Multiple choice

Data set R: 18, 22, 25, 29, 31, 35 Data set S: 16, 24, 27, 30, 33, t Each data set contains 6 numbers. If the mean of data set R equals the mean of data set S, what is the value of t?

  1. 28

  2. 30

  3. 32

  4. 34
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B Correct answer
Explanation

Mean of R = (18+22+25+29+31+35)/6 = 160/6. Mean of S = (16+24+27+30+33+t)/6 = (130+t)/6. Since means are equal, 160 = 130 + t, so t = 30.

AI explanation

Calculate the sum of data set R by adding 18, 22, 25, 29, 31, and 35 to get 160. Equating the means means both data sets must have the same sum, so the sum of data set S must also equal 160. The sum of the known numbers in data set S is 16 plus 24 plus 27 plus 30 plus 33, which is 130. Subtracting this sum from 160 gives the value of t as 30.

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