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The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. The value of this 13th observation is​
  • a)
    28
  • b)
    29
  • c)
    30
  • d)
    31
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The mean of a data set with 12 observations is calculated as 19.25. If...
Given: Mean of a data set with 12 observations = 19.25
Mean of the new data set with 13 observations = 20

To find: Value of the 13th observation

Step-by-step solution:

1. We know that the formula for calculating the mean of a data set is:

Mean = (Sum of all observations) / (Number of observations)

2. Using this formula, we can write two equations for the given information:

19.25 = (Sum of 12 observations) / 12 ... equation (1)
20 = (Sum of 13 observations) / 13 ... equation (2)

3. From equation (1), we can find the sum of the 12 observations:

Sum of 12 observations = 19.25 x 12 = 231

4. Substituting this value in equation (2), we get:

20 = (231 + 13th observation) / 13

Multiplying both sides by 13, we get:

260 = 231 + 13th observation

Subtracting 231 from both sides, we get:

13th observation = 29

Therefore, the value of the 13th observation is 29.
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Community Answer
The mean of a data set with 12 observations is calculated as 19.25. If...
29
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The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. The value of this 13thobservation isa)28b)29c)30d)31Correct answer is option 'B'. Can you explain this answer?
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