how do you find the iqr?\nin what shape distributions is it better to use the mean?\ndraw all four shape…

how do you find the iqr?\nin what shape distributions is it better to use the mean?\ndraw all four shape distributions?\nwhen is the mean > then the median?\nwhen is the mean < then the median?\nwhen is the mean = median?\ndefine variability.\nwhat do we use to describe variability in a box plot?\nhow can you determine if you have an outlier? what are the two rules?

how do you find the iqr?\nin what shape distributions is it better to use the mean?\ndraw all four shape distributions?\nwhen is the mean > then the median?\nwhen is the mean < then the median?\nwhen is the mean = median?\ndefine variability.\nwhat do we use to describe variability in a box plot?\nhow can you determine if you have an outlier? what are the two rules?

Answer

Explanation:

Step1: Find IQR

The inter - quartile range (IQR) is found by subtracting the first quartile ($Q_1$) from the third quartile ($Q_3$), i.e., $IQR = Q_3 - Q_1$.

Step2: Distributions for mean

The mean is a better measure of central tendency for symmetric distributions (such as the normal distribution) as the data is evenly distributed around the center.

Step3: Draw distributions

Common distributions include symmetric (bell - shaped like normal), right - skewed (tail on the right), left - skewed (tail on the left), and uniform (rectangular - shaped). However, drawing is beyond text - based response. In a right - skewed distribution, the mean is pulled in the direction of the tail, so mean > median. In a left - skewed distribution, the mean is pulled in the direction of the tail, so mean < median. In a symmetric distribution, mean = median.

Step4: Define variability

Variability refers to how spread out a set of data is. It can be measured in different ways such as range, variance, standard deviation, and IQR.

Step5: Variability in box plot

In a box plot, the IQR (the length of the box) is used to describe the variability of the middle 50% of the data.

Step6: Determine outliers

The two common rules for determining outliers are: 1. The 1.5 * IQR rule: Any value less than $Q_1-1.5\times IQR$ or greater than $Q_3 + 1.5\times IQR$ is considered an outlier. 2. The 3 - standard - deviation rule (for normal distributions): Values more than 3 standard deviations away from the mean are considered outliers.

Answer:

  1. $IQR = Q_3 - Q_1$
  2. Symmetric distributions
  3. Cannot draw in text, but types are symmetric, right - skewed, left - skewed, uniform
  4. In right - skewed distributions, mean > median
  5. In left - skewed distributions, mean < median
  6. In symmetric distributions, mean = median
  7. Variability is how spread out data is
  8. IQR
    1. $Q_1-1.5\times IQR$ and $Q_3 + 1.5\times IQR$ rule; 2. 3 - standard - deviation rule (for normal distributions)