Statistical Tools MCQ Quiz in मल्याळम - Objective Question with Answer for Statistical Tools - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Statistical tests:

1. A statistical test provides a mechanism for making quantitative decisions about a process or processes.
2. The intent is to determine whether there is enough evidence to "reject" a conjecture or hypothesis about the process.
3. The conjecture is called the null hypothesis.
4. Not rejecting may be a good result if we want to continue to act as if we "believe" the null hypothesis is true.
5. Or it may be a disappointing result, possibly indicating we may not yet have enough data to "prove" something by rejecting the null hypothesis.

The coefficient of determination :

1. The coefficient of determination is a statistical measurement that examines how differences in one variable can be explained by the difference in a second variable when predicting the outcome of a given event.
2. In other words, this coefficient, which is more commonly known as R-squared (or R²), assesses how strong the linear relationship is between two variables, and is heavily relied on by researchers when conducting trend analysis. 
3. This correlation, known as the "goodness of fit," is represented as a value between 0.0 and 1.0. A value of 1.0 indicates a perfect fit, and is thus a highly reliable model for future forecasts, while a value of 0.0 would indicate that the calculation fails to accurately model the data at all. 

Therefore, if a researcher wants to know whether a student's attendance is randomly distributed throughout the academic year. The type of statistical test she should use is the Co-efficient of determination.

1. t-test: In t-test, the mean of the two given samples are compared. A t-test is used when the population parameters (mean and standard deviation) are not known.
2. Binomial test: In statistics, the binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories. 
3. Chi-square test: The Chi-Square Test of Independence determines whether there is an association between categorical variables (i.e., whether the variables are independent or related). It is a nonparametric test. This test is also known as the Chi-Square Test of Association.

D, B, A, C is the correct answer.

Key Points

• Coefficient of Variation (CV): The coefficient of variation is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation to the mean and is often expressed as a percentage.
  • The formula for CV is: CV = (σ / x̅) * 100
• Calculating CV for Each Dataset: We calculate the CV for each of the given datasets using the provided means (x̅) and standard deviations (σ).
  • Dataset A: ( x̅ = 21, σ = 4.0 )
    • CV_A = (4.0 / 21) * 100 ≈ 19.05%
  • Dataset B: ( x̅ = 19, σ = 2.5 )
    • CV_B = (2.5 / 19) * 100 ≈ 13.16%
  • Dataset C: ( x̅ = 24, σ = 5.2 )
    • CV_C = (5.2 / 24) * 100 ≈ 21.67%
  • Dataset D: ( x̅ = 15, σ = 1.8 )
    • CV_D = (1.8 / 15) * 100 ≈ 12.00%
• Arranging Datasets by Increasing Order of CV:
  • Dataset D: CV ≈ 12.00%
  • Dataset B: CV ≈ 13.16%
  • Dataset A: CV ≈ 19.05%
  • Dataset C: CV ≈ 21.67%
• Result:
  • Hence, the datasets in increasing order of their coefficient of variation are: D, B, A, C.

The normal distribution is a symmetrical continuous probability distribution on both sides of the mean, with the right side of the center mirroring the left.

Key Points

• The whole area under the normal distribution curve equals one and the area under the curve reflects probability. 
• In a normal distribution, most continuous data values cluster around the mean, and the further a value is from the mean, the less likely it is to occur.
•  Normal distributions are continuous and asymptotic, meaning that their tails approach but never touch the x-axis.
• The mean, median, and mode of a completely normal distribution will all be the same value. 
• The probability density graph of the normal distribution resembles a bell which is commonly referred to as the bell curve.

Thus, the characteristics of a normal distribution curve are bell‐shaped, mean, mode, and median coincide at the center of the distribution and the curve is based on an infinite number of observations.

Statistical software is a specialized computer program for analysis in statistics and econometrics.

Important Points

Hence, the correct answer is A, B, D, and E only.

Qualitative Data Analysis Software is a system that helps with a wide range of processes that help in content analysis, transcription analysis, discourse analysis, coding, text interpretation, recursive abstraction, grounded theory methodology, and interpreting information so as to make informed decisions.

Key Points

NVivo software:

• NVivo is a software program used for qualitative and mixed-methods research.
• Specifically, it is used for the analysis of unstructured text, audio, video, and image data, including (but not limited to) interviews, focus groups, surveys, social media, and journal articles.
• It is produced by QSR International. As of July 2014, it is available for both Windows and Macintosh operating systems

Additional Information

R is a programming language for statistical computing and graphics.

• It compiles and runs on a wide variety of UNIX platforms, Windows and MacOS.
• Qualitative data analysis tools can help organize, process, and analyze data for actionable insights. 
• Qualitative data analysis software is used across a wide range of sectors and industries such as healthcare, the legal industry, e-commerce businesses,

SPSS is a software program. it stands for Statistical Package for the Social Sciences, and it's used by various kinds of researchers for complex statistical data analysis.

