An IQ score 1 standard deviation above the mean is 115, and 1 standard deviation below the mean is 85.
Understanding IQ Scores and Standard Deviation
IQ (Intelligence Quotient) scores are designed to measure cognitive abilities relative to a typical population. For the general population, the mean (average) IQ score is established at 100. This central point helps to benchmark an individual's score against the norm.
The concept of standard deviation (often denoted by the Greek letter σ, sigma) is crucial for understanding how much individual scores typically vary from this mean. It quantifies the spread or dispersion of a set of data. For IQ scores, the standard deviation is 15 points. This means that most people's IQ scores fall within a certain range around the average.
Calculating the Scores
To determine the IQ scores that are one standard deviation away from the mean, you simply add or subtract the standard deviation from the mean:
- 1 Standard Deviation Above the Mean:
- Mean IQ Score + Standard Deviation = 100 + 15 = 115
- 1 Standard Deviation Below the Mean:
- Mean IQ Score - Standard Deviation = 100 - 15 = 85
Summary of IQ Scores at One Standard Deviation
The table below summarizes these key IQ scores:
| Description | Calculation | IQ Score |
|---|---|---|
| Mean IQ Score | 100 | |
| 1 Standard Deviation Above the Mean | 100 + 15 | 115 |
| 1 Standard Deviation Below the Mean | 100 - 15 | 85 |
Practical Significance
These scores are significant because they define a substantial portion of the population. In a normal distribution, approximately 68% of all IQ scores fall within one standard deviation above and below the mean. This range (85 to 115) is generally considered to be the average or typical range of intellectual ability.
- An IQ score of 115 indicates that an individual's cognitive abilities are moderately above average.
- An IQ score of 85 suggests that an individual's cognitive abilities are moderately below average, but still within the broad average range.
Understanding these benchmarks helps to interpret individual IQ scores within the context of the overall population distribution.
