Question And Answers-Statistics-Notes, Study notes of Statistics

Download Question And Answers-Statistics-Notes and more Study notes Statistics in PDF only on Docsity! http://www.vustudents.net Question: what is meant by marginal probability function?. Answer: The individual probability function of the random variables,from the joint probability function,is known as marginal probability function. Question: What is ORDINAL or RANKING SCALE. Answer: Where nominal scales don't allow comparisons in degree, this is possible with ordinal scales. Say you think it is better to live in Karachi than in Lahore but you don't know by how much. Example: 1-People or objects with a higher scale value have more of some attribute. 2-The intervals between adjacent scale values are indeterminate. 3-Scale assignment is by the property of "greater than," "equal to," or "less than." Question: What is the descriptive and inferential Statistics. Answer: Descriptive Statistics uses graphical and numerical techniques to summarize and display the information contained in a data set. Inferential Statistics uses sample data to make decisions or predictions about a larger population of data. Question: What is Skewness? Answer: Skewness is defined as asymmetry in the distribution of the sample data values. Values on one side of the distribution tend to be further from the 'middle' than values on the other side. docsity.com http://www.vustudents.net For skewed data, the usual measures of location will give different values, for example, mode<median<mean would indicate positive (or right) skewness. Positive (or right) skewness is more common than negative (or left) skewness. If there is evidence of skewness in the data, we can apply transformations, for example, taking logarithms of positive skew data. Question: Define Variable,Discrete Variable and continuous Variable. Answer: Variable is a characteristic under study that assumes different values for different elements. For example, Height of students in a class, No. of rooms in a house Discrete Variable: A DISCRETE variable is one which may take on only a countable number of distinct values such as 0, 1, 2, 3, 4,......... Discrete variables are usually (but not necessarily) counts. If a variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, the number of defective light bulbs in a box of ten. Continuous Variable: A CONTINUOUS variable is one which takes an infinite number of possible values. Continuous variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile. Question: What is correletion coefficient? Answer: Correlation Coefficient: A correlation coefficient is a number between -1 docsity.com http://www.vustudents.net of sugar in an orange, the time required to run a mile. Question: Explain the concept of inferential statisticts. Answer: Inferential statistics: In Inferential Statistics we try to get an idea about population parameters using sample data because it is not possible, in many situations, for us to study the whole of population. We therefore resort ourselves to the sample estimates. In drawing conclusion, the decision maker makes use of probability theory Question: What is continuity correction? Answer: Continuity Correction Factor A value of .5 that is added to and/or subtracted from a value of a Binomial random variable X when the continuous normal probability distribution is used to approximate the discrete binomial probability distribution Question: what is hypereomatric distribution. Answer: Hypergeometric Distribution: In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the number of successes in a sequence of n draws from a finite population without replacement. Question: What is probablity density function and what is it's significance. Answer: Dear Student, Probability density function (pdf) is a mathematical docsity.com http://www.vustudents.net expression or formula which gives probabilities for a range of values of a continuous random variable. It is denoted by f(x). It has certain very important properties which we have sent you by email. Probability density functions are of great significance in Statistics. In fact all the conclusions that are made in Inferencial Statistics are due to using appropriate probability density function. Most important probability distributions which are used in Inferencial Statistics are normal distribution, t-distribution, F distribution and chi-square distribution. Question: What is random variable and how the fdp is related to it? Answer: RANDOM VARIABLE: Such a numerical quantity whose value is determined by the outcome of a random experiment is called a random variable. For example, no. of children in a family, daily income of a medical store etc. It is of two types (i) Discrete random variable (ii) Continuous random variable Probability density function (pdf) is the expression or formula which gives us the probability for given range of values of the continuous random variable. Question: What is the concept of normal distribution. Answer: Gaussian (Normal) Distribution The Normal or Gaussian distribution plays a central role in statistics and has been found to be a very good model for many continuous distributions that occur in real situations. The function is symmetric about the mean, it gains its maximum value at the docsity.com http://www.vustudents.net mean, the minimum value is at plus and minus infinity. The distribution is often referred to as "bell shaped". Question: Define Hypothetical population and non