Question

The descriptive summary of a TV show, the number of minutes audience spend watching in a typical week, is given below Mean St Dev Min Show Time 135.8 177.18 Q1 50 Median Q3 90 150 Max 2000 a) What is the shape of the corresponding histogram? Explain. (symmetric /right-skewed / left-skewed) b) Are there any outliers? Explain. When describing centre and spread, which set of summary c) statistics should be used? Why? (mean and standard deviation or median and IQR)

Answer 1

a) For a symmetric distribution, mean=median=mode

Here since mean>median it's not symmetric

For a right tailed distribution, mean>median>mode

So this is a right tailed distribution.

b) here, IQR= Q3-Q1= 100

Lower fence= Q1- 1.5*IQR= 50- 1.5*100= -100

Upper fence= Q3 + 1.5*IQR= 150 + 1.5*100= 300

All values outside this range(-100, 300) are outliers

Here since max= 2000, clearly it's an outlier

c) We generally use median and IQR to describe the center and spread of the dataset. (Median= middle of the dataset, and IQR is the Q3-Q1)

I) The median of the dataset is always the middlemost value.

ii) r close to -1 means strong negative inverse relationship between the two variables.