Tag: measures of dispersion

Quizzes (8) Questions (118)

Questions Related to measures 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

For a large sample, the sampling distribution of $X^2$ may form________.

  1. a continuous curve

  2. severely skewed curve

  3. the symmetrical curve

  4. either (B) or (C)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a large sample, the sampling distribution of Chi square distribution may form a continuous curve. Chi square distribution helps in measuring how well the observed distribution of data fits with the distribution that is expected.

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

${X}^2$ test is equal to____________.

  1. ${\sum _{i = 1}^{n}} {A{x}^1} = A{x}^1 + A{x}^2 + ... + A{x}^n$
  2. $V = (r - 1) (e - 1)$
  3. $\dfrac {{\Sigma}(O - E)^2}{E}$
  4. $ r = \dfrac {{\Sigma} _{xy}}{\sqrt{{\Sigma}{{x}^2}{{y}^2}}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The correct formula for the estimation of Chi-Square test is mentioned in Option C, where O represents the frequency observed while E represents the frequency expected.

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

T-distribution is symmetrical like normal distribution and its mean value is____________.

  1. zero

  2. -1

  3. 1

  4. 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The mean of t distribution is always equal to 0 and also the variance is always greater than 1 and it is symmetrical like normal distribution.

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 simple formula to calculate the standard error is___________.

  1. $S _{yx} =$ ${\sigma} _{y}{\sqrt{1 - {r}^2}}$
  2. $S _{xy} =$ ${\sigma} _{x}{\sqrt{1 - {r}^2}}$
  3. $S _{yx} = $ S.E.

  4. Both (A) and (B)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Standard error can be calculated by applying two formulas mentioned in option A and option B that shows how a sample mean deviates from the mean of whole population.

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 value of $X^2$ describes the magnitude of the difference between___________.

  1. two normal distributions

  2. expected and observed frequency

  3. both (A) and (B)

  4. two samples
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Chi square distribution is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis.

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 size of the sample increases, the curve becomes___________.

  1. continuous

  2. severely skewed to one side

  3. more symmetrical

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

In the curve, with the large sample size, there are more samples with a mean around the middle and fewer with sample means at the extreme, the curve becomes more symmetrical. Larger samples tend to have lower standard errors

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 are true or false?
a) T-distribution varies from+infinity to-infinity.
b)The variance of t distribution and the variance of normal distribution become closer and closer as the size of the sample increases.

  1. both (a) and (b) are true

  2. both (a) and (b) are false

  3. (a) is true but (b) is false

  4. (a) is false but (b) is true
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Both (a) and (b) statements regarding students t-distribution is correct i.e. its value varies from +infinity to-infinity and the variance of t distribution and the variance of normal distribution become closer and closer as the sample size increases and also the variance of t distribution is always greater than 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

If the sample size is small, the curve may be__________.

  1. a continuous one

  2. more symmetrical

  3. severely skewed to one side

  4. none of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the sample size of the population is small, then the curve would be skewed on one side and also as the sample size increases the sampling distribution of the mean gets narrower.

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 standard deviation is small, we define a new variable known as ________.

  1. student's F-distribution

  2. student's T-variable

  3. chi-square distribution

  4. student's G-variable
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If the standard deviation is small, it signifies that data are closely distributed around the mean value instead of widely spread and here, we define a new variable as Students T-variable.

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 coefficient correlation between x and y is 0.8, the covariance being 20. If the standard deviation of x is 4 find the standard deviation of y___.

  1. 6.25

  2. 10

  3. 11.25

  4. 9.10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for correlation coefficient r is r = Cov(x,y) / (SDx * SDy). Plugging in the values: 0.8 = 20 / (4 * SDy). Thus, 0.8 = 5 / SDy, so SDy = 5 / 0.8 = 6.25.