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Rewriting: Paraphrase or rewrite your friend's essay with similar meaning at reduced cost   ## Categorical Data

Data is the small fragments of raw information collected for study and analysis for making it useful in form an informed conclusion. Data is of three types namely, Categorical, discrete numerical and continuous numerical. Categorical data is also understood as the qualitative data which represents various characteristics like gender, marital status, city, etc. Such data may have a numerical value but which don’t have any mathematical meaning.

On the other hand, numerical data, as the name itself suggest, is with quantitative characteristic of measurement, like height, weight, etc. Further dividing into two as Discrete data which can be counted and have possible values which is either fixed or in a range going on to infinity; and Continuous data represent measurements that can be described using intervals.

As per the views of Cressie (2015), mmeasurement scales are of three types namely, Nominal, ordinal, interval and ratio scale. The nominal scale measures variable with a descriptive category, but have no Natural Numerical Value. The ordinal scale has both identity and magnitude property. The interval scale has identity, magnitude and equal intervals as its properties (Willer and Lernoud, 2016). The ratio scale has all four properties of measurement namely, identity, magnitude, equal intervals and minimum value of zero.

What is your gender? (Male = 0, Female = 1)

Data Type: Categorical data with qualitative characteristic of a gender.

Measurement Level: Nominal scale of measurement as satisfies only identity property.

Data Type: Discrete data with finite possible values.

Measurement Level: Ordinal scale of measurement satisfying both identity and magnitude as property.

About how many hours per week do you expect to work at an outside job this semester?

Data Type: Discrete date with infinite possible values.

Measurement Level: Ordinal scale of measurement satisfying both identity and magnitude as property.

What do you think is the ideal number of children for a married couple?

Data Type: Discrete data with finite possible values.

Measurement Level: Interval scale of measurement with identity, magnitude and equal intervals.

On a 1 to 5 scale, which best describes your parents? (1 = Mother clearly dominant ? 5 = Father clearly dominant)

Data Type: Discrete data

Measurement Level: Ordinal scale of measurement satisfying both identity and magnitude as property.

No. of Students (N): 30

Monthly Rent paid: 730           730    730      930      700      570

690      1,030   740      620      720      670

560       740    650      660      850      930

## Discrete Data

600       620    760      690      710      500

730       800    820      840      720      700

(a)

Total of values = 18850

Mean = x = Σx / n

= 18850/30 = 628.33

Median = [(n/2)+(n/2+1)] / 2

= [(30/2)+(30/2+1)] / 2 = (15+16) / 2

= 15.5 i.e. average of the 15th and 16th value = 820+930/2 = 875

Mode = The values occurring more than once therefore it’s a multimodal data, thus grouping will give the more appropriate mode which is 730 occurring 4 times.

(b) Agreement of the measure of Central Tendency:

Since the values of mean, median and mode are not very close to each other, the measures of central tendency are more scattered. Since mean takes into account all the values; median calculates the mid value and mode analyses value that occurs more frequently, any value over 730 would be more favorable and agreeable situation.

(c) Calculation of Standard Deviation =

 Value Mean A-B Square (A-B) A B C 560 628.33 -68.33 4668.989 600 628.33 -28.33 802.5889 690 628.33 61.67 3803.189 730 628.33 101.67 10336.79 730 628.33 101.67 10336.79 730 628.33 101.67 10336.79 1030 628.33 401.67 161338.8 620 628.33 -8.33 69.3889 740 628.33 111.67 12470.19 800 628.33 171.67 29470.59 730 628.33 101.67 10336.79 740 628.33 111.67 12470.19 650 628.33 21.67 469.5889 760 628.33 131.67 17336.99 820 628.33 191.67 36737.39 930 628.33 301.67 91004.79 620 628.33 -8.33 69.3889 660 628.33 31.67 1002.989 690 628.33 61.67 3803.189 840 628.33 211.67 44804.19 700 628.33 71.67 5136.589 720 628.33 91.67 8403.389 850 628.33 221.67 49137.59 710 628.33 81.67 6669.989 720 628.33 91.67 8403.389 570 628.33 -58.33 3402.389 670 628.33 41.67 1736.389 930 628.33 301.67 91004.79 500 628.33 -128.33 16468.59 700 628.33 71.67 5136.589

Sum of Square of (A-B) = C = 657169.267

Mean of C = D = 21905.64223

Square Root of D = 148.0055404

(d) Sort and standardize the data.

