance. Statistics is also an issue that is relevant to daily living, and, as such, cannot be limited to any specific field.

7. 156 participants responded that they had received valuable information in filing their tax forms. These positive respondents represented 29.5% of the total (528 individuals) surveyed (146/528). The adjusted frequency of the whole (the approximate percentage comparison of the whole) was 29.8%. On the other hand, far more participants (n= 368) found the suggestions unhelpful or trivial. This number represented 69.5% of the whole. As comparison, or adjusted frequency (as consider plotting this on a pie chart for illustration) it would approximate 70.2%. Of those who didn't know, 1% responded here with 2% of this segment missing (i.e., unreadable). Similarly, 1% responded with uncertainty regarding the helpfulness of the information, with 2% data missing (i.e. illegible). 2% of the data were returned blank, and 4% missing (which probably missing data was totally unreadable).