Answer :
The standard deviation for the weight of cat food in boxes is approximately 193.0 grams.
The Data:
100.1, 100.2, 101.2, 101.3, 10.9, 100.1, 100.1, 100.1, 100.3, 100.3, 100.2, 100.1, 400.0, 405.0, 400.1
Step 1: Calculate the Sample Mean (X)
Mean = (Σ(data points)) / n
Mean = (100.1 + 100.2 + ... + 400.1) / 15
≈ 140.13 grams (rounded to two decimal places).
Step 2: Calculate the Squared Differences (Deviations)
We'll calculate the squared difference for each data point and the mean.
Data Point (x_i) Difference (x_i - Mean) Squared Difference
100.1 -40.03 1602.41
100.2 -39.93 1594.41
101.2 -38.93 1528.41
101.3 -38.83 1513.69
10.9 -129.23 16641.69
100.1 -40.03 1602.41
100.1 -40.03 1602.41
100.1 -40.03 1602.41
100.3 -39.83 1584.49
100.3 -39.83 1584.49
100.2 -39.93 1594.41
100.1 -40.03 1602.41
400.0 259.87 67168.09
405.0 264.87 69852.89
400.1 259.97 67184.09
Step 3: Sum Up the Squared Differences
Σ(Squared Deviation) = sum of all squared deviations calculated in step 2.
The Σ(Squared Deviation) ≈ 382,243.34 grams^2.
Step 4: Calculate Sample Variance (S^2)
Variance = Σ(Squared Deviation) / (n - 1)
Variance = (Σ(Squared Deviation)) / 14
Variance = 382,243.34 grams^2 / 14 ≈ 27,303.09 grams^2 (rounded to two decimal places).
Step 5: Calculate Standard Deviation (S)
Standard Deviation = √(Variance)
Standard Deviation = √(27,303.09 grams^2)
Standard Deviation ≈ 193.0 grams (rounded to one decimal place).
Therefore, the standard deviation for the weight of cat food in boxes is approximately 193.0 grams.