217k views
1 vote
Consider a set of data in which the sample mean is 64 and the sample standard deviation is 21 for the following specific values, calculate the z-score and interpret the results

a: x=80 b: x=64 c: x=40

User Simshaun
by
7.5k points

1 Answer

1 vote

Answer:

Explanation:

To calculate the z-score for a given value, we can use the formula: z = (x - μ) / σ where: - x is the given value - μ is the sample mean - σ is the sample standard deviation Let's calculate the z-scores for each of the given values: a) For x = 80: z = (80 - 64) / 21 = 0.7619 b) For x = 64: z = (64 - 64) / 21 = 0 c) For x = 40: z = (40 - 64) / 21 = -1.1429 Now, let's interpret the results: a) For x = 80: The z-score is 0.7619, which means the value of 80 is 0.7619 standard deviations above the sample mean. This suggests that the value of 80 is relatively higher than the average value in the sample. b) For x = 64: The z-score is 0, indicating that the value of 64 is exactly equal to the sample mean. Therefore, the value of 64 is at the average level in the sample. c) For x = 40: The z-score is -1.1429, meaning the value of 40 is 1.1429 standard deviations below the sample mean. This suggests that the value of 40 is relatively lower than the average value in the sample.

User Marcos Placona
by
7.9k points

No related questions found