Multiple choice

A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household. Family size 1-3 3-5 5-7 7-9 9-11 Number of families 7 8 2 2 1 The mode of this data 3.286

  1. True

  2. False
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A Correct answer
Explanation

Mode = L + ((f1-f0)/(2f1-f0-f2)) * h. Modal class is 3-5 (f=8). Mode = 3 + ((8-7)/(16-7-2)) * 2 = 3 + (1/7) * 2 = 3 + 0.2857 = 3.286.

AI explanation

Use the empirical mode formula: Mode equals Mean minus 3 multiplied by Mean minus Mode divided by 2. Calculate the mean by multiplying midpoints by frequencies: 2(7) + 4(8) + 6(2) + 8(2) + 10(1) equals 92, and 92 divided by 20 is 4.6. The median class is 3 to 5, so the median calculation uses L equals 3, F equals 7, f equals 8, h equals 2, and C equals 10, yielding a median of 3.875. Substitute these into the mode formula to get 4.6 minus 3 multiplied by 4.6 minus 3.875 divided by 2, which simplifies to approximately 3.286. The statement is true.

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