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 data)5,10,11,13,15,17,20,20,25,30,31,33,40,42... Calculate: (a)...

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 data)

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

Calculate: (a) Mean  (b) Mode  (c) Median  (d) First Quartile & Third Quartile  (e) Standard Deviation   (f) comment on the distribution?

Asked on by fockfui89

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hery | College Teacher | (Level 1) Honors

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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.

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