Question

Consider the following data: 43 54 55 63 67 68 69 77 85 Suppose that the last value is actually 115 instead of 85. What effect would this new maximum have on the median of the data?

increase the value of the median

decrease the value of the median

no effect

1. Approximately, what z-score divides the lower 75% of the data from the upper 25%?

   1. z = 0.75

   2.   z = 0.675

   3.   z = - 0.675

   4.   z = -0.25

   5.   none of the above

Answer 1

Solution:

Question 1)

Given data is: 43 54 55 63 67 68 69 77 85

the last value is actually 115 instead of 85.

We have to determine if there is effect on median due to this new maximum observation.

Since median is middle most observation in arranged data, there is no effect on median due to change in extreme observations.

Lets find median for given data: 43 54 55 63 67 68 69 77 85

n = Number of observations = 9

thus

Now find median if we change maximum observation from 85 to 115.

43 54 55 63 67 68 69 77 115

Thus there is no effect on median due to change in extreme observation.

Question 2)

We have to find z-score which divides the lower 75% of the data from the upper 25%.

That is find z such that:

P( Z < z) = 75%

P( Z < z ) = 0.7500

Look in z table for area = 0.7500 or its closest area and find z value.

Area 0.7500 is between 0.7486 and 0.7517 and both area are nearly same distance from 0.7500

thus we find both z values for both area and then find average.

z value for area 0.7486 is 0.67 and

z value for area 0.7517 is 0.68

Thus Average of both z = ( 0.67 + 0.68 ) / 2 = 1.35 / 2 = 0.675

Thus required answer for z is 0.675