Business Statistics Assignment

Interpret the measures of central tendency and variation within the linguistic context of this problem. Why should the party producing the tea bags be concerned about the central tendency and variation? Because getting an exact amount of tea in a bag is debatable because of variation in the density of the tea bag, and the extremely fast filling operation of the machine. D) Are the information skewed? If so, how? Left skewed. Because the mean is less than the median. What argon the differences among the various measures of variation, such as the range, intrauterine range, variance, regular deviation, and coefficient of variation, and what are the advantages and disadvantages of each? (a) regularize Range of a data set is deference amidst the largest and the smallest data value. It is the bare(a)st 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 qu artile and the graduation 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 span the whole distributions. Disadvantages 1) it uses only two of the observations and so provoke be distorted by extreme determine 2) Does not indicates any concentrations of the observations Cannot be use in calculating of the obse rvation. (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) delicate 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 disparate 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 t o zero, the coefficient of variation will approach timelessness 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.