1.
Which of the following statements about statistics is not correct?
Correct Answer
D. Statistics is of two types: descriptive and inferential.
Explanation
The statement "Statistics is of two types: descriptive and inferential" is not correct. Statistics is not limited to just two types; it encompasses various branches and methods such as exploratory data analysis, probability theory, regression analysis, and more. Descriptive statistics involves summarizing and presenting data, while inferential statistics involves making inferences or predictions about a population based on sample data. However, these two types are just a small part of the broader field of statistics.
2.
Which of the following statements describes "Statistics" most appropriately?
Correct Answer
C. Statistics is concerned with the collection, presentation and analysis of data leading to valid conclusions.
Explanation
The correct answer is "Statistics is concerned with the collection, presentation, and analysis of data leading to valid conclusions." This statement accurately describes the main purpose and focus of statistics. It highlights that statistics involves gathering data, organizing and presenting it in a meaningful way, and analyzing it to draw valid conclusions. This process allows for the interpretation and understanding of patterns, trends, and relationships within the data, which can then be used to make informed decisions or draw reliable conclusions.
3.
Which of the following is the most accurate method of classifying data?
Correct Answer
C. Method depending on the nature of information required for a particular situation/ problem.
Explanation
The most accurate method of classifying data is to use a method that depends on the nature of the information required for a particular situation or problem. This means that the classification method should be tailored to the specific needs and context of the situation, ensuring that the data is categorized in a way that is relevant and meaningful. Using a method that considers the specific requirements of the situation will result in a more accurate classification of the data.
4.
The first step in the formation of a frequency table is?
Correct Answer
C. Deciding an appropriate number of class groupings.
Explanation
The first step in the formation of a frequency table is deciding an appropriate number of class groupings. This involves determining how many classes or categories the data should be divided into. The number of class groupings will depend on the range and distribution of the data. Once the number of class groupings is decided, the data can then be classified into the appropriate classes. Choosing a suitable size or width of class intervals and establishing the boundaries of each class interval are subsequent steps in the formation of a frequency table.
5.
The sum of deviations taken from arithmatic mean is?
Correct Answer
B. Zero
Explanation
The sum of deviations taken from the arithmetic mean is zero because the arithmetic mean is calculated by summing all the values and dividing by the total number of values. This means that the positive deviations cancel out the negative deviations, resulting in a sum of zero.
6.
When calculating median of data set, the first step is:
Correct Answer
B. Arrange the data in ascending or descending order
Explanation
The correct answer is to arrange the data in ascending or descending order. This is because the median is the middle value of a data set when it is ordered. By arranging the data in ascending or descending order, we can easily identify the middle value and calculate the median accurately.
7.
Which of the following statements is not correct?
Correct Answer
C. Some data sets do not have mean
Explanation
The statement "Some data sets do not have mean" is not correct. The mean is a measure of central tendency that can be calculated for any data set, as long as there is numerical data available. Even if the data set has extreme values or is weighted, the mean can still be calculated. Therefore, it is incorrect to say that some data sets do not have a mean.
8.
Which of the following statement is not correct in respect of the range as a measure of dispersion?
Correct Answer
A. It is difficult to calculate
Explanation
The given statement "It is difficult to calculate" is not correct in respect of the range as a measure of dispersion. The range is actually very easy to calculate as it only requires finding the difference between the maximum and minimum values in a data set. It does not involve any complex calculations or statistical formulas. Therefore, the statement that it is difficult to calculate is incorrect.
9.
Which of the following is not true in respect of mean deviation?
Correct Answer
C. It is capable of further algebric treatment.
Explanation
Mean deviation is a measure of dispersion that calculates the average distance between each data point and the mean. It is simple to understand because it involves finding the absolute differences between each data point and the mean, and then taking the average of these differences. It considers each and every item in a series because it takes into account the deviations of all data points from the mean. The extreme items have less effect on its magnitude because the absolute differences are used, making it less sensitive to outliers. However, mean deviation is not capable of further algebraic treatment because it does not have the same mathematical properties as other measures of dispersion, such as variance or standard deviation.
10.
Which of the curves is more peaked than the normal curve?
Correct Answer
C. Lapokurtic
Explanation
The term "kurtosis" refers to the measure of the shape of a probability distribution curve. A mesokurtic curve has the same amount of peakiness as the normal curve, while a platykurtic curve is less peaked. Therefore, a lapokurtic curve is more peaked than the normal curve.