random sampling. Answer: Hypothetical population: A population is not necessarily real; it may be hypothetical or imaginary. For example, outcomes of an experiment, that is carried out infinitely, make a hypothetical population. It consists of all conceivable ways in which an event can occur, e.g. all possible throws of a die. Such a population does not exist in an actual manner but is only to be thought of. Non-random Sampling: ‘Nonrandom sampling’ implies that kind of sampling in which the population units are drawn into the sample by using one’s personal judgment. In this sampling personal judgment (of an every person) decide that which sampling unit (of population) should be selected for the sample. Question: what are the main and detailable concept of dispersion Answer: Dispersion means the extent to which the data/values are spread out from the average. Example: There are many situations in which two different data having the same average e.g. Data 1:5, 5,5,5,5 having mean=5 Data 2:1, 5,6,6,7 having mean=5 Hence in such a situation we, need a measure which tell us how dispersed the data are. The measure used for this docsity.com http://www.vustudents.net data. Question: What are the different ways of representing the frequency distribution graphically? Answer: There are three ways of graphical representation of frequency distribution. HISTOGRAM: A histogram consists of a set of adjacent rectangles whose bases are marked off by class boundaries along the X-axis, and whose heights are proportional to the frequencies associated with the respective classes. FREQUENCY POLYGON: A frequency polygon is obtained by plotting the class frequencies against the mid-points of the classes, and connecting the points so obtained by straight line segments. FREQUENCY CURVE: When the frequency polygon constructed over class intervals made sufficiently small for a large number observation, is smoothed, it approaches a continuous curve, such a curve is called Frequency Curve. Types of Frequency Curves: The frequency distribution occurring in practice, usually belong to one of the following four types. You will study about them in your next lecture. 1. The Symmetrical Distribution. 2. Moderately Skewed Distribution. docsity.com http://www.vustudents.net 3. Extremely Skewed or J-shaped Distribution 4. U-Shaped Distribution Question: What is meant by 5-Number Summary? Answer: 5-Number Summary: A 5-number summary is especially useful when we have so many data that it is sufficient to present a summary of the data rather than the whole data set. It consists of 5 values: the most extreme values in the data set (maximum and minimum values), the lower and upper quartiles, and the median. A 5-number summary can be represented in a diagram known as a box and whisker plot. In cases where we have more than one data set to analyze, a 5- number summary is constructed for each, with corresponding multiple box and whisker plots. Question: What is meant by mid-rang and mid-quartile range and what is the difference between these two ranges.? Answer: MID-RANGE: If there are n observations with x0 and xm as their smallest and largest observations respectively, then their mid-range is defined as Mid range=X0+Xm/2. It is obvious that if we add the smallest value with the largest, and divide by 2, we will get a value which is more or less in the middle of the data-set. MID-QUARTILE RANGE: If x1, x2… xn are n observations with Q1andQ3 as their first and third quartiles respectively, then their mid-quartile range is defined as Mid Quartile docsity.com http://www.vustudents.net range= Q1+Q3 /2. Difference: They both used as measures of central tendency because they both provide us with more or less the middle value of data. The difference is that the mid-quartile range is an attempt to address the problem of the range being heavily dependent on extreme scores. An mid-quartile range represents the middle 50% of the scores in the distribution. Question: What is meant by Loaded die?. Answer: A biased die is known as Loaded die. Question: What is the difference between Probability distribution and sampling distribution?. Answer: The probability distribution of any statistic (such as the mean, the standard deviation, the proportion of successes in a sample, etc.) is known as its sampling distribution. Question: DISCUSS STATUS,STATISTICS AND STATISTIC. Answer: Latin words status, meaning a political state is believed to be the origin of the word “statistics” Statistics: Today the word statistics is used in three different meanings. Firstly, it is used in the sense of data for example price statistics, death statistics etc Secondly, it is used as the plural of the word “statistic” meaning the information obtained from the sample data. docsity.com http://www.vustudents.net measurement. A relative measure of dispersion is useful for comparison of data of different nature. A measure of central tendency together with a measure of dispersion gives an adequate description of data. We will be discussing four measures of dispersion i.e. the range, the quartile deviation, the mean deviation, and the standard deviation. Question: WHAT IS MOMENTS Answer: Moments are the arithmetic means of the powers to which the deviations are raised. Thus the mean of the first power of the deviations from mean is the first moment about the mean; the mean of the second power of the deviations from mean is the second moment about the mean and so on. First four moments about mean are