S.Y.B.Sc. IT Sem IV Internal Examiniation 2018 - Cost

Variance is the measure of how spread out the data points in a data set are. It is calculated by taking the average of the squared differences between each data point and the mean. The square of the standard deviation is equal to the variance. Standard deviation measures the amount of variation or dispersion from the average, and squaring it gives us the variance. Therefore, the correct answer is variance.

If the occurrence of any event does not depend on another event, then the two events are said to be independent. This means that the outcome of one event has no influence or impact on the outcome of the other event. In other words, the probability of one event happening does not affect the probability of the other event happening.

The mean is calculated by adding up all the values in the data set and then dividing by the total number of values. In this case, the sum of the values is 10 + 20 + 30 + 55 + 60 = 175. Since there are 5 values in the data set, the mean is 175/5 = 35.

The mean is obtained by dividing the sum of values by the number of items. This is a commonly used measure of central tendency that provides the average value of a set of numbers. It is calculated by adding up all the values and then dividing by the total number of values. The mean is useful for finding the average value or representing the typical value in a dataset.

Quartiles divide a series into four equal parts. Each quartile represents 25% of the data, with the first quartile (Q1) representing the lower 25%, the second quartile (Q2) representing the middle 50% (which is also the median), and the third quartile (Q3) representing the upper 25% of the data. Therefore, the correct answer is 4.

Data frames are created using the data.frame() function. This function takes in input vectors and combines them into a data frame structure, where each vector becomes a column in the data frame. The data.frame() function is specifically designed for creating data frames in R, making it the correct answer.

The interquartile range is the difference between the upper quartile and the lower quartile. It is a measure of the dispersion or spread of a dataset, specifically the middle 50% of the data. By subtracting the lower quartile from the upper quartile, we can determine the range of values that fall within this middle range. This range is useful in identifying the variability or spread of the data, while also being less affected by outliers compared to the full range of the data.

The mode is the value that appears most frequently in a set of observations. In this case, the value 22 appears 6 times, which is more than any other value in the set. Therefore, the mode of the given observations is 22.

The sum of all probability distributions in a given set should always equal 1. This is because the total probability of all possible outcomes in an event or experiment should add up to 100% or complete certainty. In this case, the sum of the given probability distribution values is 1, indicating that the probabilities assigned to each outcome cover all possibilities and are consistent with the principles of probability theory.

The range is the difference between the two extreme values in a set of data. It measures the spread or variability of the data. By calculating the difference between the highest and lowest values, we can determine the range of the data set.

The harmonic mean is the ratio between the number of items and the sum of the reciprocals of the items. It is a measure of central tendency that is used when dealing with rates or ratios. It is calculated by dividing the number of items by the sum of their reciprocals. The harmonic mean is useful when dealing with quantities that have a reciprocal relationship, such as speed and time. It gives more weight to smaller values, making it suitable for situations where extreme values need to be minimized.

The median is the value that divides a series into two equal parts. It is the middle value of a dataset when arranged in ascending or descending order. The median is a measure of central tendency and is useful for finding the typical or average value in a dataset. It is different from the mean, which is affected by extreme values. The median is a good measure to use when there are outliers or when the data is not normally distributed.

Kurtosis is a statistical measure that describes the shape of a distribution. It specifically measures the "peakness" or the degree of peakedness of a curve. A high kurtosis value indicates a sharper, more peaked curve, while a low kurtosis value indicates a flatter, less peaked curve. Therefore, the term "peakness" is a suitable explanation for the given correct answer.

The word "REETA" has 5 letters. To find the number of permutations, we use the formula for permutations of distinct objects, which is n!, where n is the number of objects. In this case, n=5. Therefore, the number of permutations of the letters of the word "REETA" is 5! = 5x4x3x2x1 = 120. However, since the letter 'E' appears twice, we need to divide the total number of permutations by 2 to account for the repeated letter. Therefore, the correct answer is 120/2 = 60.

To find the value of p, we need to calculate the sum of all the numbers and then subtract the sum of the given numbers (6, 4, 7, and 10) from the total sum. The sum of the given numbers is 27 (6+4+7+10) and the mean is 8. The mean is calculated by dividing the sum by the number of values, so the total sum is 8 multiplied by 5 (the number of values), which is 40. To find p, we subtract the sum of the given numbers (27) from the total sum (40), which gives us 13. Therefore, p = 13.

