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Agriculture in Education: an educational resource for the Year 8 Maths Curriculum

Statistics and Probability ? Data representation and interpretation

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Statistics and Probability ? Data representation and interpretation > Dairy Herd Data

Year 8 Maths Resource

Resource 1: Dairy Herd Data

Maths

Content Descriptor:

Investigate the e ect of individual data values, including outliers, on the mean and median

ACMSP207

learn

discuss web

work task

work task

Learning Outcome/s

Students explain issues related to the collection of data and the e ect 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 nd the mean and median and the e ect 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 e ect 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 bene t or disadvantage the farmers.

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 embed/Ss2XGxblNZY

CHORE (Roar Parody) by the Peterson Brothers embed/toyN81wZzLw?list=PLpniJUeAKfupMAobWOtCvEmjosZiPX07S

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 nd 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 e ect 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 bene cial 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 e ects of the additional data.

Further exercises related to outliers, means and medians will challenge and sca old student.

Assessment:

The student answers on these worksheets will serve as very strong evidence for the learning outcomes.

Statistics and Probability ? Data representation and interpretation

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Statistics and Probability ? Data representation and interpretation > Dairy Herd Data

Year 8 Maths Resource > Work Task 1: Worksheet

work task

Work Task 1: Worksheet ? Means, Medians and Outliers

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

Day

1

2

3

4

5

6

7 Total Mean Median

Cow

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 Flo

27

29

30

28

25

24

26

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

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

Statistics and Probability ? Data representation and interpretation

2

Year 8 Maths Resource > Statistics and Probability ? Data representation and interpretation > Work Task 1: Worksheet Dairy Herd Data

discuss

work task

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 nd the median, your data must be rst listed in numerical order. If there are "x" numbers in your data then count x/2 from each end to nd 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 nd two "middle" numbers, in which case you will need to add the two middle numbers together and divide by two to

nd 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 + 12) ? 2 = 11.5

An Outlier in a set of data is a number that is at the extreme end of the range of numbers, e.g. 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 a ect 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.

3

Statistics and Probability ? Data representation and interpretation

Statistics and Probability ? Data representation and interpretation > Dairy Herd Data

Year 8 Maths Resource > Work Task 1: Worksheet

work task

Data Set 2

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% more feed. The data showing the milk yield each for the trial is in "data set 2"

Day

Percentage

Cow

1

2

3

4

5

6

7

Total

Mean Median Di erence

Daisy

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

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

"Average Cow"

Statistics and Probability ? Data representation and interpretation

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