• The SPSS software package was created for the management and statistical analysis of social science data.

STATA is a powerful statistical software developed by StataCorp for data manipulation, visualization, statistics, and automated reporting.

• It enables users to analyze, manage, and produce graphical visualizations of data.
• It is primarily used by researchers in the fields of economics, biomedicine, and political science to examine data patterns.​

Frequency distribution is a set of organized data that is used to depict the frequency of occurrence of each outcome which has a possibility of repeatable events. It is used for summarizing categorical variables.

• In the above question, for any frequency distribution, the 50th percentile and median are the same.
• Median is a positional average as it is based on the position of the given observation of data in the series. Median is the value that divides the data into two equal parts. Median is the 50^th percentile value.
• Percentile divides the data into 100 equal parts and contains 1 percentile in each part. 50^th percentile divides the data into two equal parts and is equal to the median.

Additional Information

• Quartile distributes the data into four parts and there are 3 quartiles. The 2^nd quartile distributes the data into two parts and is the same as the median.
• Decile divides the data into 10 equal parts and is known as D1, D2…. till D9.
• There exists a relationship between percentile, decile, quartile, and median i.e.,
• P25=Q1,
• P50=D5=Q2= Median
• P75=Q3
• Mean is the most common value in a set of data. It is also the average of given data set and is a measure of central tendency along with mode and median. It can be calculated by calculating the sum of all the values divided by the total number of observations.
• Standard deviation is measure in statistics that depicts the dispersion of a dataset in relation to its mean and it can be calculated by doing the square root of the variance.

Thus, option 2 is the correct answer.

 Key Points

SPSS

• SPSS (Statistical Package for the Social Sciences) is a widely used software for statistical analysis in social science.
• It is also used by market researchers, health researchers, survey companies, government, education researchers, marketing organizations, data miners, and others.
• Hence, Statement A is correct.

MINITAB 

• MINITAB is a statistics package developed at Pennsylvania State University by researchers Barbara F. Ryan, Thomas A. Ryan, Jr., and Brian L. Joiner in 1972.
• It is specifically designed for the teaching of introductory statistics and is also used in some more advanced applications. Hence, Statement C is correct.

R

• R is a programming language and free software environment for statistical computing and graphics supported by the R Foundation for Statistical Computing.
• It is widely used among statisticians and data miners for developing statistical software and data analysis. Thus, Statement D is correct.

Additional Information

Ithenticate  

Ithenticate is a plagiarism detection service and does not perform statistical analysis. It is primarily used for checking the originality of content. Therefore, Statement B is incorrect for the context of statistical analysis.

GIVEN:

Mode - Median = 2

FORMULA USED:

Mode = 3 Median - 2 Mean 

CALCULATION:

Mode - Median = 2.......(1)

⇒ Mode = 3 Median - 2 Mean .....(2)

On solving these two equation

∴ Median - Mean = 1

If a dataset has a negative kurtosis, it means that "The dataset is platykurtic"

Key Points

• Negative kurtosis indicates that the dataset has fewer outliers and flatter tails than a normal distribution.
• A platykurtic distribution has a lower peak and a wider distribution compared to a normal distribution.

Additional Information

• Kurtosis is a statistical measure that describes the shape of a distribution.
• A positive kurtosis value indicates a more peaked distribution with heavier tails than a normal distribution, while a negative kurtosis value indicates a flatter distribution with lighter tails than a normal distribution.
• The kurtosis value of a normal distribution is 3, so any dataset with a kurtosis value less than 3 is platykurtic.
• Platykurtic distributions are also known as "flat" or "leptokurtic" distributions.

Important Points

• Understanding the kurtosis of a dataset is important in data analysis and can provide insights into the shape and behavior of the data.
• Platykurtic distributions are relatively rare, and they often occur in datasets with a large number of observations.
• In finance, platykurtic distributions are associated with lower risk and less volatility, while leptokurtic distributions are associated with higher risk and greater volatility.

The mean, median, mode, percentiles, range, variance, and standard deviation are the most commonly used numerical measures for quantitative data. 

Key Points

• The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation.
• In statistics, a sample mean deviates from the actual mean of a population; this deviation is the standard error of the mean.
• The standard error tells you how accurate the mean of any given sample from that population is likely to be compared to the true population mean.
• When the standard error increases, i.e. the means are more spread out, it becomes more likely that any given mean is an inaccurate representation of the true population means.

Additional Information

• In cluster sampling, researchers divide a population into smaller groups known as clusters. They then randomly select among these clusters to form a sample. Cluster sampling is a method of probability sampling that is often used to study large populations, particularly those that are widely geographically dispersed.
• The normal distribution is symmetrical, bell-shaped distribution in which the mean, median, and mode are all equal. It is a central component of inferential statistics.

Therefore, the standard error is a statistical measure of the extent to which a sample mean is likely to differ from the population mean.