The frequency distribution below shows the distribution for IQ scores for a rand
ID: 3232591 • Letter: T
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 between 90 and 129, inclusive?
(c) Which of the following IQ score groups does the median of this distribution belong to?
70 – 89, 90 – 109, or 110 – 129? Why?
Explanation / Answer
Let the frequency of class 90-109 = x
Let the frequency of class 110-129 = y
(23 + 249 + x) / 1000 = 0.743
or, x = 743 - (23 + 249)
or, x = 471
y = 1000 - (23 + 249 + 471 + 25)
or, y = 232
a)
IQ scores Frequency Cumm relative frequency
50-69 23 23/1000 = 0.023
70-89 249 (23+249)/1000 = 0.272
90-109 471 (23 + 249 + 471)/1000 = 0.743
110-129 232 (23 + 249 + 471 + 232)/1000 = 0.975
130-149 25 (23 + 249 + 471 + 232 + 25)/1000 = 1
b) percentage of the adults in this sample has an IQ score between 90 and 129 = (471 + 232) / 1000 = 0.703
c) Median of this distribution belongs to 90-109. Because, the cumm relative frequency group for 0.5 is 90-109
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