Basic Statistics MCQs with Answers 15

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

7. A term used to describe frequency curve is

 
 
 
 

8. Simple classification and manifold classification are types of

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

19. The type of classification in which a class is subdivided into subclasses and one attribute is assigned for statistical study is considered 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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Binomial Random Variables

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Introduction

A discrete random variable $x$ is said to have a binomial distribution if $x$ (binomial random variable) satisfies the following conditions:

  • An experiment is repeated for a fixed number of trials $n$.
  • All the trials of the experiments are independent of each other.
  • All possible outcomes for each trial of the experiment can be classified into two mutually (complementary) events: one is $S$ (called success) and the other is $F$ (called failure).
  • The probability of success $P(S)$ has a constant value of $p$ for every trial (that is, the probability of success is fixed for each trial) and hence the probability of failure $P(F)$ has a constant/fixed value of $q$ for every trial, where $q=1-p$.
  • The random variable $x$ counts the number of trials on which $S$ (success) occurred.

Calculating Probabilities for a Binomial Random Variable

If $X$ is a binomial random variable with $n$ trials, probability of success $p$ (and probability of failure $q$), then by the fundamental counting principle, the probability of any outcome in which there are $x$ successes (and therefore $n-x$ failures) is

Binomial random variables

To count the number of outcomes with $x$ successes and $n-x$ failures, one can observe that the $x$ successes could occur on any $x$ of the $n$ trials. The number of ways of choosing/selecting $x$ trials out of $n$ is $\binom{n}{x}$, so the probability of $x$ successes becomes:

$$P(X=x)=\binom{n}{x} p^x q^{n-x}$$

Example of Binomial Random Experiments

Example: Consider the experiment of flipping a coin 5 times. Let the event of getting Tails on a flip is considered a “success”. Also, suppose that the random variable $T$ is the number of tails obtained, the $T$ will be binomially distribution with $n=5, p=\frac{1}{2}$, and $q=\frac{1}{2}$.

Solution:
Suppose the random variable $T$ represents the number of trials when a coin is flipped three times.
$$P(X=2) = \binom{3}{2}\left(\frac{1}{2}\right)^2 \left(\frac{1}{2}\right)^1 = 0.375$$

Properties of Binomial Distributions

In many cases, one may be interested in the mean and standard deviation of the binomial random variable. If $x$ is a binomial random variable with $n$ trials with probability of success $p$ and probability of failure $q$, then the mean and standard deviation of $x$ can be computed as

  • Mean: $E(X) = \mu(x) = np$
  • Standard Deviation: $\sigma(x) = \sqrt{npq}$
  • Variance: $npq$

Note that

  • A binomial distribution is symmetric if $p=q$,
  • left skewed if $p>q$ and
  • right-skewed if $p<q$

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Important Probability MCQs Online Test 9

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The post is about the Probability MCQS Online Test. There are 20 multiple-choice questions covering the basics of probability, events and types of events, rules of probability, subjective and classical probability, etc. Let us start with the Probability MCQs Online Test.

Please go to Important Probability MCQs Online Test 9 to view the test

Probability MCQs Online Test

Probability MCQs Online Test
  • A die is rolled. What is the probability that the number rolled is greater than 2 and even
  • If you have two standard decks of cards (one with a blue back and the other with a red back), you draw one card from each. What is the probability that the blue-backed card is a heart or the red-backed card is a black card?
  • If you roll a pair of dice, what is the probability that (at least) one dice is a 1 or the sum of the dice is 9?
  • If a card is chosen from a standard deck of cards, what is the probability of getting a diamond or a club?
  • If a card is chosen from a standard deck of cards, what is the probability of getting a two or a five?
  • If a card is chosen from a standard deck of cards, what is the probability of getting a five or a face card?
  • If a letter is chosen at random from the 10 letters of the word STATISTICS, what is the probability that it is a vowel?
  • From the following table, what is the probability of selecting a female university graduate student from this group?
  • Subjective probabilities are assigned to the events $A$ and $B$, which comprise a sample space. Which of the following probability statements is not valid?
  • A personal manager selects an applicant at random from a large group for an interview. The probability of the applicant being male is 0.60. The probability of selecting an adult is 0.70. The probability of selecting an adult male is 0.45. Given that a male is selected, the probability that he is an adult is:
  • Which of the following is a collection of all mutually exclusive events representing a card randomly selected from a deck of ordinary playing cards?
  • Which of the following are collectively exhaustive events representing a card randomly selected from a deck of ordinary playing cards?
  • Indicate in which one of the following situations the events $A$ and $B$ are independent:
  • Which one of the following statements is false?
  • A marginal probability might be found by any but which one of the following?
  • Which one of the following statements is not true?
  • If $A$ and $B$ are independent events, $P(A) = 0.45, P(B) = 0.60$ then $P(A \cap B)$ is
  • The probability of drawing one white ball from a bag containing 2 white, 3 blue, and 3 black balls is
  • A letter is chosen at random from the word MATHEMATICS, the probability of getting $M$ is
  • If $P(B|A) = P(B)$ then $A$ and $B$ are
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How to Convert Continuous Variables in SPSS: A Quick Guide

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There may be situations in which one may want to convert continuous variables in SPSS to categorical. For example, one may want to find out how many females earn a starting salary of more than 80,000 using the data of the University of say Florida. For this numeric data, we need to change into categorical variables. In SPSS, this type of transformation is called the recoding of continuous variables to categorical.

Convert Continuous Variables in SPSS to Categorical

Step-by-Step Procedure

In SPSS there are three basic options for recoding the variables.

  • Recode into different variables
  • Recode into the same variable
  • DO IF syntax

Recode into different variables and DO IF syntax creates a new variable without modifying the original variable, while recode into the same variable will permanently overwrite the original variable. Best to record a variable into a different variable. To recode into different variables,

Click Transform > Recode into different variables

Convert Continuous Variables in SPSS to Categorical

The Recode into different variables dialog box will appear as:

Convert Continuous Variables to Categorical in SPSS Input Variable Output variable

The left-side pane of the dialog box lists all of the variables. Select the variable of interest to recode and move the variable to the right-side pane by clicking the arrow button in between the left and right-side dialog box. Let us have the salary variable to transform.

  • Input Variable -> Output
    The center text box lists the variables(s). In this case, we have only a salary variable.
  • Output Variable
    Define the name and label (label is optional) for your recoded variable(s) by typing them in the text field. The new name of the recoded variable (say) will be “new-salary” and then click change.
  • Old and New Variables
  • Click the “old and new values” to specify the categories of the selected variable. A new dialog box will appear, where one needs to specify how to transform the values will appear.
Convert Continuous Variables to Categorical in SPSS Old new Values

Old Values and New Values

The “Old -> New” box specifies the type of value of a recode variable. For example, the value of the recode variable (new value) is 1 or range of 20000 through the highest.

A short description of “Old Values” options.

  • Value:
    Enter a numeric code that represents the category. for example, give the value 1 for 1st category or group.
  • System Missing:
    Apply any system missing value(.).
  • Range or Through:
    This option is used to enter the lower and upper limits that should be coded. The recode category includes both limits (inclusive). For example, 20000 to 40000.
  • Range, Lowest through Value:
    Recode all values greater than or equal to some number.
  • All Other Values:
    Applies any value not explicitly accounted for by the previous recoding rules.

A short description of the “Old -> New” option:

Enter the required group/ category numerical code in the “New Value” and then click the add button below. Repeat this step for each group value that you wish to recode. All the required groups are recorded by adding an “Old -> New” box. Finally, click the continue button. Click the OK button to transform the continuous variable into a categorical variable.

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