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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. Value of this 13th observation is
- a)28
- b)29
- c)31
- d)30
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The mean of a data set with 12 observations is calculated as 19.25. If...
Suppose be all twelevth terms = x
Mean = Terms / Observation
19 . 25 = x / 12
x = 19.25 × 12
x = 231 .00
Now let thirteenth term will be y
Mean = 20
So, 20 = x + y / 13
20 = 231 + y / 13
20 × 13 = 231 + x
260 = 231 + x
260 - 231 = x
29 = x
Mean = Terms / Observation
19 . 25 = x / 12
x = 19.25 × 12
x = 231 .00
Now let thirteenth term will be y
Mean = 20
So, 20 = x + y / 13
20 = 231 + y / 13
20 × 13 = 231 + x
260 = 231 + x
260 - 231 = x
29 = x
Most Upvoted Answer
The mean of a data set with 12 observations is calculated as 19.25. If...
Suppose be all twelevth terms = x
Mean = Terms / Observation
19 . 25 = x / 12
x = 19.25 × 12
x = 231 .00
Now let thirteenth term will be y
Mean = 20
So, 20 = x + y / 13
20 = 231 + y / 13
20 × 13 = 231 + x
260 = 231 + x
260 - 231 = x
29 = x
That's why 29 is the correct answer .
Mean = Terms / Observation
19 . 25 = x / 12
x = 19.25 × 12
x = 231 .00
Now let thirteenth term will be y
Mean = 20
So, 20 = x + y / 13
20 = 231 + y / 13
20 × 13 = 231 + x
260 = 231 + x
260 - 231 = x
29 = x
That's why 29 is the correct answer .
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Community 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
Solution:
Let's assume the sum of the 12 observations in the original data set is S.
Step 1: Calculate the sum of the 12 observations:
Mean is calculated by dividing the sum of the observations by the number of observations. Therefore,
Mean = S/12
19.25 = S/12
S = 19.25 * 12
S = 231
So, the sum of the 12 observations in the original data set is 231.
Step 2: Calculate the sum of the 13 observations in the new data set:
We are given that the mean of the new data set with 13 observations is 20.
Mean = Sum of observations / Number of observations
20 = (231 + x) / 13
Multiply both sides by 13 to eliminate the fraction:
260 = 231 + x
x = 260 - 231
x = 29
Therefore, the value of the 13th observation is 29 (option B).
- 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
Solution:
Let's assume the sum of the 12 observations in the original data set is S.
Step 1: Calculate the sum of the 12 observations:
Mean is calculated by dividing the sum of the observations by the number of observations. Therefore,
Mean = S/12
19.25 = S/12
S = 19.25 * 12
S = 231
So, the sum of the 12 observations in the original data set is 231.
Step 2: Calculate the sum of the 13 observations in the new data set:
We are given that the mean of the new data set with 13 observations is 20.
Mean = Sum of observations / Number of observations
20 = (231 + x) / 13
Multiply both sides by 13 to eliminate the fraction:
260 = 231 + x
x = 260 - 231
x = 29
Therefore, the value of the 13th observation is 29 (option B).
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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. Value of this 13th observation isa)28b)29c)31d)30Correct answer is option 'B'. Can you explain this answer?
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