Basic Statistics MCQs with Answers 15

This post is about Basic Statistics MCQs with Answers. There are 20 multiple-choice questions from the construction of frequency distribution, cumulative frequency, class intervals, class boundaries, and class width. Let us start with Basic Statistics MCQs with Answers.

Multiple-Choice Questions about Frequency Distribution Table

1. Frequencies of all specific values of x and y variables with total calculated frequencies are classified as

 
 
 
 

2. The class interval classification method which ensures data continuity is classified as

 
 
 
 

3. ‘less than type’ cumulative frequency distribution is considered as correspondence to

 
 
 
 

4. Table in which data represented is extracted from some other data table is classified as

 
 
 
 

5. The classification method in which the upper and lower limits of the interval are also in the class interval itself is called

 
 
 
 

6. Which one of the following is the class frequency?

 
 
 
 

7. The type of classification in which a class is subdivided into subclasses and subclasses are divided into more classes is considered as

 
 
 
 

8. Cumulative frequency distribution which is the ‘greater than’ type is correspondent to

 
 
 
 

9. The ‘less than type distribution’ and ‘more than type distribution’ are types of

 
 
 
 

10. The type of classification in which a class is subdivided into subclasses and one attribute is assigned for statistical study is considered as

 
 
 
 

11. Frequency distribution which is the result of cross-classification is called

 
 
 
 

12. A complex type of table in which variables to be studied are subdivided with interrelated characteristics is called as

 
 
 
 

13. A distribution which requires the inclusion of open-ended classes is considered as

 
 
 
 

14. Simple classification and manifold classification are types of

 
 
 
 

15. The exclusive method and inclusive method are ways of classifying data on the basis of

 
 
 
 

16. A term used to describe frequency curve is

 
 
 
 

17. General tables of data used to show data in an orderly manner are called as

 
 
 
 

18. Distribution which shows a cumulative figure of all observations placed below the upper limit of classes in distribution is considered as

 
 
 
 

19. The type of table in which study variables provide a large number of information with interrelated characteristics is classified as

 
 
 
 

20. The type of cumulative frequency distribution in which class intervals are added in bottom-to-top order is classified as

 
 
 
 

Basic Statistics MCQs with Answers

Online Basic Statistics MCQs with Answers
  • The classification method in which the upper and lower limits of the interval are also in the class interval itself is called
  • General tables of data used to show data in an orderly manner are called as
  • Frequencies of all specific values of x and y variables with total calculated frequencies are classified as
  • A term used to describe frequency curve is
  • Distribution which shows a cumulative figure of all observations placed below the upper limit of classes in distribution is considered as
  • A distribution which requires the inclusion of open-ended classes is considered as
  • The type of cumulative frequency distribution in which class intervals are added in bottom-to-top order is classified as
  • The ‘less than type distribution’ and ‘more than type distribution’ are types of
  • The exclusive method and inclusive method are ways of classifying data on the basis of
  • The type of classification in which a class is subdivided into subclasses and subclasses are divided into more classes is considered as
  • Frequency distribution which is the result of cross-classification is called
  • The type of table in which study variables provide a large number of information with interrelated characteristics is classified as
  • Table in which data represented is extracted from some other data table is classified as
  • The class interval classification method which ensures data continuity is classified as
  • Which one of the following is the class frequency?
  • A complex type of table in which variables to be studied are subdivided with interrelated characteristics is called as
  • ‘less than type’ cumulative frequency distribution is considered as correspondence to
  • The type of classification in which a class is subdivided into subclasses and one attribute is assigned for statistical study is considered as
  • Cumulative frequency distribution which is the ‘greater than’ type is correspondent to
  • Simple classification and manifold classification are types of
Basic Statistics MCQs with Answers 15

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Best MCQs Data and Variable 14

The post is about MCQs Data and Variables. There are 20 multiple-choice questions related to variables, data, population, sample, and types of variables. Let us start with MCQs Data and Variable with Answers.

