Question

The red blood cell counts (in 10⁵ cells per microliter) of a healthy adult measured on 6 days are as follows.

55,51,54,48,49,49
Find the standard deviation of this sample of counts. Round your answer to two decimal places.

Answer 1

The standard deviation of the red blood cell counts given is approximately 2.90 x 10^5 cells per microliter, after calculating the mean, subtracting the mean from each count, squaring the deviations, summing those up, and then taking the square root of the variance.

Step-by-step explanation:

To calculate the standard deviation of the red blood cell counts, we will follow these steps:

1. Calculate the mean (average) of the red blood cell counts.
2. Subtract the mean from each of the counts to find the deviation of each count.
3. Square each of the deviations to get the squared deviations.
4. Add up all the squared deviations.
5. Divide this total by one less than the number of data points (n - 1) to get the variance.
6. Take the square root of the variance to get the standard deviation.

Using the provided data (55, 51, 54, 48, 49, 49) in 105 cells per microliter, let's calculate each step.

1. Mean = (55 + 51 + 54 + 48 + 49 + 49) / 6 = 306 / 6 = 51
2. Deviations: 4, 0, 3, -3, -2, -2
3. Squared Deviations: 16, 0, 9, 9, 4, 4
4. Total of Squared Deviations = 16 + 0 + 9 + 9 + 4 + 4 = 42
5. Variance = 42 / (6 - 1) = 42 / 5 = 8.4
6. Standard Deviation = √8.4 ≈ 2.90 (rounded to two decimal places)

Therefore, the standard deviation of the red blood cell counts is approximately 2.90 x 105 cells per microliter.