Standardized value = X – μ / σ

Where:

X is the value

μ is the mean

σ is the standard deviation

Data is sorted from smallest to largest in the following table with their standard values:

 Value Mean SD Standardized Data A B C (A-B)/C 500 628.33 148.0055 -0.86706 560 628.33 148.0055 -0.46167 570 628.33 148.0055 -0.39411 600 628.33 148.0055 -0.19141 620 628.33 148.0055 -0.05628 620 628.33 148.0055 -0.05628 650 628.33 148.0055 0.146413 660 628.33 148.0055 0.213979 670 628.33 148.0055 0.281544 690 628.33 148.0055 0.416674 690 628.33 148.0055 0.416674 700 628.33 148.0055 0.484239 700 628.33 148.0055 0.484239 710 628.33 148.0055 0.551804 720 628.33 148.0055 0.619369 720 628.33 148.0055 0.619369 730 628.33 148.0055 0.686934 730 628.33 148.0055 0.686934 730 628.33 148.0055 0.686934 730 628.33 148.0055 0.686934 740 628.33 148.0055 0.754499 740 628.33 148.0055 0.754499 760 628.33 148.0055 0.889629 800 628.33 148.0055 1.159889 820 628.33 148.0055 1.295019 840 628.33 148.0055 1.43015 850 628.33 148.0055 1.497715 930 628.33 148.0055 2.038235 930 628.33 148.0055 2.038235 1030 628.33 148.0055 2.713886

(e) Are there outliers or unusual data values?

Values which have a standardized value or Z-score of over 2 are the unusual value like 930 and 1030.

(f) Using the Empirical Rule, do you think the data could be from a normal population?

For Normal Distribution, the Empirical rule is defined as values that fall in 1 Standard Deviation of the mean is 68%, 95% falls in 2 standard deviation of the mean and 99.73% in 4 standard deviation of the mean. That means

 % of Values falling in range Higher Value Lower Value 68% mean ± sd 776.3355 480.3245 95% mean ± 2 sd 924.341 332.319 99.73% mean ± 3 sd 1220.352 36.308

Considering the Empirical Rule data is from the normal population apparently.

Find the mean, median, and mode for each quiz.

 I II III IV 60 65 66 10 60 65 67 49 60 65 70 70 60 65 71 80 71 70 72 85 73 74 72 88 74 79 74 90 75 79 74 93 88 79 95 97 99 79 99 98 Mean 72 72 76 76 Median 72 72 72 86.5 Mode 60 65 72, 74

Do these measures of center agree? Explain.

Yes the measures of centre agree as the mean and median and mode are closely related.

For each data set, note strengths or weaknesses of each statistic of center.

 Quiz Strength Weakness I Mean: Very useful measure results into average score of class. Median: The mid value derived minimize the error in skewed distribution Mode: Easily markable. Mean: Unusually high scores affect the average score Median: Insensitive to extreme values of the sample. Mode: Least useful information scope. II Mean: Symmetric average score. Median: Minimized error in skewed distribution Mode: Easily spotted. Mean: Minimal difference affect the average score. Median: High sensitivity to fresh additions. Mode: Two common scores create multimodal result.. III Mean: Very useful central tendency result. Median: Minimized skewed distribution errors Mode: Mode easily spot able. Mean: Competitive scores affect the average score. Median: Close scattering of scores. Mode: Small sample of frequency. IV Mean: Blend for average score of class. Median: The mid value minimize the error in skewed distribution Mode: Couldnot be spotted. Mean: Very scattered scores does not portray correct potential of class. Median: Mid values too high than least values. Mode: No frequency of two similar scores could be spotted

Are the data symmetric or skewed? If skewed, which direction?

Data of quiz II, III and I is symmetric in order of its mention with the long tail of skewness extending to right. However the scores of quiz IV is very asymmetric with higher levels of variation and differences and also median is higher than mean, resulting into data skewed to left.

## Continuous Data

Briefly describe and compare student performance on each quiz.

