What is/are the appropriate measure(s) of central tendency for each of the variables in Columns B-F? Explain your answers in no more than two sentences each. Attached dataset; a b c d e f Run Ethanol Glycerol Acidity Temp pH 1 4.8 3.5 0.84 24 3.8 2 9.6 7.3 0.27 24 3.8 3 10.2 7.2 0.27 24 3.8 4 8.5 5.1 0.55 24 3.8 5 7.3 3.2 0.68 24 3.1272 6 4.8 1.2 1.24 30 4.2 7 7.9 4.4 0.65 18 3.4 8 6.7 4.3 0.65 30 3.4 9 9.8 6.9 0.47 24 3.8 10 10.2 7.2 0.32 24 3.8 11 9.8 5.8 0.51 24 3.8 12 10.2 7.5 0.28 24 3.8 13 8.2 5.1 0.49 18 4.2 14 7.1 3.9 0.6 18 3.4 15 8.2 4.8 0.46 13.908 3.8 16 5.6 3.3 0.68 18 4.2 17 7.5 4.5 0.58 30 4.2 18 6.7 3.8 0.75 24 4.4728 19 5.5 3.8 0.45 30 3.4 20 6.5 4 0.79 34.092 3.8
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
1)What is/are the appropriate measure(s) of
Attached dataset;
a b c d e f
Run | Ethanol | Glycerol | Acidity | Temp | pH |
1 | 4.8 | 3.5 | 0.84 | 24 | 3.8 |
2 | 9.6 | 7.3 | 0.27 | 24 | 3.8 |
3 | 10.2 | 7.2 | 0.27 | 24 | 3.8 |
4 | 8.5 | 5.1 | 0.55 | 24 | 3.8 |
5 | 7.3 | 3.2 | 0.68 | 24 | 3.1272 |
6 | 4.8 | 1.2 | 1.24 | 30 | 4.2 |
7 | 7.9 | 4.4 | 0.65 | 18 | 3.4 |
8 | 6.7 | 4.3 | 0.65 | 30 | 3.4 |
9 | 9.8 | 6.9 | 0.47 | 24 | 3.8 |
10 | 10.2 | 7.2 | 0.32 | 24 | 3.8 |
11 | 9.8 | 5.8 | 0.51 | 24 | 3.8 |
12 | 10.2 | 7.5 | 0.28 | 24 | 3.8 |
13 | 8.2 | 5.1 | 0.49 | 18 | 4.2 |
14 | 7.1 | 3.9 | 0.6 | 18 | 3.4 |
15 | 8.2 | 4.8 | 0.46 | 13.908 | 3.8 |
16 | 5.6 | 3.3 | 0.68 | 18 | 4.2 |
17 | 7.5 | 4.5 | 0.58 | 30 | 4.2 |
18 | 6.7 | 3.8 | 0.75 | 24 | 4.4728 |
19 | 5.5 | 3.8 | 0.45 | 30 | 3.4 |
20 | 6.5 | 4 | 0.79 | 34.092 | 3.8 |
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