defined as: m1 = (X – Xbar)/n m2 = (X – Xbar)2/n m3 = (X – Xbar)3/n m4 = (X – Xbar)4/n Question: What is difference between independent and independence variable. Answer: Two events A and B in the same sample space S, are defined to be independent if the probability that one event occurs, is not affected by whether the other event has or has not occurred. Two events A and B in the same sample space S, are defined to be Dependent if the probability that one event occurs, is affected by whether the other event has or has not occurred. Question: Explain the Condititional Probability with the help of example. Answer: In conditional probability we are dealing with two events .One event is docsity.com http://www.vustudents.net that for which we have to find the probability and about 2nd event we have some priori information.To illustrate the concept of conditional probability let us consider an example. Let a die is rolled. S={1,2,3,4,5,6} A is the event of getting a" 5" & a prior information is given that on a particular throw of a die ,the outcome is an odd number (event B) .Hence B={1,3,5}now the probability of getting a "5" in this reduce sample space is 1/3 which is known as conditional probability of event "A". Note. Priori means already known information before starting the experiment Question: what is loaded die? Answer: We can say that, a biased unfair die is a loaded die Question: Explain Nominal and ordinal levels of measurement and also tell me what is EPAmileage rating. Answer: Nominal Scales When measuring using a nominal scale, one simply names or categorizes responses. The essential point about nominal scales is that they do not imply any ordering. Nominal scales embody the lowest level of measurement. It is used for identifying individuals, groups or regions. Ordinal Scales Where nominal scales don't allow comparisons in degree, this is possible with ordinal scales. Say you think it is better to live in Karachi than in Lahore but you don't know by how much. EPA docsity.com http://www.vustudents.net means Environmental Protection Agency US government agency for the protection of the environment which ranks the most fuel-efficient vehicle. Question: Explain bivarite. Answer: Bivariate Data Before we looked at one measurement on an observation (or individual), say X is height. Now we're interested in more than one measurement per observation (individual), say X is height and Y is weight. Let's say we have n individuals we're taking the measurements on. Then our data would be as follows (X1,Y1), (X2, Y2).....(Xn, Yn) Question: What is meadian Answer: abc Question: Quartiles & their Uses. Answer: Quartile: The values which divide the distribution into four equal parts are called quartiles. Quartiles divide the data into four equal-sized and non-overlapping parts. One fourth of the data lies below the Q1 (first quartile). Half of the data lies below Q2 (second quartile) similarly, three quarters of the data lies below Q3 (third quartile) Q2 (second quartile) is also known as median. Use of quartiles: In order to describe a data set without listing all the data, we have measures of location such as the mean and median, measures of spread such as the range and standard deviation. Quartiles are also used to describe the data in combination with other measures. For example they are used in five number summary of docsity.com http://www.vustudents.net population of data. Question: What is bais and how it is differnt from random error? Answer: A systematic error which deprive our resluts from there representativeness. Biase id different from random error in the sence that random error balance out in the long run while biase is cumulative (addition of error) and does not become balance out in long the run. Question: what is Point Estimation. Answer: Point estimation of a population parameter provides, as an estimate, a single value calculated from the sample that is likely to be close in value to the unknown parameter. For example the value of the statistic (Xbar) computed from a sample of size n, is a point estimate of the population parameter (u) Question: state what is Grouped and Row data? Answer: Grouped data The data presented in the form of frequency distribution is also known as grouped data. Raw data Data that have not been processed in any manner. It often refers to uncompressed text that is not stored in any priority format. It may also refer to recently captured data that may have been placed into a database structure, but not yet processed. Question: define theMean Deviation. docsity.com http://www.vustudents.net Answer: The mean deviation is used to characterize the dispersion among the measures in a given population. To calculate the mean deviation of a set of scores it is first necessary to compute their average (mean or median) and then specify the distance between each score and that mean without regard to whether the score is above or below( negative and positive) the mean. The mean deviation is defined as the mean of these absolute values. Question: What is meant by variability? Answer: Variability is the spread or dispersion in a set of data. Consider the following sets of data. 9, 9, 9, 9, 9, 9, 9, 9, 9, 9 10, 6, 2, 8, 4, 14, 16, 12 13, 10, 7, 6, 21, 3, 7, 5 All these three sets of data have same mean ( 9 ) but they are different in variability. First set of values has no dispersion and there is greater variability is third data set as compared to second set of data as its values are more spread