11.
In a symmetrical series:
Correct Answer
D. Mean=mode=median
Explanation
In a symmetrical series, the mode represents the value that occurs most frequently, while the mean is the average of all the values, and the median is the middle value when the series is arranged in ascending or descending order. When the mean, mode, and median are equal, it indicates that the series is perfectly symmetrical. In other words, all the values are evenly distributed around the center, resulting in the same value for the mean, mode, and median.
12.
If the outcome of one event doesnot influence another event, then the two events are:
Correct Answer
C. Independent
Explanation
If the outcome of one event does not influence another event, then the two events are considered independent. This means that the occurrence or non-occurrence of one event has no effect on the probability of the other event happening. In other words, the outcome of one event does not provide any information or affect the likelihood of the outcome of the other event.
13.
What is the probability of getting an even number when a die is tossed?
Correct Answer
B. 1/2
Explanation
When a fair six-sided die is tossed, there are three even numbers (2, 4, and 6) and three odd numbers (1, 3, and 5). Since the probability of getting an even number is the number of favorable outcomes (3) divided by the total number of possible outcomes (6), the probability is 3/6, which simplifies to 1/2.
14.
What is the probability of drawing an ace from a bunch of playing cards?
Correct Answer
B. 1/13
Explanation
The probability of drawing an ace from a bunch of playing cards is 1/13. This is because there are 4 aces in a standard deck of 52 playing cards, and the probability of drawing one specific ace is 1/52. Since there are 4 aces in total, the probability of drawing any ace is 4/52, which simplifies to 1/13.
15.
When the sample size increases, which of the following is correct?
Correct Answer
C. The standard error declines
Explanation
As the sample size increases, the standard error declines. This is because the standard error measures the variability or dispersion of the sample mean from the true population mean. With a larger sample size, there is more data available, which reduces the variability and leads to a more precise estimate of the population mean. Therefore, the standard error decreases as the sample size increases.
16.
When the two regression lines coincide, then "r" is:
Correct Answer
C. 1
Explanation
When the two regression lines coincide, it means that the correlation coefficient "r" is equal to 1. A correlation coefficient of 1 indicates a perfect positive linear relationship between the variables being analyzed. This means that as one variable increases, the other variable also increases in a consistent and proportional manner. Therefore, when the regression lines coincide, it suggests that the variables have a strong positive correlation and can be accurately predicted using a linear regression model.
17.
What will be the range of "r" when we find that the dependent variable increases as the independent variable increases?
Correct Answer
C. 0.1 to 1
Explanation
When the dependent variable increases as the independent variable increases, it indicates a positive correlation between the two variables. In this case, the range of "r" would be between 0.1 and 1, as these values represent a strong positive correlation. Values below 0.1 would indicate a weaker positive correlation, and values above 1 would not be possible as the correlation coefficient "r" cannot exceed 1.
18.
Which of the following correlation coefficients shows the highest degree of association?
Correct Answer
D. Both a & b
Explanation
Both a correlation coefficient of -1 and a correlation coefficient of 1 indicate a perfect linear relationship between two variables. A correlation coefficient of -1 means that as one variable increases, the other variable decreases in a perfectly linear fashion. On the other hand, a correlation coefficient of 1 means that as one variable increases, the other variable also increases in a perfectly linear fashion. Therefore, both of these correlation coefficients show the highest degree of association between the variables.
19.
When the correlation coefficient between x and y is positive, then as variable x decreases, variable y :
Correct Answer
C. Decreases
Explanation
When the correlation coefficient between two variables, x and y, is positive, it indicates a positive linear relationship between them. This means that as variable x decreases, variable y tends to decrease as well. In other words, there is an inverse relationship between x and y, where a decrease in x is associated with a decrease in y.
20.
Which of the following components is used for a short-term forecast?
Correct Answer
D. None of the rest options
Explanation
The components mentioned in the options (cyclical, trend, seasonal) are used for long-term forecasts rather than short-term forecasts. Short-term forecasts typically focus on predicting immediate or near-future outcomes and do not consider long-term patterns or fluctuations. Therefore, the correct answer is "none of the rest options" as none of the components mentioned are specifically used for short-term forecasting.