Tag: measures of dispersion

Questions Related to measures of dispersion

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

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

  1. a continuous curve

  2. severely skewed curve

  3. the symmetrical curve

  4. either (B) or (C)

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Correct Option: A
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.

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

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

  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}}}$

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Correct Option: C
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.

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

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

  1. zero

  2. -1

  3. 1

  4. 2

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Correct Option: A
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.

A simple formula to calculate the standard error is___________.

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

  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)

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Correct Option: D
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.

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

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

  1. two normal distributions

  2. expected and observed frequency

  3. both (A) and (B)

  4. two samples

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Correct Option: B
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.

If the size of the sample increases, the curve becomes___________.

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

  1. continuous

  2. severely skewed to one side

  3. more symmetrical

  4. intermittent

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Correct Option: C
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

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.

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

  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

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Correct Option: A
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.

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

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

  1. a continuous one

  2. more symmetrical

  3. severely skewed to one side

  4. none of the above

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Correct Option: C
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.

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

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

  1. student's F-distribution

  2. student's T-variable

  3. chi-square distribution

  4. student's G-variable

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Correct Option: B
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.

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___.

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

  1. 6.25

  2. 10

  3. 11.25

  4. 9.10

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Correct Option: A