Question

by cach family is given below Let X be the munber of cars owned, and X, be the pos- sible valus of X. Use this data to answer the following questions: (a) Write down the relative-frequency distribution for X (b) Find the median of number of cars owned. (c) Find the mean of mumber of cars owned (d) Using (b) and (c), are there more than 50% of values X, above the meau, or less? Explain your answe

Answer 1

a)

Relative frequency table

Xi	Frequency	Relative Frequency
0	1	0.05
1	4	0.20
2	5	0.25
3	5	0.25
4	3	0.15
5	1	0.05
6	1	0.05

Sum of frequencies = 20

{Relative Frequency = freq/total}

b) First arrange the data in increasing order : 0,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,5,6

median=(10th+11th obs)/2 =(2+3)/2=5/2 = 2.5

c) mean=(0+1+1+1+1+2+2+2+2+2+3+3+3+3+3+4+4+4+5+6)/20= 52/20= 2.6

d)No. Actually 50% of values  Xi's are less than the mean as median(2.5)<mean(2,.6). This will get clear from the definition of median:

"The median is the value separating the higher half from the lower half of a data sample (a population or a probability distribution). For a data set, it may be thought of as the "middle" value."

Here median is less than mean which simply means that more than 50% of the values are less than mean.