To find the standard deviation of the given sample of red blood cell counts, we'll follow a step-by-step calculation process:
1. List the data: The counts are [tex]\(49, 55, 52, 54, 50\)[/tex].
2. Calculate the mean ([tex]\(\overline{x}\)[/tex]):
[tex]\[
\overline{x} = \frac{\sum_{i=1}^{n} x_i}{n}
\][/tex]
Where [tex]\( n \)[/tex] is the number of data points.
[tex]\[
\overline{x} = \frac{49 + 55 + 52 + 54 + 50}{5} = \frac{260}{5} = 52.0
\][/tex]
3. Calculate each data point's deviation from the mean and square the result:
[tex]\[
(49 - 52)^2 = (-3)^2 = 9
\][/tex]
[tex]\[
(55 - 52)^2 = 3^2 = 9
\][/tex]
[tex]\[
(52 - 52)^2 = 0^2 = 0
\][/tex]
[tex]\[
(54 - 52)^2 = 2^2 = 4
\][/tex]
[tex]\[
(50 - 52)^2 = (-2)^2 = 4
\][/tex]
4. Sum these squared deviations:
[tex]\[
9 + 9 + 0 + 4 + 4 = 26
\][/tex]
5. Calculate the variance (s^2) using the sample variance formula:
[tex]\[
s^2 = \frac{\sum_{i=1}^{n} (x_i - \overline{x})^2}{n-1}
\][/tex]
[tex]\[
s^2 = \frac{26}{4} = 6.5
\][/tex]
6. Calculate the standard deviation (s):
The standard deviation is the square root of the variance.
[tex]\[
s = \sqrt{s^2} = \sqrt{6.5} \approx 2.5495097567963922
\][/tex]
7. Round the standard deviation to two decimal places:
[tex]\[
s \approx 2.55
\][/tex]
Therefore, the standard deviation of this sample of red blood cell counts is approximately [tex]\( 2.55 \)[/tex] (rounded to two decimal places).
