Example Final Exam
| categories: Quiz Prep
Here is an example of the sorts of questions I may ask on the final exam. The final exam will not be limited to the scope of this sample. Anything we have discussed all semester is fair game. Of course, the material I emphasized is more likely to appear on the final.
1. The SouthEastern regional climate center,
http://www.dnr.state.sc.us/climate/sercc/, has historical weather data
from many weather stations. Here is some sample data for the Chapel
Hill station, including the maximum and minimum temperatures for each
day of the year, averaged over 30 years (1961 through 1990).
<TITLE> CHAPEL HILL 2 W, NORTH CAROLINA 30 Year Daily Summary </TITLE>
<BODY BGCOLOR="#FFFFFF"><H1> CHAPEL HILL 2 W, NORTH CAROLINA </H1>
<H3>30 Year Daily Temperature and Precipitation Summary </H3>
<PRE>
STATION 311677 AVERAGES FROM AVAILABLE YEARS IN PERIOD 1961 TO 1990 .
DOY MON DY TMAX #YRS TMIN #YRS PRECIP #YRS SD MAX SD MIN
1 1 1 49.1 30. 26.9 30. 0.116 30. 10.895 10.164
2 1 2 49.0 30. 26.8 30. 0.115 30. 10.868 10.169
3 1 3 48.8 30. 26.7 30. 0.115 30. 10.864 10.104
•
•
•
360 12 25 50.9 30. 28.4 30. 0.121 30. 10.816 10.073
361 12 26 50.6 30. 28.2 29. 0.121 30. 10.799 10.042
362 12 27 50.4 29. 28.0 30. 0.118 30. 10.831 10.013
363 12 28 50.0 30. 27.7 30. 0.120 30. 10.831 10.056
364 12 29 49.8 30. 27.5 30. 0.118 30. 10.878 10.154
365 12 30 49.5 30. 27.3 30. 0.118 30. 10.961 10.219
366 12 31 49.3 30. 27.1 30. 0.117 30. 10.939 10.161
</PRE>
a) Assume for these first 4 subparts that you have read the max and
min temperatures into column vectors TMAX and TMIN and the standard
deviations for max and min temperatures into column vectors SDMAX and
SDMIN. (Standard deviation is a statistic that tries to capture how
far we would expect to find the temperature from the day's max or
min. E.g., if max temperature is normally distributed, we expect that
90% of the days are less than 1.28 standard distributions above TMAX.)
Each vector has the same number of rows.
Write Python expressions that will do the following.
i. Plot the average temperature maxima (red) and minima (blue)
ii. Determine the highest maximum temperature.
iii. Determine which day (1 – 366) has the highest maximum temperature.
iv. Determine, for each day, the temperature range between max and
min. (E.g., for day 360, which is Dec 25, the range is 22.5 degrees.)
b) Complete function tempExceptional which, given today's day number
(daynum) and temperature (temp), should determine if temp is within
the historical max/min range for that day, and if not, determine how
many standard deviations above the historical max for that day, or how
many standard deviations below the historical min for that day.
Set result = 0 for normal, result = a positive number of standard
deviations if above the max, or result = a negative number of standard
deviations if below the min.
def tempExceptional(daynum, temp, TMAX, TMIN, SDMAX, SDMIN):
# daynum = the day number today (1 - 366)
# temp = the current temperature in degrees
# TMAX, TMIN, SDMAX, SDMIN column vectors as in a).
2. Write functions to solve at least 3 of the following 5 challenges.
a) Function twomin(x) should take a list of numbers in a vector x,
find the two smallest, and return them in a list result being careful
to properly handle duplicated items in the list.
b) Write a function dist(p,q) that takes a point p represented as a
1×d row vector, and a list of n points q, represented as an n×d
matrix, and returns an n×1 vector of the distance from point p to each
point q[i,:].
c) Write a function pairdist(p,q) that takes two matrices, say m×d and
n×d, and returns the m×n matrix of distances between all pairs of
rows. You may use the function dist() from b), even if you choose not
to write that one.
d) isPrime(n) returns True if the number N is prime, False otherwise.
e) isPalindrome(s) returns True if s is a palindrome (same read left
to right as right to left), False otherwise.
