The number of bags potato crisps sold per day in a bar was recorded over a two week period. The results are shown below.(population...

This data is already in order from decending to the
ascending

5   10  11  13  15  17  20  20  25  30   31   33
  40   42

X1 X2  X3  X4  X5  X6  X7 X8  X9 X10 X11 X12 X13
X14

n= 14

(a) Mean=∑Xi/n
=[5+10+11+ ... + 42]/14 = 22.29

(b) Mode is the value that
occurs most frequently in a data set or a probability distribution. In this data set, 20
accurs twice => Mode=20

(c) Median is the middle
value of a set of numbers when the numbers are arranged in either ascending or
descending order. The median separates the data into two equal halves; 50% of the
numbers are below the median, 50% of the numbers are above the median.  If there is an
even number of values, the median is the mean of the two middle
values.

This data set n=14 (even). Thus the Median
is

(X7+X8)/2 = (20+20)/2 =
20

(d) First Quartile: the
value in which 25% of the numbers are below it, 75% of the numbers are above it when the
numbers are arranged in ascending (increasing) order.

5  
10  11  13 15  17  20  20  25  30   31
  33   40   42

________      
 ________________________________

25%                      
              75%

Q1 =
13

Third Quartile: the value
in which 75% of the numbers are below it, 25% of the numbers are above it when the
numbers are arranged in ascending (increasing) order.

5  
10  11  13  15  17  20  20  25  30  
31 33   40  
42

______________________________        
_________

75%    
                                25%

Q3=
31

(e)

We have to count the
(Xi-X)2

Go to this link to look at the help table for
counting (Xi-X)2: http://bit.ly/n43JMG

We know that the
(Xi-X)2 = 1714.86

Put in the
formula:

s =
sqr(1714.86/(14-1))

=
11.49

(f) Comment on the
distribution:

From day to day, the number of potatoes sold
on this bar is increasing. In the first quartile of the two weeks period the number of
selling is not as good as the last quartile of the period. The mean/average selling
cannot be used to predict this increasing, if we not really pay attention to the trend
of increasing in number of selling from day to day.