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The mean of 10 observation is 25. If one observation namely 25, is deleted, the new mean is :-
- a)Occurs most frequenty
- b)Divides observations into two equal parts
- c)Is a representative of whole group
- d)Is the sum of observation
Correct answer is option 'C'. Can you explain this answer?
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The mean of 10 observation is 25. If one observation namely 25, is del...
The mean is a measure of central tendency that represents the average value of a set of observations. In this case, the mean of 10 observations is given as 25.
If one observation, specifically 25, is deleted from the set of observations, we need to find the new mean. To do this, we need to calculate the sum of the remaining 9 observations and divide it by 9.
Let's denote the sum of the 10 observations as S and the sum of the remaining 9 observations as S'. The mean of the 10 observations is given as:
Mean = S/10 = 25
To find the sum of the remaining 9 observations, we can subtract the observation that is deleted from the sum of the 10 observations:
S' = S - 25
Now, let's calculate the new mean using the sum of the remaining 9 observations:
New Mean = S'/9 = (S - 25)/9
To determine whether the new mean is a representative of the whole group, we need to compare it to the original mean. If the new mean is similar to the original mean, it suggests that the deleted observation did not significantly affect the overall average and that the new mean is still a representative value.
To evaluate this, let's simplify the expression for the new mean:
New Mean = (S - 25)/9
Expanding the numerator:
New Mean = S/9 - 25/9
Since we know that the original mean is 25, we can substitute it in the expression for the new mean:
New Mean = 25 - 25/9
Simplifying further:
New Mean = 225/9 - 25/9
New Mean = 200/9
This shows that the new mean is approximately 22.22.
Since the new mean is close to the original mean of 25, it indicates that the deleted observation did not significantly affect the overall average. Therefore, the new mean can still be considered a representative value of the whole group.
If one observation, specifically 25, is deleted from the set of observations, we need to find the new mean. To do this, we need to calculate the sum of the remaining 9 observations and divide it by 9.
Let's denote the sum of the 10 observations as S and the sum of the remaining 9 observations as S'. The mean of the 10 observations is given as:
Mean = S/10 = 25
To find the sum of the remaining 9 observations, we can subtract the observation that is deleted from the sum of the 10 observations:
S' = S - 25
Now, let's calculate the new mean using the sum of the remaining 9 observations:
New Mean = S'/9 = (S - 25)/9
To determine whether the new mean is a representative of the whole group, we need to compare it to the original mean. If the new mean is similar to the original mean, it suggests that the deleted observation did not significantly affect the overall average and that the new mean is still a representative value.
To evaluate this, let's simplify the expression for the new mean:
New Mean = (S - 25)/9
Expanding the numerator:
New Mean = S/9 - 25/9
Since we know that the original mean is 25, we can substitute it in the expression for the new mean:
New Mean = 25 - 25/9
Simplifying further:
New Mean = 225/9 - 25/9
New Mean = 200/9
This shows that the new mean is approximately 22.22.
Since the new mean is close to the original mean of 25, it indicates that the deleted observation did not significantly affect the overall average. Therefore, the new mean can still be considered a representative value of the whole group.
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The mean of 10 observation is 25. If one observation namely 25, is deleted, the new mean is :-a)Occurs most frequentyb)Divides observations into two equal partsc)Is a representative of whole groupd)Is the sum of observationCorrect answer is option 'C'. Can you explain this answer?
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