If Q3 - Q2 > Q2 - Q1, the value of Bowley's coefficient of skewness is:
positive
To determine the value of Bowley's coefficient of skewness given the condition Q3 - Q2 > Q2 - Q1, we use the formula for Bowley's coefficient of skewness (Sk):
Sk = (Q3 + Q1 - Q2 - Q2) / (Q3 - Q1)
Where:
- Q3 is the third quartile.
- Q2 is the second quartile (median).
- Q1 is the first quartile.
Given that Q3 - Q2 > Q2 - Q1, we interpret this as the distance from the median to the third quartile being greater than the distance from the first quartile to the median. This implies that Q3 is further from Q2 compared to Q1, indicating a longer upper tail, which results in a positively skewed distribution.
Substituting the inequality into the Bowley's formula:
- The numerator (Q3 + Q1 - 2*Q2) will be positive because Q3 is larger compared to Q1 when the difference with Q2 is greater.
- The denominator (Q3 - Q1) is always positive as Q3 > Q1.
Therefore, Sk > 0, indicating a positive skewness.
In conclusion, if Q3 - Q2 > Q2 - Q1, Bowley's coefficient of skewness is positive.
Similar Questions
The weighted aggregate price index with base year quantities taken as weights is known as:
If X ~ N(5,16), then the first quartile of X is equal to:
β2 of normal distribution is _____.
Which of the following is true?
For the uniformly distributed random variable X with a = 0 and b = θ, the value of the ratio of raw moments (μ'3/μ'4) is.
If n1 = 10, n2 = 5 are the sizes of a male and female student group with mean ages x̄1 = 10, x̄2 = 4, respectively, with an equal standard deviation σ1 = σ2 = 1, the standard deviation of the combined series with size n1 + n2 and combined mean x̄ = 8 is equal to:
For the given distribution of female weight in a colony, the quartiles are 60.1, 61.3, 62.6. The value of Bowley's coefficient of skewness is:
The regression assumption is that the deviations from the regression line (residuals) follow a:
If the two lines of regression are x + 2y - 5 = 0 and 2x + 3y - 8 = 0, the means of X and Y are:
If the mean, median, mode and standard deviation for the distribution are 61.4, 61.25, 61.13, 1.76, respectively, Karl Pearson's first coefficient of skewness equals to:
Important Questions from Statistics
Methods of presentation of data are:
Consider 35 i.i.d. observations X1, X2, ...., X15 and Y1, Y2, ..., Y20. Let R be the Wilcoxon's rank sum statistic based on the ranks of the X' s in the combined sample. Then the expected value of R is
Let I, J > 5. Consider two-way ANOVA, where the observations satisfy the linear model
yij = α + βi + γj + εij, 1 ≤ i ≤ I, 1 ≤ j ≤ J
E(εij) = 0, Var(εij) = σ2, \(\sum_{i=1}^{!} β_i=\sum_{j=1}^j γ_j=0 .\)
In this set - up
Let X1,X2,...,Xn be a random sample from exponential distribution with mean θ. Which of the following is NOT a sufficient statistic for θ?
A newly developed algorithm for random number generation needs to be tested. The first step is to check whether the sequence of numbers generated can be considered a random sample from the uniform distribution on the interval (0, 1). Which of the following is an appropriate nonparametric test?
