Question

1) What is the mode, and with what type of data is it most appropriate? What is the median and with what type of data is it most appropriate? What is the mean, and with what type of data is it most appropriate? 

2) For the following data, indicate which measure of central tendency you should compute. 

a. IQ scores b. Anxiety scores (which are skewed in the population) c. Blood types d. Course grades (e.g., A, A-, B+, B, etc.) 

3) The variance of a distribution is S²_x = 0. What does this indicate about the distribution? 

4) For his test grades, Guchi has a mean of 60 and S_x=20. Pluto has a mean of 60 and S_x=5 Who is the more consistent student and why OR who is more accurately described as a 60 student and why?

Answer 1

1) Mode of the data is the most frequently occurring value in it.

(Value with highest frequency.)

It is most appropriate for unskewed nominal type of data.(Attributes)

Median of the data is that value which divides the ordered data values into two groups of equal size.

(Middle value of ascending/descending data)

It is most appropriate for skewed ordinal type of data.(Attributes)

Mean of the data is the average of the data values.

Most appropriate for numerical data.(Scale)

2) a) Mean

b) Median or mean.

c) Mode

d) Median

3) This indicates that there is no variation in data values,

or in other words each data value is equal. So the distribution is degenerate.

4) Pluto is more consistent student or accurately described as a 60 student because he has much lower value of standard deviation than Guchi. In fact Pluto will most probably score within the range 45 to 75 but Guchi's marks will lie between 0 to 100( if we assume normal distribution).