NGRD E 2700 F10 Homework 1 Solutions
(65 points total)
1. What fraction of the calls are cancelled? (5 points)
To get the number of calls canceled, the students can use the fil ter and wipe out all
t he data with pre-cancel t ime -1, the answer of percentile is 883 / 15,000 = 5.9%.
T here are also many other methods to get the answer, e.g. by sorting or COUNTIF
f unction. (there are many ways of computing this number and so long as the method
used is explained and the answer is correct, students should receive full points, 3
points for describing the working, 2 points for the percentile)
2 . Provide a histogram for the time in seconds until cancellation for all of those calls that are
eventually cancelled. Explain why your histogram allows us to conclude that cancellation times greater
than about 840 seconds (14 minutes) can be disregarded as outliers. (No formal de_nition of outlier is
necessary.) (6 points)
You can fi rst copy the pre-cancel t ime of canceled calls, and scale them in to seconds
by *24*60*60. Then draw a histogram from these pre-cancel time data. From the
h istogram, you can see that there are very rare data with cancellation t ime greater
t han 840s. (6 points broken down as follows: 2 points for ensuring the histogram
doesn't include the "-1"s that indicate a non-cancelled call. 1 point for scaling to
seconds from days. 1 point if the histogram axes are both labeled and there is a t i t le
(0 if any of these labels are missing). 2 points for explaining their working and
reasoning)
3. Now provide a second histogram for the time until cancellation for all those calls that are eventually
cancelled within 840 seconds (14 minutes). Based on your new histogram, what is the most common
value for the time until cancellation of a call? (4 points)
Fil ter the data in question 2 to get all calls canceled within 840s and draw the
h istogram. I ts easy to see that the most common value for cancellation time is
approximately 300 seconds (5 minutes). (2 points for histogram to ensure that i t does
not contain -1s or calls with pre-cancel time greater than 840s, 2 points for
i ndicating the most common values of time. Deduct a point if the t ime given as the
most common value is either too specific (say to the nearest second) or too broad
(greater than 3 minutes))
4. From now on let us just focus on the non-cancelled calls. What fraction of these calls require
transport to a hospital? (2 points)
Fil ter out all the data with Time_Ar rive_Hosp equal to -1. Then we find that the
n umber of calls require t ransport is 9999. So the fraction is 9999/14117 = 70.8% (2
points for calculating the percentile, ensuring that they got the number of calls
require t ransport rather than just the percentile)
5. What are the mean and median times spent at the scene? Be sure to remove any outliers before
computing your answer, and to explain how you arrived at your answer. Why is the median smaller
than the mean? (7 points)
From histogram we can see that data with t ime larger than approximately 3,600s
should be outliers. The mean is 1102.4s and the median is 1020.1s, which are
obtained by AVERAGE and MEDIAN functions in Excel. The reason why median is
smaller than mean is because there are many extremely large data which will affect
mean a lot but have li t t le effect on median. (1 points for indicating outliers, 4 points
for MEAN and MEDIAN (not necessarily completely the same, nearby is okay), 2
points for explanation for why median is smaller than mean.)
6. What are the mean and median times required to transfer a patient into the hospital once the
ambulance arrives there? Be sure to remove any outliers before computing your answer, and to explain
how you arrived at your answer. Why are the mean and median closer to each other than was the case
for the time required to transport a patient to the hospital? (7 points)
We can t reat data larger than 3,600s to be outliers. Then, we can get the mean and
median, which are 1603.5s, 1581.3s. The reason why they are much closer is that the
d istribution of the data is more symmet ric a nd there are few extreme values. (1
point for outliers, 4 points for mean and median (not necessarily completely the same,
nearby is okay), 2 points for explanation)
7. Generate a scatter plot of the time spent traveling to the scene (time en route till the time of arrival at
scene) versus the time spent at scene. If in Excel, change size the of the points to their smallest visible
setting and uncheck shadow." Notice the many values near the axes. Why do you think that a large
time spent traveling to the scene is sometimes followed by only seconds spent at the scene? And why
are incredibly short travel times often followed by long periods at the scene? Hint: The time stamps we
used are recorded by ambulance drivers pushing a button on their dashboard at the appropriate times.
(10 points)
Drivers occasionally forget to push the button on the dashboard and when they
realize their mistake push the button multiple times to "catch up", or they make
accidentally push the button twice when they meant to push it once. (5 points for the
scatter plot, including t i t le and appropriate axis labels, 5 points for a plausible
explanation)
8. EMS providers are usually measured by the fraction of calls that they receive that have response
times (the elapsed time from when the call was initially received till a vehicle arrives at scene) that fall
below some threshold. This threshold is typically 10 minutes for high-priority calls, and larger than that
for lower-priority calls, or calls arising in remote areas. What fraction of non-cancelled calls in this
dataset have response times under 10 minutes? Contracts typically stipulate that this fraction should be
at least 80%. What is the 80% percentile for the response times in this data set? (7 points)
T here are 14117 uncancelled calls in total. So, the 80% of them is 11294. By fil tering,
we find that among all the non-canceled calls, there are 8769 of them which has
response t ime less than 10mins. The fraction of calls with response t ime less than 10
m inutes is 8769/14117 = 62.1%. The 80% percentile is 16.94mins. (1 point for number
of non-cancelled calls, 1 point for the number of 80% non-cancelled calls, 1 point for
n umber of calls with response time less than 10mins, 1point for the fraction of calls
w ith response t ime less than 10min, 1 point for number of non-cancelled calls, 3
points for 80% percentile)
9. A subdivision of 20 houses has a mean price of $300,000, a median of $260,000, and a standard
deviation of $30,000. A new house is then built in the subdivision that has a price of $2,000,000.
(a) What is the new mean house price? (3 points)
(b) Can the new standard deviation also be computed? If so, then compute it. If not, then explain. (6
points)
(c) Does the 45% percentile increase, decrease, or stay the same after the new house is built? Or can no
conclusion be made? Explain. (3 points)
(a) Since the mean is defined as
--------- 1 point
So we can get the sum of house prices, 300000*20 = 6000000
Then, we can calculate the new mean by adding new house to the sum and then
d ividing i t by the new group size: (6000000+2000000)/21 = 380950 ----------- 2points
(b)The
definit ion
of
variance
is
------------ 1 point
So, we can get the quadratic sum of house prices by
20*300^2+19*30^2 = 1817100 ------- 2points
Then, we can get new standard deviation by
Sqrt((1817100 + 2000^2 21*380.95^2)/21) = 363.15542The new standard deviation
is 363155.------3 point
(c) the 45% percentile may stay the same or increase. In the original case, the 45%
percentile i s the 9th lowest house price, but now, since the new house price is higher
t han that, the new 45% percentile w ill be the average of original 9th and 10th lowest
house prices. If the two houses have the same prices, the 45% percentile w ill stay the
same, otherwise, i t will increase. --------3 points. 1 point if they say i t stays the same
and give a nearly plausible reason (even though that is wrong)
10. A certain hospital administrator once learned that the bed utilization (fraction of beds used per unit
time) in a year was 90%. The administrator wanted this number to be 100% (true story). Explain why
the hospital administrators goal is untenable from a practical perspective in two or three sentences.
(5 points)
To run at 100% utilization means that all beds are filled all the time. This leaves no room to
accommodate day-to-day fluctuations in bed needs that are the inevitable result of fluctuations in
demand for hospitalization. There has to be some spare capacity. (How much spare capacity is required
depends on many factors. You can learn more about this in ORIE classes at the senior level.) (5 points
for anything reasonable, get some points off for strange answer.)