3. Multiple choice (circle the roman numerals for all that apply)
a) If A is a 4x6 matrix, in assignment A[2:3,4:5] = B; the value of B
can be
i. []
ii. scalar
iii. a 2x2 matrix
iv. a 4x1 matrix
v. a 4x6 matrix
b) If M is a 3x2 matrix, the value of M[:] is a
i. error
ii. 3x2 matrix
iii. 2x3 matrix
iv. row vector 1x6
v. column vector 6x1
c)The differences between for and while loops include:
i. You will always use a colon : in a for loop
ii. A while loop can run forever, but a for loop cannot.
iii. A for loop defines a variable; a while loop may not even need a variable.
iv. A for loop executes the indented statements at least once; a while loop
may never execute the statements.
d) The differences between floating point and integer numbers include:
i. floats cannot be used as array indicies.
ii. integer arithmetic is exact, floating point is approximate.
iii. the exponentiation operator ** cannot be used on integers.
iv. the range function only works on integers.
4. Floating point numbers are unlike the real numbers we study in
mathematics. They approximate the behavior of real numbers reasonably
well but they differ in important ways that mostly result from their
limited precision. For example X+1 == X is never true for real numbers
but is sometimes true for floating point. Show a fragment of Python
code that finds the smallest X such that X+1 == X.
5. The following 3 mystery functions inefficiently implement methods
that are provided by numpy arrays. Give me the names of the
corresponding functions from numpy.
def F1(A):
if len(A) == 1:
return A[0]
else:
t = F1(A[1:])
if t > A[0]:
return t
else:
return A[0]
def F2(A):
t = 0
for x in A:
t += x
return t
def F3(A):
s = 0
for x in A:
s += 1
return s
6. Show how to create the following arrays.
a. array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
b. array([[ 0, 4, 8],
[ 1, 5, 9],
[ 2, 6, 10],
[ 3, 7, 11]])
c. array([0, 1, 4, 9, 16, ..., n**2]) for any positive integer value of N
d. A 12x12 checkerboard pattern with alternating 0's and 1's. Like
this 4x4 version only bigger.
[ [ 0, 1, 0, 1],
[ 1, 0, 1, 0],
[ 0, 1, 0, 1],
[ 1, 0, 1, 0] ]
e. array([[ 0., 0., 0., 0., 0.],
[ 0., 1., 1., 1., 0.],
[ 0., 1., 0., 1., 0.],
[ 0., 1., 1., 1., 0.],
[ 0., 0., 0., 0., 0.]])
7. Suppose you are given an array named W with the birth weight of N babies.
Use numpy array methods to find the following.
a. the weight of the heaviest baby.
b. the mean weight of all the babies.
c. the median weight for all the babies.
d. the standard deviation of the weights.
e. the mean of the weight of babies that were heavier than 3 pounds.
8. Mark the following statements with the data types they produce. The
first is done for you as an example. Mark X for error, otherwise mark
with an uppercase letter for the basic type and a lowercase letter for
the shape.
F float
I integer
B boolean
S string
s scalar
v vector
m matrix
X error
Assume these values for the variables: x = np.arange(4.0); y = x**2; z = np.eye(4);
F v a) x+y
__ __ b) y.sum()
__ __ c) z*z
__ __ d) np.dot(x,z)
__ __ e) x == np.sqrt(y)
__ __ f) y < 5
__ __ g) y[x>2]
__ __ h) float('3.1415')
__ __ i) str(1.5)
9. What are the differences between the return statement and the print statement?
10. A newbie programmer has written the following code and is
surprised that it doesn't terminate after printing the 10 lines but
just keeps on printing ever larger numbers. Explain what is going
wrong.
i = 0
while i != 1:
i = i + 0.1
print i