Please go to Best MCQs Data and Variable 14 to view the test

MCQs Data and Variable with Answers

MCQs Data and Variable with answers
  • When data are collected in a statistical study for only a portion or subset of all elements of interest we are using:
  • In statistics, a population consists of:
  • In statistics, a sample means:
  • In statistics, conducting a survey means:
  • A data set is a:
  • A variable is a:
  • An observation is the:
  • A quantitative variable is one that can:
  • A qualitative variable is the one that:
  • Time-series data are collected:
  • Cross-section data are collected:
  • Which one of the following is an example of qualitative data?
  • Which one of the following is an example of cross-section data?
  • Which one of the following is a continuous variable?
  • What tasks are involved in data cleaning? Select all that apply
  • What is the main objective of data cleaning?
  • A statistician wants to determine the total annual medical costs incurred by all districts of Pakistan from 1981 to 2001 as a result of health problems related to smoking. He polls each of the districts annually to obtain health care expenditures, in dollars, on smoking-related illnesses. Which one of the following is not a true statement?
  • A scientist is experimenting to determine the relationship between the consumption of a certain type of food and high blood pressure. He conducts a random sample on 2,000 people and first asks them a “yes” or “no” question: Do you eat this type of food more than once a week? He also takes the blood pressure of each person and records it (for example: 120/80). Which one of the following statements is true?
  • Variables whose measurement is done in terms such as weight, height, and length are classified as
  • Government and non-government publications are considered as
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Errors in Statistics: A Comprehensive Guide

To learn about errors in statistics, we first need to understand the concepts related to true value, accuracy, and precision. Let us start with these basic concepts.

True Value

The true value is the value that would be obtained if no errors were made in any way by obtaining the information or computing the characteristics of the population under study.

The true value of the population is possible obtained only if the exact procedures are used for collecting the correct data, every element of the population has been covered and no mistake or even the slightest negligence has happened during the data collection process and its analysis. It is usually regarded as an unknown constant.

Accuracy

Accuracy refers to the difference between the sample result and the true value. The smaller the difference the greater will be the accuracy. Accuracy can be increased by

  • Elimination of technical errors
  • Increasing the sample size

Precision

Precision refers to how closely we can reproduce, from a sample, the results that would be obtained if a complete count (census) was taken using the same method of measurement.

Errors in Statistics

The difference between an estimated value and the population’s true value is called an error. Since a sample estimate is used to describe a characteristic of a population, a sample being only a part of the population cannot provide a perfect representation of the population (no matter how carefully the sample is selected). Generally, it is seen that an estimate is rarely equal to the true value and we may think about how close will the sample estimate be to the population’s true value. There are two kinds of errors, sampling and non-sampling errors.

  • Sampling error (random error)
  • Non-sampling errors (nonrandom errors)

Sampling Errors

A sampling error is the difference between the value of a statistic obtained from an observed random sample and the value of the corresponding population parameter being estimated. Sampling errors occur due to the natural variability between samples. Let $T$ be the sample statistic and it is used to estimate the population parameter $\theta$. The sampling error may be denoted by $E$,

$$E=T-\theta$$

The value of the sampling error reveals the precision of the estimate. The smaller the sampling error, the greater will be the precision of the estimate. The sampling error may be reduced by some of the following listed:

  • By increasing the sample size
  • By improving the sampling design
  • By using the supplementary information

Usually, sampling error arises when a sample is selected from a larger population to make inferences about the whole population.

Errors in Statistics, Sampling Error

Non-Sampling Errors

The errors that are caused by sampling the wrong population of interest and by response bias as well as those made by an investigator in collecting, analyzing, and reporting data are all classified as non-sampling errors (or non-random errors). These errors are present in a complete census as well as in a sampling survey.

Bias

Bias is the difference between the expected value of a statistic and the true value of the parameter being estimated. Let $T$ be the sample statistic used to estimate the population parameter $\theta$, then the amount of bias is

$$Bias = E(T) – \theta$$

The bias is positive if $E(T)>\theta$, bias is negative if $E(T) <\theta$, and bias is zero if $E(T)=\theta$. The bias is a systematic component of error that refers to the long-run tendency of the sample statistic to differ from the parameter in a particular direction. Bias is cumulative and increases with the increase in size of the sample. If proper methods of selection of units in a sample are not followed, the sample result will not be free from bias.

