11.25 IQ test scores. The Wechsler Adult Intelligence Scale (WAIS) is the most commonly used “IQ test.” The scale of scores is set separately for each age group and is approximately Normal with mean 100 and standard deviation 15. Use the 68–95–99.7 rule to answer the following questions.What percent of people have WAIS scores above 100? Above 145? Below 85?The organization MENSA, which calls itself “the high IQ society,” requires an IQ score of 130 or higher for membership. What percent of adults would qualify for membership?People with WAIS scores below 70 are considered mentally retarded when, for example, applying for Social Security disability benefits. About what percent of adults are mentally retarded according to this criterion?

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Description: 11.25 IQ test scores. The Wechsler Adult Intelligence Scale (WAIS) is the most commonly used “IQ test.” The scale of scores is set separately for each age group and is approximately Normal with mean 100 and standard deviation 15. Use the 68–95–99.7 r

Given, Score mean is 100 and standard deviation is 15. 68 - 95 - 99.7 rule states that, i) 68% of data falls within the first standard deviation from the mean. ii) 95% of data falls within the two standard deviation from the mean. iii) 99.7% of data falls within the three standard deviation from the mean. 1)By using 68 - 95 - 99.7 rule, i) Above 100, We know the mean of data is 100 and it is symmetric then 50% people score above 100. ii)Above 145, μ+3σ=100+3(15)=100+45=145 Then, Within 3 standard deviation 99.7% then outside that 0.3% data falls both sides. One side it is 0.15% data. Hence, 0.15% people score above 145 iii)Below 85, We, Know that 68% of data falls inside the first standard deviation from the mean. Outside that 32% on both the sides. Then at one side it is 16%. μ-σ=100-15=85 Hence, 68% of people score less than 85.b) Above 130, 95% of data falls within two standard deviation from the mean. Outside that 5% on both side. for one side it is 2.5%. Then, μ+2σ=100+2(15)=100+30=130 Hence, 2.5% of the people who is in MENSA organization. c) μ-2σ=100-2(15)=100-30=70 Hence, 2.5% of the people are mentally retarded

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11.25 IQ test scores. The Wechsler Adult Intelligence Scale (WAIS) is the most commonly used “IQ test.” The scale of scores is set separately for each age group and is approximately Normal with mean 100 and standard deviation 15. Use the 68–95–99.7 rule to answer the following questions.
1. What percent of people have WAIS scores above 100? Above 145? Below 85?
2. The organization MENSA, which calls itself “the high IQ society,” requires an IQ score of 130 or higher for membership. What percent of adults would qualify for membership?
3. People with WAIS scores below 70 are considered mentally retarded when, for example, applying for Social Security disability benefits. About what percent of adults are mentally retarded according to this criterion?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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