midrange: average of highest and lowest value on the series.
median: mid value
Central tendency: mean, median
Spread: range, std
range: highest - lowest value on the series.
IQR (Inter Quartile Range): Difference between middle of first half and second half from the median.
When to use which central tendency to explain data?
Median when there is huge outlier values. Because the mean gets skweded towards direction of outlier but not the median.
IQR is more robust when there is more skweded data.
z score: how many std away from the mean.
comparin z score, how many std away from the mean. ex. A scored 172 in x and 50 on 37 on y. While mean and std for x and y are (151, 10) and (25.1, 6.4) resp. Z score for both is, 2.1, 1.86. A scored relatively better in x than y.
mean also shifts by same amount as the data shift(add) amount. mean increases by amount as the data was increased by amount.
median has property as same as of mean for shift and scale.
std doesnot shift but scales by amount.
IQR has same property as of std.
spreadness and central tendency has different shift and scale rule.