Question

On most modern IQ tests, a score of 115 would be: A. about normal. B. about \(15 \%\) higher than the average of one's agemates. C. an indication of genius. D. one standard deviation above the mean.

Short answer

A. The score is about normal. B. The score is 15% higher than the average. C. The individual is a genius. D. The score is one standard deviation above the mean. Answer: B, D

Step-by-step solution

Calculate how much higher the given score is from the mean

First, let's find out how much higher the score of 115 is compared to the mean score of 100. We can do this by subtracting the mean from the given score: $$115 - 100 = 15$$

Determine as a percentage how much higher the score is from the mean

To calculate this percentage, divide the difference we found in Step 1 by the mean and multiply the result by 100: $$ \frac{15}{100} \times 100 = 15 \% $$

Compare the difference to the standard deviation

Next, we need to determine how many standard deviations the given score is above the mean. Divide the difference we found in Step 1 by the standard deviation (15): $$ \frac{15}{15} = 1 $$ The given score is one standard deviation above the mean.

Select the correct answer

Now we can analyze the provided options: A. The given score is 15% higher than the average, so "about normal" isn't accurate. B. We calculated the score is 15% higher than the average, so this statement is true. C. A score of 115 doesn't represent genius-level intelligence, so this is false. D. Our calculations showed one standard deviation above the mean, so this statement is true. Therefore, the correct answer choices are B and D.

Key concepts

Standard Deviation

Standard deviation is a crucial concept in statistics. It measures how much the scores in a data set tend to deviate from the mean.
For instance, when evaluating IQ scores, the standard deviation usually is set at 15. This means if most people have IQ scores close to the mean, you will see numbers like 95 or 105.
Standard deviation helps you understand how spread out the data points are.

• A small standard deviation means scores are close to the mean.
• A large standard deviation shows that scores are spread out over a wide range.

When you find that an IQ score is "one standard deviation above the mean," it means the score is 15 points above the average IQ of 100.

Mean Score

The mean score, often just called the mean, is the average of a set of numbers. To find a mean, you add up all the numbers in the set and then divide by the number of values.
In the context of IQ tests, the mean score is typically 100. This means that if you averaged out the IQ scores of all the people who took the test, the result should be around 100.

• The mean score is helpful because it gives us a central value to compare other scores to.
• It helps us determine how a particular score relates to the general population.

If someone scores above or below the mean, it can give us an idea of how their performance compares to the average.

Intelligence Quotient

Intelligence Quotient, or IQ, is a score designed to assess human intelligence. It is calculated using standardized tests and is set up so that most people score around the mean of 100.
IQ tests evaluate various cognitive abilities and provide a single score meant to serve as an indicator of a person’s intellectual abilities.

• IQ scores usually range from 85 to 115 for about 68% of the population.
• Scores above 115 are considered above average.

However, it's important to remember that IQ tests measure specific types of intellectual ability and may not capture the entirety of an individual's intelligence.

Average Score

The average score is another term for the mean score. In statistics, the average gives us an idea of the typical score in a dataset.
When talking about IQ tests, the average score serves as a benchmark to assess if someone is average, above average, or below average.

• An average IQ score is one that falls around 100.
• Above average scores indicate higher cognitive abilities compared to the general population.

The average score is crucial in education and psychology to tailor learning according to different mental abilities.