Question

the red blood cell counts (in $10^{5}$ cells per microliter) of a healthy adult measured on 5 days are as follows. 54, 50, 51, 55, 50. send data to calculator. find the standard deviation of this sample of counts. round your answer to two decimal places.

Explanation:

Step1: Calculate the mean

First, find the sum of the data values: $54 + 50+51 + 55+50=260$. There are $n = 5$ data - points. The mean $\bar{x}=\frac{260}{5}=52$.

Step2: Calculate the squared differences

For each data - point $x_i$, calculate $(x_i-\bar{x})^2$:

• For $x_1 = 54$: $(54 - 52)^2=4$.
• For $x_2 = 50$: $(50 - 52)^2 = 4$.
• For $x_3 = 51$: $(51 - 52)^2=1$.
• For $x_4 = 55$: $(55 - 52)^2 = 9$.
• For $x_5 = 50$: $(50 - 52)^2 = 4$.

Step3: Calculate the sum of squared differences

The sum of squared differences $\sum_{i = 1}^{n}(x_i-\bar{x})^2=4 + 4+1 + 9+4=22$.

Step4: Calculate the sample variance

The sample variance $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}=\frac{22}{4}=5.5$.

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{s^2}=\sqrt{5.5}\approx2.35$.

Answer:

$2.35$