Multiple choice

Given table shows the weights of various people. Find the mean of the given data. Weight (in kg) 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80 Frequency 11 8 9 14 6

  1. 57.7 kg

  2. 56.8 kg

  3. 54.7 kg

  4. 42.7 kg
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C Correct answer
Explanation

Use midpoints of classes: 35.5, 45.5, 55.5, 65.5, 75.5. Mean = (35.5*11 + 45.5*8 + 55.5*9 + 65.5*14 + 75.5*6) / (11+8+9+14+6) = (390.5 + 364 + 499.5 + 917 + 453) / 48 = 2624 / 48 = 54.666... which rounds to 54.7.

AI explanation

Using the direct method for grouped data, the mean is calculated by summing the products of the class marks and their frequencies, then dividing by the total frequency. The class marks are 35.5, 45.5, 55.5, 65.5, and 75.5, which when multiplied by their frequencies of 11, 8, 9, 14, and 6 give a sum of 2619. Dividing this sum by the total frequency of 48 results in a mean of 54.7 kg.

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