Agriculture in Education:
an educational resource for the Year 8 Mathematics
Statistics and Probability – Data representation and interpretation
Resource: Dairy Herd Data
Content Descriptor:
Investigate the effect of individual data values, including outliers, on the mean and median
(ACMSP207)
Source:
Australian Curriculum, Assessment and Reporting Authority (ACARA), downloaded from the Australian Curriculum website on 18
December 2014
Learning Outcome:

Students explain issues related to the collection of data and the effect of outliers on means
and medians in that data.
Description:
This resource provides a context to engage students in an investigation of data including exercises
to find the mean and median and the effect of outliers on means and medians in that data.
The context is that of three farmers trying to increase the milk yield of their dairy herds. Students
will investigate the yield data for individual cows in the herds and analyse the effect of increasing
feed to these cows. From this data they will draw conclusions and make suggestions about how
the farmers can increase their yields most economically. They will also look to investigate how
combining herds would benefit or disadvantage the farmers.
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Setting the scene:
This resource is ideal to include as an activity alongside an agriculture program such as Cows
Create Careers. It will also work well standalone, however as a way to make the resource more
relevant and to engage students, teachers might consider showing one of the following YouTube
videos that are amusing parodies with positive messages about farming.

“Feedin’A Nation”- Dairy Farming parody song

“CHORE” (Roar Parody) by the Peterson Brothers
Explain to students that they are each going to support a dairy farmer who owns a small herd of
cows. The farmer has been trying to find a way to improve the output or yield of milk that his cows
produce and has been keeping a record of the yield that each cow produces.
Work Task 1:
Means, Medians and Outliers
Each student should be given a worksheet with the two sets of data (data sets 1 and 2) and
instructions to help them help the farmer.
This task involves calculating means, medians, and the effect of outliers on a data set and
comparison of two linked data sets. Students are asked to comment on the validity of the data and
interpret it for a simulated real world scenario, thereby demonstrating their understanding of what
the data represents.
Work Task 2: Extension Activity – Interpreting Data
Explain to students that three farmers have decided to see if by working together they can do
things more economically.
It may be beneficial for students to work in pairs or groups of three for this task in order to promote
broader ideas and discussion. Provide students with the worksheet for this task, explaining that it
provides a summary of the data for the two other farms.
The worksheet invites students to combine data and analyse the effects of the additional data.
Further exercises related to outliers, means and medians will challenge and scaffold student.
Assessment:
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The student answers on these worksheets will serve as very strong evidence for the learning
outcomes.
Teacher support resources
For further ideas, Agriculture in the Classroom website, although an American website, has some
wonderful resources. Also see http://www.growtolearn.org/view/schoolgarden101
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Worksheet – Means, Medians and Outliers
Work Task 1:
Farmer Jones has been recording how much milk each cow has been producing each day over a
typical week and has given you the data in a table:
Data Set 1
1
2
3
4
5
6
7
Daisy
29
28
30
32
30
31
29
Helga
33
29
30
30
31
30
32
Rosy
25
28
27
29
26
27
29
Gina
31
30
32
28
28
27
30
Beryl
28
27
29
26
28
27
29
Gertie
30
30
31
30
32
28
28
Tessa
28
25
24
26
28
25
24
Trish
30
27
33
35
30
29
28
Ethel
28
28
27
30
31
32
31
Clarice
27
29
30
28
25
24
26
Flo
31
32
31
32
30
31
29
Martha
38
37
38
39
36
37
38
Shirl
27
30
31
29
30
27
33
Mildred
26
29
26
28
27
29
26
Lilly
30
32
30
31
29
30
27
Doris
30
30
31
30
32
28
28
Barbara
27
29
26
27
29
27
29
Lazy Lou
10
12
11
10
10
12
9
Page 4
Total
Mean
Median
1
2
3
4
5
6
7
Minnie
29
26
28
27
29
26
27
Bessie
31
30
32
28
28
27
30
Star
48
46
45
45
43
44
49
Maude
26
27
29
30
28
25
24
Betty
16
18
15
14
17
17
15
Nancy
22
24
22
20
23
25
22
Judy
36
35
33
35
31
36
33
Total
Mean
Median
What you need to know:
The mean and median are measures of the centre of a set of data. The Mean is what we
commonly refer to as the “average” of a set of numbers, where you add up all the numbers and
then divide by the number of numbers.
The Median is the “middle” value in the list of numbers. To find the median, your data must be first
listed in numerical order. If there are “x” numbers in your data then count x /2 from each end to
find the middle number(s).
If there is an odd number of data, x/2 will give you a number including a half value. In this case
