Math Problem Statement
Solution
Let's go through the three problems shown in the image:
1. Determine the coefficient of skewness for each and describe the result.
The formula for the coefficient of skewness is: Where:
- is the mean,
- is the median,
- is the standard deviation.
We'll calculate the skewness for each case.
(a)
Since the skewness is positive, the distribution is skewed to the right.
(b)
This positive skewness also indicates right-skewness.
(c)
Here, the skewness is negative, indicating left-skewness.
(d)
This negative skewness also indicates left-skewness.
2. Find the coefficient of skewness of the following data set: 5, 10, 15, 17, 20, 35.
To calculate the skewness, we'll need to compute the mean, median, and standard deviation of this data set.
- Mean () =
- Median () =
- Standard deviation : We'll first calculate the variance.
Thus, .
Now we can calculate the skewness: This is a small positive skewness, indicating a slight right-skew.
3. The mean and variance of a distribution are 40 and 625, respectively. Find the median if the skewness is -0.2.
We know:
- Mean () = 40,
- Variance = 625, so standard deviation ,
- Skewness = .
Using the skewness formula: Substitute the known values: Solve for : So, the median is approximately .
Would you like more details or explanations?
Here are 5 related questions to further explore:
- How does the sign of skewness affect the shape of a distribution?
- What are the different types of skewness and how do they impact data interpretation?
- How is skewness related to the mean, median, and mode of a data set?
- Can skewness be zero, and what does it signify?
- How does outlier data affect skewness?
Tip: Skewness can indicate whether data is more spread out on one side of the mean, helping to understand the distribution's shape better!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Skewness
Descriptive Statistics
Mean
Median
Standard Deviation
Formulas
Skewness = (3 * (Mean - Median)) / Standard Deviation
Variance = sum((x - mean)^2) / n
Standard Deviation = sqrt(Variance)
Theorems
-
Suitable Grade Level
Grades 10-12
Related Recommendation
Calculate the Coefficient of Skewness for x̄ = 17, s = 2.3, Median = 18
Calculate Karl Pearson’s Coefficient of Skewness for Data Set x: 25 15 23 40 27 25 23 25 20
Calculate Skewness Using Moments of Distribution
Calculate Coefficient of Skewness Using Quartiles and Median
Solving Frequency Distribution and Skewness in Statistics