Consider two different quantitative variables, 𝑥 & 𝑦. If 𝑥¯ = 20.7 (sample mean of variable 𝑥) and 𝑠𝑥 = 8.0 (sample standard deviation of variable 𝑥), find the 𝐳 score of 𝑥1 = 10.0 (a particular observation of variable 𝑥). Give your answer to 2 decimal places.
Question
Consider two different quantitative variables, 𝑥 & 𝑦. If 𝑥¯ = 20.7 (sample mean of variable 𝑥) and 𝑠𝑥 = 8.0 (sample standard deviation of variable 𝑥), find the 𝐳 score of 𝑥1 = 10.0 (a particular observation of variable 𝑥). Give your answer to 2 decimal places.
Solution
The z-score is a measure of how many standard deviations an element is from the mean. To find the z-score of a particular observation, we use the formula:
z = (X - μ) / σ
where:
- X is the observation,
- μ is the mean of the sample, and
- σ is the standard deviation of the sample.
In this case, we have:
X = 10.0 (the observation), μ = 20.7 (the mean), and σ = 8.0 (the standard deviation).
Substituting these values into the formula, we get:
z = (10.0 - 20.7) / 8.0 z = -10.7 / 8.0 z = -1.3375
Rounding to two decimal places, the z-score of the observation X = 10.0 is -1.34.
Similar Questions
Find the value of variables :7𝑞+18𝑚−450=0 and
A number that quantifies two aspects of the relationship between the data. Represented by the variable, r𝑟.
As X variable increases, even the Y variable decreases. This indicates?
G) For two random variables 𝑋 and 𝑌, 𝐸(𝑋𝑌) = 𝐸(𝑋)𝐸(𝑌) hold if 𝑋 and 𝑌 are _______
Consider two different quantitative variables, 𝑥 & 𝑦. If 𝑥¯ = 20.7 (sample mean of variable 𝑥) and 𝑠𝑥 = 8.0 (sample standard deviation of variable 𝑥), find the 𝐳 score of 𝑥1 = 10.0 (a particular observation of variable 𝑥). Give your answer to 2 decimal places.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.