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Answers to various questions related to statistics and probability concepts, including transformations, geometric and harmonic means, logistic systems and inventories, standard normal distribution, continuity correction, confidence intervals, component bar charts, weighted mean, properties of discrete probability distributions, point estimators, statistical inference, and limitations of statistics. It also covers topics such as attributes, data, ratio and interval scales, and measurement errors.
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Question: What is meant by Transformation? Answer: If we change one variable into another variable, this is called transformation. For example, If we have values of variable X, then we can find the values of other variables using transformations like Y = X + 3 or Z = 2X - 5 Question: what is difference b/w Geometric mean and Harmonic means? Answer: The Geometric Mean is used primarily to average data for which the ratio of successive terms remain approximately constant. T his occurs with data as rates of change, ratios, economic index numbers, and population sizes over successive time periods and the like. On the other hand, Harmonic Mean is most frequ ently used in average speeds of various distances covered. Where the distances remain constant, and also in finding the average cos t of commodity, such as mutual funds, when several different purchases are made by investing the same amount of money each time. Question: what is a logistic system and what is a inventry? Answer: Logistics system: The total flow of products from the a cquisition of raw materials to the delivery of finished goods to users, including the related flow of information that controls and records the movement of those products. Inventory System: Procedures that govern how supplies are received, stored, handled, and issued is called inventory system. http://www.vustudents.net Question: Define the standard normal distribution. Answer: The Standard normal distribution: A normal distribution whose mean is zero and whose standard deviation is 1 is known as the s tandard normal distribution. This distribution has a very important role in computing areas under the normal curve. The reason is that the mathematical eq uation of the normal distribution is so complicated that it is not possible to find areas under the no rmal curve by ordinary integration. Areas under the normal curve have to be found by the more advanced method of numerical integration. The point to be noted is that areas under the normal curve have been computed for that particular normal distribution whose mean is zero and whose standard deviation is equal to 1, i.e. the standard normal distribution. Question: Explain the concept of Continuity Correction. Answer: Continuity Correction: In testing of hypothesis, we use a continuity correction of ±1/ whenever we consider the normal approximation to the binomially distributed random variable X. Because the normal distribution can take all real numbers (is continuous) but the binomial dis tribution can only take integer values (is discrete) so there for in using normal curve areas to approximate binomial probabilities, a discrete value of the binomial variable is to be replace d by an interval before the z values are computed. Accordingly a discrete value x becomes the interval from x-0.5 to x+0.5 and this sort of adjustment is called continuity correction. Thus, the discrete value 5, adjusted means 4.5 to 5.5. Question: Define confidence interval. Answer: Confidence interval: A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. In interval estimation of an unknown population parameter we find an interv al for which we have very high confidence (probability) that it contains the unknown parameter. This level of confidence is dented by (1 – a). It is always very high probability usually 95%, 98%, 99% etc. and the chance that our interval does not contain unknown parameter is called level of significance and it is denoted by a. Question: Component bar chart e. What is range? Answer: Component bar charts: When you want to draw a bar chart to illustrate your data, it is often the case that the totals of the figures can be broken down into parts or components. You start by drawing a simple bar chart with the total figures. The columns or bars are then divided into the component parts. Remember to put a key on the diagram. Range: It is the difference between the largest and the smallest value of the data. Suppose largest value is denoted by Xm and smallest
value is denoted by Xo then, range is given by, Range = Xm - Xo Question: Explain " Weighted Mean". Answer: Weighted Mean Weighted Mean is used when one is concerned with averaging average values, which is best explained with an example: If I have a class of 30 students for whom the mean score on a test is 75, and another class of 50 students for whom the mean score is 80; then the su m of all the scores is (30)(75)+(50)(80), hence the overall mean is ((30)(75)=(50)(80))/( 30+50) = 78.12. This is obtained by "weighting" the means by 30 and 50, respectively, and dividing by the sum of the weights. The result is called the weighted mean of the means. Question: Describe the properties of the discrete probability distribution. Answer: Properties of a Discrete Probability Distribution: First property of probability distribution is that 0 < P(X) < 1 It means t hat the value of probability always lies between 0 and 1. i.e. the value of probability can neither be negative nor it can exceed 1. Sigma represents the standard deviation of the probability distribution. Question: when to use Geometric mean. Answer: The geometric mean is a measure of central tendency it uses multiplication rather than addition to summarize data val ues. The geometric mean is a useful summary when we expect that changes in the data occur in percentages. For example adjustments in salary are often a percentag e amount. Geometric means are often useful summaries for highly skewed data. They are also natu ral for summarizing ratios. Don't use a geometric mean, though, if you have any negative or zero values in your data Question: Explain point estimator and method of least squares. Answer: Point estimator: A point estimator is a formula or expression p roducing a single value estimate of the population parameter. Method of least squares: A method of determining the curve that best describes the relationship between expected and observed sets of data by minimizing the su ms of the squares of deviation between observed and expected values. Question: Explaine clearly the concept of "statistical inference" and also the concept of estimation. Answer: Statistical inference is inference about a population from a random sample drawn from it. point estimation interval estimation hypothesis testing (or statistical significance testing) prediction Estimation is the procedure by which we obtain an estimate of the unknown population paramet er using sample data. For example we may estimate the mean and the variance of population by computing the mean and the variance of a sample drawn from the population Question: In which condition we use multiple bar chart and component bar chart? Answer: Multiple bar chart: A multiple bar chart shows two or more characteristic s corresponding to the values of a common variable. Component bar chart. While the component bar chart is effective technique in which each bar is divided into two or more sections. Question: Statistic and statistics. Answer: Statistic and statistics: The word statistics is used as the plural of the word statistic, which means some numerical quantity calculated from sample observations. You can say that in the plural sense it refers to a collection of numerical facts and in singular sense, denotes the science of basing decision on numerical data. Question: What is sampling & how many types of samling? Answer: Sampling: It is a statistical technique which is used in almost every filed to collect information about the population. Types: 1. Probability sampling 2. Non -