How do we know when to use range, iqr or std dev for the spread? can you choose any one at anytime?
IQR is least resistant to outliers.
We usually don’t use range in this class. If it is easy to find and the distribution is not skewed and there is no outliers, we use the mean and standard deviation. However, otherwise, we use the median and IQR as a rule of thumb since it isn’t affected by skewness and outliers
It’s always good to discuss as much as possible, meaning everything you know. IQR is used to find outliers, so make sure to reference it when you test for outliers. Range is always good to mention, and std dev is a good tool for describing spread (if you know it, which isn’t always the case)
So, if there are outliers, then we use iqr–if not, then we use range or std dev. Can we just list all for spread?
Yes use IQR if there are outliers. You can use standard deviation if there are not outliers; mean and standard deviation go with each other (for symmetrical) and median and IQR go with each other (for skewed)
when finding the range in a graph, do we include outliers to calulcate it?
Yes, range includes the highest and lowest data points - even if they are outliers.
Yes. that’s why range is not resistant.
So, we can say the mean and median for the spread?
Mean and median are both measures of center.
also, what are some tips to finding median in skewed distributions
I’m saying that if you have a symmetric distribution, use mean (center) and sd (spread). If you have a skewed distribution, use median (center) and IQR (spread)
I see now! Thank you!
When asked to describe the distribution of data from a data display, it is just fine to use the range. For example, if you are asked to describe the distribution of something given to you as a dot plot, it is perfectly acceptable to use the range (since it would take time away calculating the IQR). If you are given a box plot (box and whisker plot), it is better to use IQR since it is readily available. However, IQR is not the quickest to find when you have a display that is not a box plot.
So, my rule of thumb would be try to use the median to describe the center (you can use the mean as well, where appropriate), and use the range (except if you are given a box plot… then use IQR).
Also important to keep in mind: when “CUSSing” on the exam, you only need to choose one measure from each category. No need to find both mean/median and both range/IQR. Just one of each is a-ok! Your time is better spent on other problems.