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.