The frequency distribution below shows the distribution for IQ scores for a rand

Question

The frequency distribution below shows the distribution for IQ scores for a random sample of 1000 adults. (Show all work. Just the answer, without supporting work, will receive no credit.)

(a) Complete the frequency table with frequency and cumulative relative frequency. Express the cumulative relative frequency to three decimal places.

(b) What percentage of the adults in this sample has an IQ score of at least 110?

(c) Which of the following IQ score groups does the median of this distribution belong to?

70 – 89, 90 – 109, or 110 – 129? Why?

IQ Scores Frequency Cumulative Relative Frequency 50-69 23 70-89 249 90-109 .722 110-129 130-149 25 Total 1000

Explanation / Answer

(a)

Following is the completed table:

(b)

Cumulative relative frequency of scores that are less than 110 is 0.722. So percentage of the adults in this sample has an IQ score of at least 110 is

1 - 0.722 = 0.278 = 27.8%

(c)

Median is data value that has 50% scores less than from it. So median lie in the class 90-109.

IQ Scores Frequency Cumulative Relative Frequency Cumulative frequency 50-69 23 23/1000=0.023 23 70-89 249 272/1000=0.272 272 90-109 722-(249+23)=450 0.722 0.722*1000=722 110-129 253 0.975 722+253=975 130-149 25 1 1000 Total 1000

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