HWK 3

If the shape of the distribution is skewed, report median and ________.

IQR

What is IQR?

IQR stands for interquartile range; and it's the difference between the third and first quartiles

If given a box plot, how can you tell when the distribution is symmetric or skewed?

You can tell by the length of the whiskers from the box plot. (If the whisker under the box is longer, it's skewed left, if the top whisker is longer, it's skewed to the right, if it's relatively equal, it's symmetric)

In a given summary statistic, if the maximum value is far greater than the upper fence (or if the minimum value is far lower than the lower fence), then you have what?

an outlier !!

If a graph is skewed, will it have a high or low mean?

high

If a graph is skewed, will it have a high or low median score?

high

In a given box plot, if there's a great range and a big IQR, it shows:

instability

If a graph is unimodal, will it have a high or low IQR? (in comparison to other graphs that are skewed and/or symmetric)

low

If a graph is unimodal, will it have a high or low standard deviation?

low

Range =

max - min

If the shape of the distribution is unimodal and symmetric, report the _________.

mean

If the shape of the distribution is skewed, report the __________ as the appropriate summary of the center.

median (b/c the mean can be misleading for skewed data or for distributions with gaps or outliers)

Skewed to the left

negatively skewed distribution (the mean is usually less than the median)

Skewed to the right

positive skewed distribution (mean is typically larger than the media n)

In a given summary statistic, if the mean and median are not reasonably close to one another what type of distribution do you have?

skewed !!

When they say spread they're referring to:

standard deviation

If the shape is unimodal and symmetric, report the mean and ___________________.

standard deviation (this is the square root of the variance, s squared) (The variance is given by the formula below where y is each data value, n is the number of data values and the y (with the line over it) is the mean)

standard deviation

the following equation shows what standard deviation is: (where the x with line represents the mean, the x is each of the data values, the n is the number of data values)