If 𝑦¯ = 1.81 (sample mean of variable 𝑦) and 𝑠𝑦 = 0.5 (sample standard deviation of variable 𝑦), find the 𝐳 score of 𝑦1 = 0.94 (a particular observation of variable 𝑦). Give your answer to 2 decimal places.
Question
If 𝑦¯ = 1.81 (sample mean of variable 𝑦) and 𝑠𝑦 = 0.5 (sample standard deviation of variable 𝑦), find the 𝐳 score of 𝑦1 = 0.94 (a particular observation of variable 𝑦). 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, you can use the following formula:
z = (y1 - y¯) / sy
where:
- y1 is the particular observation,
- y¯ is the sample mean, and
- sy is the sample standard deviation.
Given that y¯ = 1.81, sy = 0.5, and y1 = 0.94, you can substitute these values into the formula:
z = (0.94 - 1.81) / 0.5
Solving the equation gives:
z = -0.87 / 0.5 = -1.74
So, the z-score of y1 = 0.94 is -1.74 (rounded to 2 decimal places).
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