The mode is the value that appears most frequently in a set of data. In this case, we are given the median as 6 and the mean as 5. Since the mean is less than the median, it suggests that the data is negatively skewed. Therefore, the mode is likely to be less than both the median and the mean. Among the given options, the only value that is less than 6 is 8. So, the mode is 8.

The range of a set of data is the difference between the highest and lowest values. In this case, the highest value is 99 and the lowest value is 59. Therefore, the range is 99 - 59 = 40.

The median is the middle value in a set of data when the data is arranged in order. In this case, when the data is arranged in ascending order, we have: 21, 24, 27, 30, 32, 34, 35, 38, 48. The middle value is 32, which is the correct answer.

A list is an object that can contain different types of elements inside it. Unlike other data structures like vectors, matrices, or frames, a list does not have any restrictions on the type of elements it can hold. It can store integers, strings, floats, or even other lists. This flexibility makes lists a versatile and commonly used data structure in programming.

The quartile deviation is a measure of the spread or dispersion of a dataset. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3) and dividing the result by 2. In this case, Q1 is 20 and Q3 is 34. Therefore, the quartile deviation is (34 - 20) / 2 = 7.

In R, to create a vector, we use the c() function. This function allows us to combine multiple elements into a single vector. It is commonly used to create numeric, character, or logical vectors by specifying the elements within the parentheses and separating them with commas.

In order to vote for 2 candidates out of a total of 6 (3 men and 3 ladies), the voter can choose any combination of 2 candidates from the total pool. The number of ways to choose 2 candidates out of 6 can be calculated using the formula for combinations, which is nCr = n! / (r!(n-r)!). In this case, n = 6 and r = 2. Plugging in these values, we get 6! / (2!(6-2)!) = 6! / (2!4!) = (6x5) / (2x1) = 15. Therefore, there are 15 ways in which one can cast his vote.

The root mean square (RMS) is a statistical measure that calculates the square root of the average of the squared values in a set of data. To find the RMS of the given data -2, 5, -8, 9, -4, we need to square each value, calculate the average, and then take the square root. The squared values are 4, 25, 64, 81, and 16. The average of these squared values is 38, and the square root of 38 is approximately 6.16. Therefore, the correct answer is 6.16.

The class of 3L is "integer" because the "L" suffix in Python represents a long integer. Long integers are used to represent whole numbers that are larger than the maximum value of the standard integer data type. Therefore, 3L is an example of a long integer, which falls under the "integer" class.

The colon operator creates a series of numbers in a sequence for a vector. It is used to generate a sequence of numbers starting from a specified value and ending at another specified value, with a specified increment between each number. This is commonly used in MATLAB and other programming languages to create vectors with a specific range of values.

The "next" statement is used when we want to skip the current iteration of a loop without terminating it. This allows the loop to continue with the next iteration and execute the statements following the "next" statement.

The quartile deviation is obtained by dividing the difference between the upper quartile and lower quartile by 2. This is because the quartile deviation measures the spread or dispersion of data around the median, and dividing by 2 allows for a standardized measure of dispersion. It represents the average amount of deviation from the median, indicating how spread out the data is within the middle 50% of the dataset.

The geometric mean is the correct answer because it is the average of a set of numbers calculated by taking the nth root of their product. In this question, the nth root of the product of n items is being referred to, which aligns with the definition of the geometric mean. The other options (harmonic mean, range, and quantile) do not involve taking the root of a product, making them incorrect choices.

The mode is the value that appears most frequently in a dataset. It represents the maximum frequency of occurrence for a particular item. In other words, it is the value that occurs the most number of times in a given set of data. The mode is used to describe the central tendency of a dataset and is particularly useful when dealing with categorical or discrete data.

The correct answer is "nlevels". In the context of factors, the "nlevels" function is used to determine the count of levels. It returns the number of distinct levels or categories present in a factor variable. This function is helpful in analyzing and understanding the variability within a categorical variable.

The geometric mean is a measure of central tendency that is calculated by taking the nth root of the product of n numbers. In this case, the geometric mean of 10, 40, and 160 is calculated by taking the cube root of (10 * 40 * 160) which equals 40. Therefore, the correct answer is 40.