Bunuel
Brian is analyzing the performance of certain stocks. He finds that for the first fifteen days of a 30 day period, the daily closing price per share of Phonexpharma Inc. conformed to the function \(f(x)=0.4x+2\) , where x represents the day in the period. He found that for the last 15 days in the same period, the stock followed the function \(f(x)=(-\frac{1}{7})x+9\), where x represents the day in the period. Approximately what is the median closing price per share of Phonexpharma Inc. for the entire 30 day period?
A. 4.7
B. 5.55
C. 6.71
D. 8
E. 11.1
The first 15 days of the 30 day period confirms the function : \(f(x)=0.4x+2\) , where x represents the day in the period.
so, x assumes the values from 1,2,3,4.... Till 15.
Let’s assume this to be
CASE 1: And, the values of
f(x) = 2.4 , when x=1
f(x) = 2.8, when x=2
f(x) = 3.2 , when x=3
then 3.6, 4.0, 4.4, 5.2, 5.6 , 6.0, 6.4, 6.8, 7.2, 7.6, 8.0
In 2.xx range, number of values = 2
In 3.xx range, number of values = 2
In 4.xx range, number of values = 2
In 5.xx range, number of values = 2
In 6.xx range, number of values = 3
In 7.xx range, number of values = 2
In 8.xx range, number of values = 1
Case 2: The last 15 days of the stock followed the pattern of : \(f(x)=(-\frac{1}{7})x+9\), where x represents the day in the period.
Numbers which are multiples of 7 after 15 are: 21 and 28.
with x = 21, f(x) = 6
with x = 28, f(x) = 5.
so the values of x=29 and x=30, should be below 5.0 mark, thus ONLY 2 VALUES falling in the 4.xx range.
The number of values in the band less than 6.0 but greater than 5.0 , that’s within the 5.xx band is (28-22)+1 = 7 values.
And we can also infer that the values for, x =16 till x =20 lies within the 6.xx band. There are 5 such values in 6.xx range.
In the 6.xx range, the number of values = 5
In 5.xx range, the number of values = 7
In the 4.xx range , the number of values = 2
Median = (15th value +16th value)/2
There are
8 values in the 2.xx and 5.xx range in case 1.
including the 4.xx range from case 2, we get 2 more values, totalling to 10 values.
5.xx range values from case 2, which lies in the median slot of 15th and 16th value.
Thus by approximation, we can arrive at the median value to be 5.xx
Option B
5.55