Question

Petroleum pollution in oceans stimulates the growth of certain bacteria. An assessment of this growth has been madew by counting the bacteria in each of 5 randomly chosen specimens of ocean water (of a fixed size). The 5 counts obtained were as follows.

41, 62, 45, 48, 69

Find the deviation of this sample of numbers. Round your answers to at least two decimal places.

Answer 1

The standard deviation of the sample of numbers is approximately 10.68, after calculating the mean, finding the deviations, squaring them, averaging the squared deviations to get the variance, and then taking the square root of the variance.

Step-by-step explanation:

The student is asking how to calculate the standard deviation of a sample of numbers. The sample given consists of the counts of bacteria found in ocean water, which are 41, 62, 45, 48, 69. To calculate the standard deviation, follow these steps:

1. Calculate the mean (average) of the sample.
2. Subtract the mean from each number in the sample to find their deviations.
3. Square each deviation to get the squared deviations.
4. Calculate the average of the squared deviations (this is the variance).
5. Take the square root of the variance to get the standard deviation.

Performing the calculations, you get:

• Mean (average): (41 + 62 + 45 + 48 + 69) / 5 = 265 / 5 = 53
• Deviation for each number: -12, 9, -8, -5, 16
• Squared deviations: 144, 81, 64, 25, 256
• Variance: (144 + 81 + 64 + 25 + 256) / 5 = 570 / 5 = 114
• Standard deviation: √114 ≈ 10.68 (rounded to two decimal places)

Answer 2

The standard deviation for given sample is 11.94

Step-by-step explanation:

We are given the following sample of count of bacteria:

41, 62, 45, 48, 69

Formula:

`\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}`

where
`x_i` are data points,
`\bar{x}` is the mean and n is the number of observations.

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`Mean =\displaystyle(265)/(5) = 53`

Deviation from mean:

-12, 9, -8, -5, 16

Sum of squares of differences =

144 + 81 + 64 + 25 + 256 = 570

`s = \sqrt{(570)/(4)} = 11.94`

Thus, the standard deviation for given sample is 11.94