Interpret the measures of central tendency and variation within the context of this problem. Why should the company producing the tea bags be concerned about the central tendency and variation? Because getting an exact amount of tea in a bag is problematic because of variation in the density of the tea bag, and the extremely fast filling operation of the machine. D) Are the data skewed? If so, how? Left skewed. Because the mean is less than the median. What are the differences among the various measures of variation, such as the range, intrauterine range, variance, standard deviation, and coefficient of variation, and what are the advantages and disadvantages of each? (a) Range: Range of a data set is deference between the largest and the smallest data value. It is the simplest measure of variability. It is very sensitive to the smallest and the largest data value. (b) Intrauterine Range: intrauterine range of a data set is the difference between the third quartile and the first quartile.
It is range for the middle 50% of data. It overcomes the sensitivity to extreme data value. (c) Variance: The variance measures the variability the utilizes all the data. It also measures the average of the squared difference between each data value and the mean. (d) Standard Deviation: Is a standard of a data set is the positive square root of the variance. It is measured in the same units as the data making it more easily interpreted than the variance. (e) Coefficient of variance: the coefficient of variance indicates how range large the standard deviation is related to them.
The advantages and disadvantages: (a) Range: Advantages: 1) Easy to understand; 2) Simple to calculate; 3) It is a good measure for comparison as it p the whole distributions. Disadvantages: 1) it uses only two of the observations and so can be distorted by extreme values; 2) Does not indicates any concentrations of the observations; Cannot be use in calculating of the observation. (b) Intrauterine range: Advantages: 1) The calculations are simple and quite to do; 20 it can be illustrated graphically; 3) It covers the central 50% of the observations and so is not distorted by extreme values.
Disadvantages: 1) Disregards all values except 1st and 3rd quartiles. Advantages: 1) Considers all data; 2) Not a terminal statistic Disadvantages: 1) Not appropriate for nominal or ordinal data; 2) Sensitive to extreme outliers. (d) Standard Deviation: (e) Coefficient of Variance: Advantages: The coefficient of variation is useful because the standard deviation of data must always be understood in the context of the mean of the data. In contrast, the actual value of the C.V. is independent of the unit in which the measurement has en taken, so it is a dimensionless number.
For comparison between data sets with different units or widely different means, one should use the coefficient of variation instead of the standard deviation. Disadvantages: 1) When the mean value is close to zero, the coefficient of variation will approach infinity and is therefore sensitive to small changes in the mean. This is often the case if the values do not originate from a ratio scale; 2) Unlike the standard deviation, it cannot be used directly to construct confidence intervals for the mean.
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