A researcher gives IQ tests to a large group of adults, and discovers that the
mean, median and mode all equal 100. The highest score in the group was 130
and the lowest was 70. Between IQ's of 75 and 125, 80% of the group was found, and 50% were found between IQ's of 90 and 110. The shape of the graphed distribution was mesokurtic.
-The standard deviation was equal to approximately
A) 0
B) 10
C) 15
D) cannot tell, since not enough information is provided

Question

A researcher gives IQ tests to a large group of adults, and discovers that the 
mean, median and mode all equal 100.  The highest score in the group was 130 
and the lowest was 70.  Between IQ's of 75 and 125, 80% of the group was found,  and 50% were found between IQ's of 90 and 110.  The shape of the graphed  distribution was mesokurtic.     
-The standard deviation was equal to approximately
A) 0
B) 10
C) 15
D) cannot tell, since not enough information is provided

Quizplus · Accepted Answer

Given that 50% of the group's IQ scores fall between 90 and 110, and considering the distribution is mesokurtic (which resembles a normal distribution), we can infer that this range represents approximately ±1 standard deviation from the mean (100). In a normal distribution, ±1 standard deviation from the mean encompasses about 68% of data, but given the specific details provided, the best approximation with the options given is 10, aligning with the characteristics of the distribution described.

A Researcher Gives IQ Tests to a Large Group of Adults