Tag: measures of dispersion and skewness

Quizzes (4) Questions (166)

Questions Related to measures of dispersion and skewness

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

If A and B are two events which have no point in common, the events A and B are ______.

  1. complementary to each other

  2. independent

  3. mutually exclusive

  4. dependent
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In probability two events are said to be independent if the occurrence of one event is not affected by the occurrence of another event. Both the variable are completely independent of each other. These events are also known as mutually exclusive event as they have no common point. 

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

Which of the following statements is true of a measure of dispersion?

  1. Mean deviation does not follow algebraic value

  2. Range is crudest measure

  3. Coefficient of variation is a relative measure

  4. All the above statements
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

  • Mean deviation is the arithmetic average of the deviations of the observed values from an  average of the observed values. Since Mean deviation do not include negative value of the deviations. Therefore, it does not follow the algebraic value of the deviations.
  • Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion. Since it is the most affected measures of dispersion by the extreme values of the series, it is regarded as the crudest measure. 
  • Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.Therefore, Coefficient of variation is a unit less or relative measure of dispersion as variation is the absolute measure of dispersion. 

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The relation between variance and standard deviation is ________.

  1. variance is the square root of standard Deviation

  2. square of the standard deviation is equal to Variance

  3. variance is equal to standard deviation

  4. standard deviation is the square of the variance
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data.

Variance is the mean of the squares of the deviations from the mean. 

Standard deviation is the square root of variance or variance is the square of standard deviation. 

S.D = {Var(X)}1/2 

or 

Var(X) = (S.D)2

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

Frequency distribution is __________________.

  1. Tabular arrangement of data with corresponding frequency

  2. Graphical arrangement of data with corresponding frequency

  3. Tabular arrangement of data without corresponding frequency

  4. Graphical arrangement of data without corresponding frequency
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A frequency distribution is a tabular summary of data showing the frequency of items in each of several non-overlapping classes. It organizes raw data into a structured table format.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

Probability can take values from ______.

  1. -3 to 3

  2. -3 to 1

  3. 0 to 1

  4. -1 to 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Probability shows the relationship between two variables in the form of ratio, percentage or proportion where there the chances of occurrence of one variable is expressed in terms of other variable. Since the value of one variable belongs to the range of value of another variable, the range o probability varies from 0 to 1. 
Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

A student obtained the mean and the standard deviation of 100 observations as 40 and 5.1. It was later found that one observation was wrongly copied as 50, the correct figure being 40. Find the correct mean and the S. D.

  1. Mean = 38.8, S. D. = 5

  2. Mean = 39.9, S. D. = 5

  3. Mean = 39.9, S. D. = 4

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

If the coefficient of correlation between $x,y$ is $0.7$ and covariance is $35$ find the standard deviation of $y$ if the standard deviation of $x$ is $5$____.

  1. $10$
  2. $9$
  3. $8$
  4. $11$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for covariance is Cov(x,y) = r * SD(x) * SD(y). Plugging in the values: 35 = 0.7 * 5 * SD(y). Thus, 35 = 3.5 * SD(y), which means SD(y) = 35 / 3.5 = 10.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The standard deviation of sample of 30 observations is 1532. If the value of each item of the observation is increased by 5. The new standard deviation will be ______.

  1. same as original

  2. increased by 5

  3. reduced by 5

  4. reduced by 5 times.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Standard deviation is a measure of dispersion. Adding a constant to every observation shifts the data but does not change the spread or distance between points, so the standard deviation remains unchanged.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

From the following data calculate the coefficient of concurrent deviation:
Number of pairs of observations=94
Number of pairs of concurrent deviation=34

  1. -0.5

  2. 0.06

  3. 1.5

  4. 0.09
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for the coefficient of concurrent deviation is r_c = +/- sqrt(+/- (2c - n) / n). Here, n = 94 and c = 34. The number of deviations is n-1 = 93. The number of concurrent deviations is 34. The formula is r_c = +/- sqrt(abs((2c - n) / (n - 1))). Calculation: (2*34 - 93) / 93 = (68 - 93) / 93 = -25 / 93 approx -0.268. The square root of 0.268 is approx 0.51. Given the options, -0.5 is the intended answer.