Statıstıcs I Final 9. Deneme Sınavı

The easiest form of data is called categorical, or qualitative. Categorical variables and data can be either nominal or ordinal. Exam grade is an ordinal categorical variable, since its categories are ordered: A is better than a B, B is better than a C, and so on. Other examples of nominal categorical variables are gender, region of residence, field of study, type of transport, type of housing, etc.

It will be zero.

The variance is a measure of the dispersion or variability for data set for continuous
random variables.

k = 60 x 40 / 100 = 24 ; k is in the 3rd class ; P(k) = 300 + (100 / 16) (24 – 14) = 300 + 62.5 = 362.5 . pg. 117. Correct answer is D.

In symmetric distributions like bell-shape and rectangular (or uniform)
ones, the mean and median are the same value. The correct answer is B.97

f(x) = 1 / (b - a) = 1 / (50 - 10) = 1 / 40 ; P (15 < X < 25) = Int(15, 25)(f(x) dx) = Int(15, 25)((1/40) dx) = girdi(15, 25)((1/40) * x) = (1/40) * (25 - 15) = 1/4 = 0.25. pg. 186. Correct answer is D.

The measures of skewness are another kind of descriptive statistics and give information about the shape of distribution of the observations. A data set which is not symmetrically distributed is called skewed. The mainly observed shapes of distribution are symmetric, left skewed (negatively skewed), and right skewed (positively skewed). If the distribution is unimodal symmetric, the mean, median, and mode are all the same. If the distribution is left skewed, having a long tail in negative direction and a single peak, the mean is pulled in the direction of the tail, and the median falls between the mode and the mean. The correct answer is B. 

A random experiment is any process that leads to two or more possible outcomes, without knowing exactly which outcome will occur.
For example, when a fair die is rolled we know that one of the six faces will show up but we will not be able to say exactly which face will actually show up. Thus, rolling a fair die is an example of a random experiment. Some further examples of random experiments are:
• Customers arriving at a particular store during some time interval.
• Airplanes taking off in a given time interval at some airport.
• Some particular customer requests in a bank.
Note that in a random experiment, although we do not know which outcome will occur, we are able to list or describe all of the possible outcomes.The set of all possible outcomes is important to understand the random experiment. Terefore, it is called a sample space, which is restated below as a definition.

The geometric mean is found by taking the square root of all the observation's multiplication. For 4, 25, 100 their multiplication is 4*25*100=10000 and the square root of 10000 is 100. The answer is A.

While all variables can take real numbers in other options, the number of the students cannot take a real number in option E. That is the number of students in a class can only take uncountable numbers.

The probability density function f (x) = 0.1 is a straight line above the values 0 to 20, therefore, it is a rectangle with one side being 0.1 value and the other 20. The area is calculated by 20*(0.1) which is equal to 2. The answer is A.

In binomial distribution, its principal assumptions are n independent trials with two possible outcomes (success or failure) for each trial, and the success probability remains constant for each trial. Therefore in binomial distribution the sampling process is carried out with replacement. On the other hand hypergeometric distribution doesn’t involve with independence assumption for each trial and accordingly the sampling process is established on without replacement. Because of these features, hypergeometric distribution is broadly used in various real life applications especially for acceptance sampling in quality control.The correct answer is C. 

The trimmed or as it may sometimes be called as the truncated mean is a slightly modified version of the
arithmetic mean. Trimmed or truncated mean is calculated after a certain number or proportion of the lowest and highest observations from the sorted data are removed (trimmed) from the calculations. First, the data is ordered from smallest to largest, as follows, 2,3,4,5,6,6,7. Then we will find how many data points will be discarded, k, since the trimming is 30% and there are 7 observations, the value of k is k = np = 7×0.30 = 2,1 which is nearly 2. Therefore two 2,3,6 and 7 is removed from the set, which yields to 4,5,6. The sum, 15 is divided to n - 2k which is equal to 7 - 2*2=3 this results in the value 5.The answer is D.

Mode is the most frequently appearing score in a data set.So the correct answer is A.

median : 12 ; arithmetic mean : m = 70 / 5 = 14 ; s = ((4² + 2² + 2² + 2² + 6²) / 4)^1/2 = 4 ; Pearson’s coefficient of skewness PCS = 3 (14 – 12) / 4 = 1.5 . pg. 122. Correct answer is D.

S = {BR , BB , RB , RR} ; C(10, 2) = 10! / (2! * (10-2)!) = 10! / (2! * 8!) = 10 * 9 / 2 = 45 ; P(BR) + P(BB) = (6 / 10) * (4 / 9) + (6 / 10).* (5 / 9) = 6 * 4 / (10 * 9) + 6 * 5 / (10 * 9) = 4 / 15 + 1 / 3 = 9 / 15 = 3 / 5. pg. 137. Correct answer is A.

The  empirical probability uses the relative frequencies to assign the probabilities to the events. The empirical probability is based on experiments. In order to find the probability of a specific event, the experiments are repeated many times and the observed outcomes of the event we are interested in is counted. We can formularize this by following equation
The more experiment we do, we may get better results for the probability that we are looking for.

The correct answer is D.