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The mean and median of 5 observations are 9 and 8 respectively. If 1 is subtracted from each observation, then the new mean and the new median will respectively be
- a)8 and 7
- b)9 and 7
- c)8 and 9
- d)Cannot be determined due to insufficient data
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The mean and median of 5 observations are 9 and 8 respectively. If 1 i...
Let the numbers be a, b, c, d and e
Mean = Sum/Number of observations
⇒ 9 = (a + b + c + d + e) /5
⇒ a + b + c + d + e = 45
Now numbers become (a – 1), (b – 1), (c – 1), (d – 1) and (e – 1)
⇒ Sum of numbers = (a + b + c + d + e – 5) = 45 – 5 = 40
⇒ Mean = 40/5 = 8
⇒ Median is the middle most number when they are arranged in ascending order
By decreasing all numbers by 1, the order does not change
⇒ New median = Old median – 1 = 8 – 1 = 7
∴ New Mean is 8 and New Mode is 7
Mean = Sum/Number of observations
⇒ 9 = (a + b + c + d + e) /5
⇒ a + b + c + d + e = 45
Now numbers become (a – 1), (b – 1), (c – 1), (d – 1) and (e – 1)
⇒ Sum of numbers = (a + b + c + d + e – 5) = 45 – 5 = 40
⇒ Mean = 40/5 = 8
⇒ Median is the middle most number when they are arranged in ascending order
By decreasing all numbers by 1, the order does not change
⇒ New median = Old median – 1 = 8 – 1 = 7
∴ New Mean is 8 and New Mode is 7
Most Upvoted Answer
The mean and median of 5 observations are 9 and 8 respectively. If 1 i...
Mean and Median of the observations:
The mean of 5 observations is given as 9. This means that the sum of the 5 observations divided by 5 is equal to 9. Let's denote the sum of the observations as S.
Therefore, we have the equation: S/5 = 9
Multiplying both sides of the equation by 5, we get: S = 45
The median of the 5 observations is given as 8. This means that when the observations are arranged in ascending order, the middle observation is 8.
Subtracting 1 from each observation:
If we subtract 1 from each observation, the new observations will be smaller by 1 unit.
New mean and new median:
To find the new mean, we need to find the sum of the new observations and divide it by the number of observations. Let's denote the new sum of the observations as S'.
Therefore, we have the equation: S'/5 = new mean
To find the new median, we need to arrange the new observations in ascending order and find the middle observation.
Since we are subtracting the same value from each observation, the order of the observations will not change. Therefore, the new median will be the same as the original median, which is 8.
Substituting the given information into the equations:
We know that S = 45, and the new median is 8.
Substituting these values into the equation S'/5 = new mean, we get:
45/5 = new mean
9 = new mean
Therefore, the new mean is 9.
Conclusion:
After subtracting 1 from each observation, the new mean is 9 and the new median is 8. Therefore, the correct answer is option A) 8 and 7.
The mean of 5 observations is given as 9. This means that the sum of the 5 observations divided by 5 is equal to 9. Let's denote the sum of the observations as S.
Therefore, we have the equation: S/5 = 9
Multiplying both sides of the equation by 5, we get: S = 45
The median of the 5 observations is given as 8. This means that when the observations are arranged in ascending order, the middle observation is 8.
Subtracting 1 from each observation:
If we subtract 1 from each observation, the new observations will be smaller by 1 unit.
New mean and new median:
To find the new mean, we need to find the sum of the new observations and divide it by the number of observations. Let's denote the new sum of the observations as S'.
Therefore, we have the equation: S'/5 = new mean
To find the new median, we need to arrange the new observations in ascending order and find the middle observation.
Since we are subtracting the same value from each observation, the order of the observations will not change. Therefore, the new median will be the same as the original median, which is 8.
Substituting the given information into the equations:
We know that S = 45, and the new median is 8.
Substituting these values into the equation S'/5 = new mean, we get:
45/5 = new mean
9 = new mean
Therefore, the new mean is 9.
Conclusion:
After subtracting 1 from each observation, the new mean is 9 and the new median is 8. Therefore, the correct answer is option A) 8 and 7.
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The mean and median of 5 observations are 9 and 8 respectively. If 1 is subtracted from each observation, then the new mean and the new median will respectively bea)8 and 7b)9 and 7c)8 and 9d)Cannot be determined due to insufficient dataCorrect answer is option 'A'. Can you explain this answer?
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