In: Statistics and Probability
A fullservice car wash has an automated exterior conveyor car
wash system that does the initial cleaning in a few minutes.
However, once the car is through the system, car wash workers hand
clean the inside and the outside of the car for approximately 15 to
25 additional minutes. There are enough workers to handle four cars
at once during this stage. On a busy day with good weather, the car
wash can handle up to 150 cars in a 12hour time period. However,
on rainy days or on certain days of the year, business is slow.
Suppose 50 days of work are randomly sampled from the car wash’s
records and the number of cars washed each day is recorded. A
stemandleaf plot of this output is constructed and is given
below. Study the plot and write a few sentences describing the
number of cars washed per day over this period of work. Note that
the stemandleaf display is from Minitab, the stems are in the
middle column, each leaf is only one digit and is shown in the
right column, and the numbers in the left column are cumulative
frequencies up to the median and then decumulative
thereafter.
STEMANDLEAF DISPLAY: CARS WASHED PER DAY  
Stemandleaf of Cars Washed Per Day N = 50 Leaf Unit = 1.0  

From the stem and leaf display, the original raw data can be
obtained. For example, the fewest number of cars washed on any
given day are ____. The most cars washed on any given day are
_____. The modal stems are 3, 4, and 10 in which there are ___ days
with each of these numbers. Studying the left column of the Minitab
output, it is evident that the median number of cars washed is
____. There are only ___ days in which 90 some cars are washed (90
and 95) and only _____ days in which 130 some cars are washed (133
and 137).
The first number 23 in the stem plot is the lowest number of cars washed per day and the last number 147 is highest number of cars washed per day.
Therefore, the fewest numb of cars washed on any given day are 23and The most cars washed on any given day are 147.
The modal stem 3 has frequency 6 days , the modal stem 4 has frequency of 6 days and the modal stem 10 has frequency 7 days .
Therefore, the modal stems are 3,4,10 in which there are 6+6+7=19 with each of these numbers.
Median is middle most number in the data set, there are total 50 days data set therefore median would be the average of 25th and 26th observation in the given stem plot.
25th number is 81 and 26 the number is also 81 , therefore the median is (81+81)/2 = 81.
Therefore, it is evidence that the median number of cars washed is 81 .
There are only 2 days (90 and 95) in which 90 some cars are washed and only 2 days ( 133 and 137) in which 130 some car are washed.