Question

please calculate the sd of a sample of 9 data using the formula taught in class and the information below.
the mean of the sample is 5.0. the sum of all the scores squared ($\sigma x^2$) is 237.
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answer:
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for a normal distribution with a mean of 100, the z score corresponding to a raw score of 120 would be?
○ a. 1.00
○ b. 1.20
○ c. cant be determined from the information provided
○ d. 10.0
○ e. 2.00

Explanation:

Step1: Recall sample SD formula

Sample standard deviation (SD) formula:
$$s = \sqrt{\frac{\sum X^2 - \frac{(\sum X)^2}{n}}{n-1}}$$
First, calculate $\sum X$ using $\bar{X} = \frac{\sum X}{n}$, so $\sum X = \bar{X} \times n$.

Step2: Calculate sum of raw scores

$\sum X = 5.0 \times 9 = 45$

Step3: Compute numerator of variance

$$\sum X^2 - \frac{(\sum X)^2}{n} = 237 - \frac{45^2}{9} = 237 - \frac{2025}{9} = 237 - 225 = 12$$

Step4: Compute sample variance

$$\frac{12}{9-1} = \frac{12}{8} = 1.5$$

Step5: Compute sample SD

$$s = \sqrt{1.5} \approx 1.22$$

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Step1: Analyze z-score requirements

Z-score formula: $z = \frac{X - \mu}{\sigma}$. We know $X=120$, $\mu=100$, but $\sigma$ (population SD) is not provided.

Answer:

1. $\approx 1.22$
2. c. Can't be determined from the information provided