Using the Free State Province dairy cow water intake data (L/day) for 10 cows, calculate each cow’s percentage of the total water intake and the cumulative percentage.

Researchers in the Free State Province of South Africa are investigating the impact of environmental and management factors on dairy cow productivity and health. Instead of relying only on household s...

Researchers in the Free State Province of South Africa are investigating the impact of environmental and management factors on dairy cow productivity and health. Instead of relying only on household surveys or periodic farm visits, they set up a system to collect data using smart sensors and automated recording devices. Below is data collected on Water Intake (L/day) from 10 randomly selected cows:

Cow ID | Water Intake (L/day)
Cow01 | 42.3
Cow02 | 38.7
Cow03 | 45.1
Cow04 | 36.9
Cow05 | 40.5
Cow06 | 47.8
Cow07 | 39.2
Cow08 | 44.6
Cow09 | 41.0
Cow10 | 43.7

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Using the Free State Province dairy cow water intake data (L/day) for 10 cows, calculate each cow’s...

Answer

Total water intake is 419.8 L/day. Each cow’s percentage is computed as $\text{Percent} = \frac{\text{intake}}{419.8}\times 100$, and the cumulative percentage is the running total of these percentages in the given cow order. The percentages (approx.) are: Cow01 10.08%, Cow02 9.22%, Cow03 10.74%, Cow04 8.79%, Cow05 9.65%, Cow06 11.39%, Cow07 9.34%, Cow08 10.62%, Cow09 9.77%, Cow10 10.41%, with cumulative percentages ending at about 100%.

Explanation

What you are being asked to find

You have 10 water-intake values. “Percentage” here can be taken as each cow’s share of the total water intake, and “cumulative percentage” is the running total of those shares from Cow01 down to Cow10.

Step 1: Add all water intakes to get the total

$$ \text{Total} = 42.3+38.7+45.1+36.9+40.5+47.8+39.2+44.6+41.0+43.7 = 419.8\text{ L/day} $$

Step 2: Compute percentage for each cow

Use: $$ \text{Percent for cow }i = \frac{x_i}{419.8}\times 100 $$ Then compute cumulative percentage as: $$ \text{Cumulative \%}_k = \sum_{i=1}^{k} \text{Percent}_i $$

Results table (percent and cumulative percent)

(Percentages rounded to 2 decimals.)

Cow ID	Intake (L/day)	Percent of total (%)	Cumulative (%)
Cow01	42.3	10.08	10.08
Cow02	38.7	9.22	19.30
Cow03	45.1	10.74	30.04
Cow04	36.9	8.79	38.83
Cow05	40.5	9.65	48.48
Cow06	47.8	11.39	59.87
Cow07	39.2	9.34	69.21
Cow08	44.6	10.62	79.83
Cow09	41.0	9.77	89.60
Cow10	43.7	10.41	100.01

Quick check

The final cumulative percentage should be about $100\%$. Small rounding differences (here $100.01\%$) are normal when rounding each row to 2 decimals.

Skills You Achive

descriptive-statistics percent-calculations data-tables cumulative-frequency