Answer question. Negative variability, Variance, Sample variance.

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1 You read claim that variability is negative. Is this possible? Explain.
A negative variability is meaningless. Negative variability is not possible unless there is an error since the variance represents the average squared deviation from the mean. The square of any number, positive or negative is always positive, while the standard deviation is the square root of the variance and can then not be negative. The measures of variability include the range, interquartile range, variance and standard deviation.
2 Why is variance , as a measure of variability, preferred to the range , the IQR, the SIQR ?
The variance is a good representative of variability as it represents the entire distribution of variables, it is related to the mean and is not as biased is the other measures of variability. The range, the IQR, the SIQR are affected by extreme values than the variance.
3 What are the degrees of freedom for sample variance?
The degrees of freedom for sample variance is N-1
4 What does it mean to say that the sample variance is unbiased?
A statistic is unbiased when the mean of the sampling distribution is equal to the parameter estimate, and the sample variance is smallest of the unbiased estimators of the population mean (M)
5 Explain in the formula for variance.
Population Variance= E [(x- M) 2 / n)]
Sample Variance= E [(x- M) 2 / n-1)]
Variance equals the mean of the squared deviations.
* The mean is M
* Firstly is finding the deviation (x- M), which is the distance from the mean for each variable
* Secondly, squaring each deviation (x- M) 2
* Thirdly, finding the average of the squared deviations (variance) (x- M) 2 / n
6 What does the standard deviation measure?
The standard deviation is the square root of the variance and it is a measure of the standard or the average distance from the mean.
7 Based on the empirical rule what percentage of data fall within 1 SD , 2SD and 3 SD of the mean for data that are distributed normally ?
+1σx =68.3%
+2σx =95.5%
+3σx =99.7%
8 State for characteristics of the standard deviation
1. The SD is always positive
2. The SD is used to describe quantitative variables
3. SD most informative when reported with the mean
4. The value for the SD is affected by the value of every score in the distribution
9 A social scientist measures the number of minutes ( per day ) that a small hypothetical population of college students spreads online.
10 Student Minutes Student Minutes
A 98 F 92
B 77 G 94
C 88 H 98
D 65 I 88
E 24 J 82
* What the range of data in the population ?
Range= Max value –Min value 98-74=24
* What is the IQR of data...