round up to the next whole number.
If there is an even number of data when you count x /2 from both ends you will find two “middle”
numbers, in which case you will need to add the two middle numbers together and divide by two to
find the median.
Example a) 3, 6, 7, 9, 10, 16, 18 There are 7 numbers in this set, so the middle number is the
fourth number, which makes the median 9 in this case.
Example b) 2, 4, 5, 9, 11, 12, 15, 17, 18, 22. There are 10 numbers in this set so the two middle
numbers are 11 and 12. Therefore the median is (11 plus 12) divided by 2 equals 11.5
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An Outlier in a set of data is a number that is at the extreme end of the range of numbers, example
consider the set [66, 72, 74, 21, 67, 73,101, 69]. The outliers in this set are 21 and 101.
Now answer the following questions. Include your calculations where applicable.
1. The farmer would like to increase the yield of the cows but needs your help with analysing
the data. Complete the table above with weekly total yields for each cow, the mean daily
yields and the median daily yields.
2. What is the mean weekly yield per cow for the herd?
3. What is the median weekly yield?
4. There are two cows whose yield is either exceptionally bad or good. What two cows are
they?
5. The data for these two cows are the outliers for this set of data. If we remove the outlier
data from our herd’s data how does it affect the mean and median of the weekly yield per
cow of the herd?
6. The farmer wants to know what the “average” cow yield is in order to judge the cow’s
production. Should we use the mean and median including the outliers or without the
outliers?
Explain why this is important.
The farmer up to this stage has always fed the cows exactly the same amount of feed. The farmer
is wondering if their feed is increased whether their milk yield will increase at the same rate. The
farmer decides to run a trial where all the cows are fed an extra 10 percent more feed. The data
showing the milk yield each for the trial is in “data set 2”
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Data Set 2
1
2
3
4
5
6
7
32
31
33
35
33
34
32
Helga
35
31
32
32
33
32
34
Rosy
28
31
30
32
29
30
32
Gina
34
33
35
31
31
30
33
Beryl
29
28
30
27
29
28
30
Gertie
32
32
33
32
34
30
30
Tessa
32
29
28
30
32
29
28
Trish
33
30
36
38
33
32
31
Ethel
31
31
30
33
34
35
34
Clarice
27
29
30
28
25
24
26
Flo
34
35
34
35
33
34
32
Martha
39
38
39
40
37
38
39
Shirl
30
33
34
32
33
30
36
Mildred
29
32
29
31
30
32
29
Lilly
33
35
33
34
32
33
30
Doris
33
33
34
33
35
31
31
Barbara
30
32
29
30
32
30
32
Lazy Lou
15
17
16
15
15
17
14
Minnie
32
29
31
30
32
29
30
Daisy
Page 7
Total
Mean Median
Percentage
Difference
1
2
3
4
5
6
7
Bessie
33
32
34
30
30
29
32
Star
48
46
45
45
43
44
49
Maude
29
30
32
33
31
28
27
Betty
20
22
19
18
21
21
19
Nancy
26
28
26
24
27
29
26
Judy
37
36
34
36
32
37
34
Total
Mean Median
Percentage
Difference
“Average
Cow”
Now you are to compare the two sets of data that you now have. (You will need to calculate totals,
means and medians for the new data).
7. What is the difference in terms of percentage increase or decrease of the milk yield for each
cow?
8. Which cow best represents the “average” cow? Is it more valid to refer to the Mean or the
Median cow in this case? Why?
9. What does this information lead you to think about the effect of increasing the feed for the
“average” cow?
10. How reliable do you think the farmer’s data would be? What could the farmer do to make
the data more accurate?
11. What advice will you give to the farmer?
Work Task 2: Worksheet > Extension Activity – Interpreting Data
Three farmers have decided to see if by working together they can do things more economically.
You have been advising Farmer Jones. Farmer Brown and Farmer Jenkins have produced similar
data for their dairy farms and they have brought along summaries to show you.
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Farmer Brown

Has 30 cows.

The mean milk production is 28 litres per cow per day.

The median cow yield is 203 litres per week.

There are two outliers in the herd data. Their mean daily milk yields are 13 and 14 litres
respectively.
Farmer Jenkins

Has 36 cows.

The mean milk production is 32 litres per cow

The median cow yield is 270 litres per week.

There are two outliers in the herd data. Their mean daily milk yields are 16 and 44
respectively.
Answer the following questions showing any calculations needed.
1.
What is the total milk production for a week for each farmer’s herd?
2.
Farmer Brown and Farmer Jenkins both included the outliers in their calculations of the
mean and medians. By removing the outliers what would be the mean weekly yield for
Farmer Jenkin’s herd?
3.
What effect would there be on the median number for a week’s yield in Farmer Jenkin’s
herd if we remove the outliers?
4.
By the combining the herds do the farmers gain anything in terms of the new herd daily
yield per cow? Who would gain the most by combining herds?
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