Student performance in Quiz II is symmetrical in order with a very low difference in the minimum and maximum score. On the other hand performance in Quiz I and II is more competitive with higher differences in the least and the maximum score. Lastly Quiz IV results show that many students were confident and well prepared than a few who turned out to be a low performing in this case.

Total Probability (one of the alternator fail or both fail or none fails) = 1

P (alternator 1 or 2 fail) = P(1 fails) or P(2 fails) = 0.02

P (Alternator 1 or 2 works well) = P(1 works) or P(2 works) = 1 - 0.02 = 0.98

Probability that both alternator fails = P(1 fails) * P(2 fails)  (Anderberg, 2014)

= 0.02*0.02

= 0.0004

Probability that neither of Alternators fail = P(1 works) * P(2 works)

= 0.98 * 0.98

= 0.9604

Probability that one or the other alternator will fail

= P (1 fails) * P(2 works) OR P(2 fails) * P(1 works)

= 0.02 * 0.98

= 0.0196

Mean = x = Σx / n

= 59017/18

= 3278.722

 X Mean X-Mean Square(X-Mean) 3450 3278.722 171.278 29336.15 3363 3278.722 84.278 7102.781 3228 3278.722 -50.722 2572.721 3360 3278.722 81.278 6606.113 3304 3278.722 25.278 638.9773 3407 3278.722 128.278 16455.25 3324 3278.722 45.278 2050.097 3365 3278.722 86.278 7443.893 3290 3278.722 11.278 127.1933 3289 3278.722 10.278 105.6373 3346 3278.722 67.278 4526.329 3252 3278.722 -26.722 714.0653 3237 3278.722 -41.722 1740.725 3210 3278.722 -68.722 4722.713 3140 3278.722 -138.722 19243.79 3220 3278.722 -58.722 3448.273 3103 3278.722 -175.722 30878.22 3129 3278.722 -149.722 22416.68 59017 160129.6

Standard deviation = ( Rohatgi and Saleh,  2015)

= Square Root [160129.6/18]

= 94.31908

Standard error = Standard deviation / SQRT of no. of observation (Allen,  2014)

= 94.31908 / SQRT 18

= 22.23122

E = 22.23122 * 1.96 = 43.57319

95% confidence interval =  (3278.722 – 43.57319) to (3278.722 + 43.57319)

= 3235.149 to 3322.295 steps

Sample size to obtain an error of ± 20 steps with 95 percent confidence

= [(1.96 * Standard deviation)/20]^2

= 85.43804

Line chart of the data

The chart chart shows that the No. Of steps taken by Dave while jogging has gone down from the first day. But he picked up gradually after the 3rd day. But the steps again reduced on 15tg, 17th and 18th day.

References

Books and Journal

Allen, A.O., 2014. Probability, statistics, and queueing theory. Academic Press.

Anderberg, M.R., 2014. Cluster analysis for applications: probability and mathematical statistics: a series of monographs and textbooks (Vol. 19). Academic press.

Cressie, N., 2015. Statistics for spatial data. John Wiley & Sons.

Rohatgi, V.K. and Saleh, A.M.E., 2015. An introduction to probability and statistics. John Wiley & Sons.

Willer, H. and Lernoud, J., 2016. The world of organic agriculture. Statistics and emerging trends 2016 (Pp. 1-336). Research Institute of Organic Agriculture FiBL and IFOAM Organics International.

Cite This Work

My Assignment Help (2022) Types Of Data And Measurement Scales [Online]. Available from: https://myassignmenthelp.com/free-samples/sta101-statistics-for-business/natural-numerical-value-file-A9B68D.html
[Accessed 05 December 2023].

My Assignment Help. 'Types Of Data And Measurement Scales' (My Assignment Help, 2022) <https://myassignmenthelp.com/free-samples/sta101-statistics-for-business/natural-numerical-value-file-A9B68D.html> accessed 05 December 2023.

My Assignment Help. Types Of Data And Measurement Scales [Internet]. My Assignment Help. 2022 [cited 05 December 2023]. Available from: https://myassignmenthelp.com/free-samples/sta101-statistics-for-business/natural-numerical-value-file-A9B68D.html.

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