Note that non-sampling errors can be difficult to identify and quantify, therefore, the presence of non-sampling errors can significantly impact the accuracy of statistical results. By understanding and addressing these errors, researchers can improve the reliability and validity of their statistical findings.

Errors in Statistics: Potential Sources of Error

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Quartiles

Introduction to Quantiles and Quartiles

Quantiles are the techniques used to divide the data into different equal parts. For example, quantiles divide the data into four equal parts. Quartile comes from quarter which means 4th part. Deciles divide the data into ten equal parts and they come from deca means the 10th part. Percentiles divide the data into hundred parts and it comes to percent which means the 100th part.

Therefore, quartiles, deciles, and percentiles are used to divide the data into 4, 10, and 100 parts respectively. The quantiles, deciles, and percentiles are collectively called quantiles.

Quartiles

Quartiles are the rules which divide the data into four equal parts. When we divide any data into four equal parts then we cut it at e equidistant points. Therequartiles ($Q_1, Q_2$, and $Q_3$) as quartiles divide the data into four equal parts so divide the number of observations by four for each quartile.

Quartiles for Ungroup Data

\begin{align*}
Q_1 &= \left(\frac{n+1}{4}\right)th \text{ value is the} \frac{1}{4} \text{ part}\\
Q_2 &= \left(\frac{2(n+1)}{4}\right)th \text{ value is the} \frac{2}{4} \text{ part}\\
\left(\frac{3(n+1)}{4}\right)th \text{ value is the} \frac{3}{4} \text{ part}
\end{align*}

The following ungroup data has 96 observations $(n=96)$

222225253030303131333639
404042424848505152555759
818689899091919192939393
939494949596969697979898
999999100100100101101102102102102
102103103104104104105106106106107108
108108109109109110111112112113113113
113114115116116117117117118118119121

The first, second, and third quartiles of the above data set are:

\begin{align*}
Q_1 &= \left(\frac{n}{4}\right)th \text{ position } = \left(\frac{96}{4} = 24th \text{ value} = 59\\
Q_2 &= \left(\frac{2\times 96}{4}\right) = 48th \text{position} = 98\\
Q_3 &= \left(\frac{3\times n}{4}\right)th = \left(\frac{3\times 96}{}\right)th \text{ position} = 72th \text{ position} = 108
\end{align*}

Note that the above data is already sorted. If data is not sorted, first we need to arrange/sort the data in ascending order.

Quartiles for Gruoped Data

For the following grouped data one can also compute the quantiles, hence the quartiles.

ClassesfxC.B.CF
65-84974.564.5-84.59
85-1041094.584.5-104.519
105-12417114.5104.4.5-124.536
125-14410134.5124.5-144.546
145-1645154.5144.5-164.551
165-1844174.5164.5-184.455
185-2045194.5184.5-204.560
Total60   

From the above-grouped data, we have 60 observations $(n=60)= \sum\limits_{i=1}^n = f_i = \Sigma f = 60$. The three quartile will be

\begin{align*}
\frac{n}{4} &= \left(\frac{60}{4}\right)th = 15th \text{ value}\\
Q_1 &= l + \frac{h}{f}\left(\frac{n}{4} – CF\right) = 84.5 + \frac{20}{10}(15-9) = 96.5\\
\frac{2n}{4} &= \left(\frac{2\times 60}{4} \right) = 30th \text{ value}\\
Q_2 &= l + \frac{h}{f}\left(\frac{2n}{4} – CF\right) = 104.5 + \frac{20}{17}(30-19) = 117.44\\
\frac{3n}{4} &= \left(\frac{3\times 60}{4} \right) = 45th \text{ value}\\
Q_3 &= l + \frac{h}{f}\left(\frac{3n}{4} – CF\right) = 124.5 + \frac{20}{17}(45-36) = 142.5\\
\end{align*}

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