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Calculating Standard Deviations (S.D.) or Z-score by Hand

 

Survey date = 17 March 1997 (170397)

Case District HHID Child ID DOB Age Sex Weight WAZ
1 1 1 1 170396   F 9.1  
2 1 1 2 170996   F 6.5  
3 1 2 1 121295   F 11.9  
4 1 3 1 010297   M 3.9  

Example Calculations For Case Number 1:

  1. Calculate age: March 17, 1997 - March 17, 1996 = 12 months

  2. Find Median weight for 12 month old girls from the reference chart below:
    9.5 kgs  (The correct cell in the reference chart below is colored pink.)

  3. Calculate the difference between the median weight for 12 month old girls
    and the child's weight (found in the chart above): 9.1 - 9.5 = -0.4  (Notice
    that you should always put the child's actual weight first in the subtraction.)                                          

  4. Note that the child's weight falls below the median for her age group, between the median and -1 standard deviations. (The -1 standard deviation cell is colored blue in the reference chart below.)

  5. Subtract "median value" minus "-1 standard deviation value" to calculate one standard deviation: 9.5 - 8.5 = 1.0

  6. To calculate the weight-for-age z-score, divide the child's "deviation" from the median (calculated in step 3) by the standard deviation (calculated in step 5): -0.4/1.0 = - 0.40   (Notice that because the child's weight was below the median, the weight-for-age z-score is negative.)


Exercise

Use steps 1-6 above to calculate the weight-for-age z-scores for Cases 2 and 3. You can use the same reference chart for them.  However, if you were to have a boy for a case, you would need to use a separate chart for boys.  Both cases below are girls, therefore you can reference the chart provided to perform the exercise.

After you finish you can check your answers:
CASE 2 Girl:  Birthdate:  Sept. 28, 1994    Interview date: Nov.19, 1996  Weight (kg): 11.1
CASE 3 Girl:  Birthdate:  Dec. 12, 1995    Interview date: Nov. 19, 1996  Weight (kg):  9.8


 

Table 24. WEIGHT (KG) BY AGE OF GIRLS AGED 0-36 MONTHS

Age

CENTILES

STANDARD DEVIATIONS

Age

Months

3rd 5th 10th 20th 30th 40th 50th 60th 70th 80th 90th 95th 97th -3 S.D. -2 S.D. -1 S.D. Median +1 S.D. +2 S.D. +3 S.D.

