Calculating Z-Score for IQ Score of 154
Understanding Z-Score in IQ Calculation
In statistical analysis, the z-score is a measure of how many standard deviations a data point is from the mean of a group. It helps researchers compare different data points on a common scale.
Information about Cameron's Study
Cameron is performing a study on the IQ of groups in various areas. He has determined that the average IQ of Group B is 147, with a standard deviation of 10.
Calculating Z-Score for an IQ of 154
Cameron wants to find the z-score for someone with an IQ of 154. To calculate the z-score, we can use the formula:
z = (x - μ) / σ
Where z is the z-score, x is the IQ value (154 in this case), μ is the mean IQ (147), and σ is the standard deviation (10).
Multiple Choice Question:
What is the z-score for someone with an IQ of 154?
a) 0.22
b) 1.0
c) -0.70
d) 0.70
Final Answer:
The z-score for someone with an IQ of 154 is 0.7.
Explanation:
To calculate the z-score for an IQ of 154, we can substitute the values into the formula:
z = (154 - 147) / 10
z = 7 / 10
z = 0.7
Therefore, the z-score for someone with an IQ of 154 is 0.7.
Additional Question:
Why is the z-score important in analyzing IQ scores?
Answer:
The z-score is important in analyzing IQ scores because it standardizes the comparison of individual IQ scores to the group mean and provides insight into how unusual or typical a particular IQ score is within the group. This standardized measure helps researchers interpret the significance of the IQ score relative to the group's distribution.