away as compared to the values of second set of data. Question: What is EQUALLY LIKELY EVENTS? Answer: The two events are said to be equally likely if they have the same chance of occurring. For example, in our coin-tossing experiment, the two events, heads and tails, are equally likely. Both have the same chances of occurring. There is 50% chance for occurring both events. Question: What is meant by Transformation? docsity.com http://www.vustudents.net 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: Explain Primary and Secondary data. Answer: Primary and Secondary data: When people think of market research, they tend to think of collecting data directly from customers, prospects, or other stake holders (this is called primary data collection). However, secondary data can also provide a rich source of information. Secondary data are data that already exist in industry-specific reports, previous research on the topic of interest, or data from an organization’s own data base. Qualitative sources of secondary data include magazine and newspaper articles and annual reports of industry participants. Question: What is Average? Answer: A single value used to represent the distribution is called average. Most commonly used averages are Mean, Median and Mode. Question: What is Ogive and polygon. Answer: In statistics, an ogive is the curve of a cumulative distribution function. polygon and ogive are same. docsity.com http://www.vustudents.net Answer: Moments: A moment designates the power to which deviations are raised before averaging them. Moment ratio: These are certain ratios in which both numerators and the denominators are moments. Question: what is difference between arbitrary form and dispersion? Answer: Arbitrary form: We find the moment form any value other than the mean that is called the moments about the arbitrary form. Dispersion: By which we mean the extent the observation in a sample or population are spread out. And the second moment about the mean is exactly the same thing as the variance, the positive square root of which is the standard deviation, the most important measure of dispersion? Question: what is the conditinal and un conditinal probability? Answer: In many situations, once more information becomes available, we are able to revise our estimates for the probability of further outcomes or events happening. For example, suppose you go out for lunch at the same place and time every Friday and you are served lunch within 15 minutes with probability 0.9. However, given that you notice that the restaurant is exceptionally busy, the probability of being served lunch within 15 minutes may reduce to 0.7. This is the conditional probability of being served lunch within 15 minutes given that the restaurant is exceptionally busy Question: explain What is Moment ratios? docsity.com http://www.vustudents.net Answer: Moment ratios are certain ratios in which both the numerator and the denominator are moments. The most common of these moment-ratios are denoted by b1 and b2 and defined by the relations: i) b1 = (m3)2 / (m2)3 ii) b2 = m4 / (m2)2 These are independent of origin and units of measurement, i.e. they are pure numbers. b1 is used to measure the Skewness of distribution, and b2 is used to measure the kurtosis of the distribution. Question: Why the significance level is consider 0.05? Answer: By a = 5%, we mean that there are about 5 chances in 100 of incorrectly rejecting a true null hypothesis. That is, we want to make the significance level as small as possible in order to protect the null hypothesis and to prevent, as far as possible, the investigator from inadvertently making false claims. Question: What is the difference between p(type 1 error) and p(type2 error)? Answer: Type I error: On the basis of sample information, we may reject the null hypothesis H0, when it is, in fact true. This type of error is called the type I error. Type II error: On the basis of sample information we may accept the null hypothesis H0, when it is actually false. This type of error is called the type II error. docsity.com http://www.vustudents.net Question: write down the LAW OF COMPLEMENTATION and ADDITION LAW. Answer: LAW OF COMPLEMENTATION: If A is the complement of an event A relative to the sample space S, then P (A) = 1 – P (A) Complementary probabilities are very useful when we want to solve questions of the type ‘What is the probability that, in tossing two fair dice, at least one even number will appear?’ ADDITION LAW If A and B are any two events defined in a sample space S, then P (AÈB) = P (A) + P (B) – P (AÇB) Question: Define Multiplication theorem of probability for independent events. what is marginal probability. Answer: Multiplication theorem of probability for independent events is as follows: P(A Ç B) = P(A) P(B) Here A and B are independents events. P(A) and P(B) are called marginal probabilities whereas, P(A Ç B) is called joint probability of A and B. Question: define sampling with replacement and sampling without replacement. Answer: In sampling with replacement, the units are replaced back before the next unit is selected. In this sampling procedure, number of units in population remains same for all selections. Let ‘N’ be the population size and ‘n’ be the sample size then number of possible samples that can be drawn with replacement are Nn. In sampling without replacement, the units are not replaced back before the next unit is selected. In this sampling procedure, docsity.com