Months

0

2.3

2.4

2.6

2.8

3.0

3.1

3.2

3.3

3.4

3.5

3.7

3.8

3.9

1.8

2.2

2.7

3.2

3.6

4.0

4.3

0

1

2.9

3.0

3.2

3.5

3.7

3.8

4.0

4.1

4.3

4.4

4.7

4.9

5.0

2.2

2.8

3.4

4.0

4.5

5.1

5.6

1

2

3.4

3.6

3.8

4.1

4.4

4.5

4.7

4.9

5.1

5.3

5.6

5.8

6.0

2.7

3.3

4.0

4.7

5.4

6.1

6.7

2

3

4.0

4.2

4.4

4.8

5.0

5.2

5.4

5.6

5.8

6.1

6.4

6.7

6.9

3.2

3.9

4.7

5.4

6.2

7.0

7.7

3

4

4.6

4.7

5.0

5.4

5.6

5.8

6.0

6.3

6.5

6.8

7.1

7.4

7.6

3.7

4.5

5.3

6.0

6.9

7.7

8.6

4

5

5.1

5.3

5.6

6.0

6.2

6.4

6.7

6.9

7.1

7.4

7.8

8.1

8.3

4.1

5.0

5.8

6.7

7.5

8.4

9.3

5

6

5.6

5.8

6.1

6.5

6.8

7.0

7.2

7.4

7.7

8.0

8.4

8.7

8.9

4.6

5.5

6.3

7.2

8.1

9.0

10.0

6

7

6.0

6.2

6.5

6.9

7.2

7.5

7.7

7.9

8.2

8.5

8.9

9.3

9.5

5.0

5.9

6.8

7.7

8.7

9.6

10.5

7

8

6.4

6.6

7.0

7.4

7.7

7.9

8.2

8.4

8.7

9.0

9.4

9.8

10.0

5.3

6.3

7.2

8.2

9.1

10.1

11.1

8

9

6.7

7.0

7.3

7.7

8.1

8.3

8.6

8.8

9.1

9.4

9.8

10.0

10.4

5.7

6.6

7.6

8.6

9.6

10.5

11.5

9

10

7.0

7.3

7.6

8.1

8.4

8.7

8.9

9.2

9.4

9.8

10.2

10.4

10.8

5.9

6.9

7.9

8.9

9.9

10.9

11.9

10

11

7.3

7.6

7.9

8.4

8.7

9.0

9.2

9.5

9.8

10.1

10.6

10.8

11.2

6.2

7.2

8.2

9.2

10.3

11.3

12.3

11

12

7.6

7.8

8.2

8.6

9.0

9.3

9.5

9.8

10.1

10.4

10.9

11.2

11.5

6.4

7.4

8.5

9.5

10.6

11.6

12.7

12

13

7.8

8.0

8.4

8.9

9.2

9.5

9.8

10.1

10.3

10.7

11.1

11.5

11.8

6.6

7.6

8.7

9.8

10.8

11.9

13.0

13

14

8.0

8.2

8.6

9.1

9.5

9.8

10.0

10.3

10.6

10.9

11.4

11.8

12.0

6.7

7.8

8.9

10.0

11.1

12.2

13.2

14

15

8.1

8.4

8.8

9.3

9.7

10.0

10.2

10.5

10.8

11.2

11.6

12.0

12.3

6.9

8.0

9.1

10.2

11.3

12.4

13.5

15

16

8.3

8.6

9.0

9.5

9.9

10.2

10.4

10.7

11.0

11.4

11.9

12.3

12.5

7.0

8.2

9.3

10.4

11.5

12.6

13.7

16

17

8.5

8.7

9.2

9.7

10.0

10.3

10.6

10.9

11.2

11.6

12.1

12.5

12.7

7.2

8.3

9.5

10.6

11.8

12.9

14.0

17

18

8.6

8.9

9.3

9.8

10.2

10.5

10.8

11.1

11.4

11.8

12.3

12.7

13.0

7.3

8.5

9.7

10.8

12.0

13.1

14.2

18

19

8.8

9.1

9.5

10.0

10.4

10.7

11.0

11.3

11.6

12.0

12.5

12.9

13.2

7.5

8.6

9.8

11.0

12.2

13.3

14.5

19

20

8.9

9.2

9.7

10.2

10.6

10.9

11.2

11.5

11.8

12.2

12.7

13.1

13.4

7.6

8.8

10.0

11.2

12.4

13.5

14.7

20

21

9.1

9.4

9.8

10.4

10.7

11.1

11.4

11.7

12.0

12.4

12.9

13.3

13.6

7.7

9.0

10.2

11.4

12.6

13.8

15.0

21

22

9.3

9.5

10.0

10.5

10.9

11.2

11.5

11.9

12.2

12.6

13.1

13.6

13.9

7.9

9.1

10.3

11.5

12.8

14.0

15.2

22

23

9.4

9.7

10.2

10.7

11.1

11.4

11.7

12.0

12.4

12.8

13.3

13.8

14.1

8.0

9.3

10.5

11.7

13.0

14.2

15.5

23

24

9.6

9.9

10.3

10.9

11.3

11.6

11.9

12.2

12.6

13.0

13.6

14.0

14.3

8.2

9.4

10.7

11.9

13.2

14.5

15.8

24

25

9.7

10.0

10.5

11.0

11.4

11.8

12.1

12.4

12.8

13.2

13.8

14.2

14.6

8.3

9.6

10.8

12.1

13.4

14.7

16.0

25

26

9.9

10.2

10.6

11.2

11.6

11.9

12.3

12.6

13.0

13.4

14.0

14.5

14.8

8.5

9.7

11.0

12.3

13.6

14.9

16.3

26

27

10.1

10.3

10.8

11.4

11.8

12.1

12.4

12.8

13.1

13.6

14.2

14.7

15.0

8.6

9.9

11.2

12.4

13.8

15.2

16.6

27

28

10.2

10.5

11.0

11.5

11.9

12.3

12.6

13.0

13.3

13.8

14.4

14.9

15.2

8.8

10.1

11.3

12.6

14.0

15.4

16.8

28

29

10.4

10.7

11.1

11.7

12.1

12.4

12.8

13.1

13.5

14.0

14.6

15.1

15.5

8.9

10.2

11.5

12.8

14.2

15.6

17.1

29

30

10.5

10.8

11.3

11.8

12.3

12.6

12.9

13.3

13.7

14.2

14.8

15.3

15.7

9.1

10.3

11.6

12.9

14.4

15.9

17.3

30

31

10.6

11.0

11.4

12.0

12.4

12.8

13.1

13.5

13.9

14.4

15.0

15.6

15.9

9.2

10.5

11.8

13.1

14.6

16.1

17.6

31

32

10.8

11.1

11.6

12.2

12.6

12.9

13.3

13.7

14.1

14.6

15.2

15.8

16.1

9.3

10.6

11.9

13.3

14.8

16.3

17.8

32

33

10.9

11.2

11.7

12.3

12.7

13.1

13.4

13.8

14.2

14.7

15.4

16.0

16.3

9.4

10.7

12.1

13.4

15.0

16.5

18.1

33

34

11.0

11.4

11.9

12.5

12.9

13.3

13.6

14.0

14.4

14.9

15.6

16.2

16.6

9.5

10.9

12.2

13.6

15.2

16.7

18.3

34

35

11.2

11.5

12.0

12.6

13.0

13.4

13.8

14.2

14.6

15.1

15.8

16.4

16.8

9.6

11.0

12.4

13.8

15.4

16.9

18.5

35

36

11.3

11.6

12.1

12.7

13.2

13.6

13.9

14.3

14.8

15.3

16.0

16.6

17.0

9.7

11.1

12.5

13.9

15.5

17.1

18.8

36

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