The mean and median of 100 observation is 50 and 52 respectively. it i...
Solution no. 1:-
Arithmetic Mean = ∑X/N
Given : Mean = 50 and N = 100
Therefore,
50 = ∑X/100
∑X (Wrong) = 5000
Correct value = 110
Incorrect value = 100
Correct Arithmetic Mean = {∑X (Wrong) + Correct value of observation - Incorrect value of observation }/N
⇒ Correct Mean = (5000 + 110 - 100)/100
⇒ Correct mean = 5010/100
⇒ Correct Mean = 50.1
Answer Solution no. 2 :-
In this question, 'the value of the largest item' should be written instead of 'latest item'.
The value of the Median will not change because whatever values are added or subtracted from median, the total observation will remain 100 and median is the centrally located value of a series such that the half of the value or items of the series are above it and the other half are below it.
Formula of median = Size of (N+1)/2th Item
Total observations = 100
Size of (N+1)/2th item
⇒(100+1)/2th Item
⇒ 101/2
⇒ 50.5th Item
110 is corrected observation instead of 100 and 110 is the largest of all the observation. So it will not make any difference in value of median. The value of Median will be 52.
This question is part of UPSC exam. View all Class 9 courses
The mean and median of 100 observation is 50 and 52 respectively. it i...
Given Information:
- Mean of 100 observations = 50
- Median of 100 observations = 52
- The greatest observation 110 was misread as 100
To find:
- Correct mean and median
Solution:
Step 1: Find the sum of all observations
- The mean is the sum of all observations divided by the total number of observations.
- Mean = Sum of all observations / Total number of observations
Given that the mean is 50, we can write the equation as:
50 = Sum of all observations / 100
Cross-multiplying, we get:
Sum of all observations = 50 * 100 = 5000
Step 2: Find the sum of all observations by replacing the misread observation with the correct value.
- The greatest observation was misread as 100 instead of the correct value, which is 110.
- So, we need to subtract 100 and add 110 to the sum of all observations calculated in Step 1.
Correct sum of all observations = Sum of all observations - Misread value + Correct value
= 5000 - 100 + 110
= 5010
Step 3: Find the correct mean
- The correct mean can be calculated by dividing the correct sum of all observations by the total number of observations.
Correct mean = Correct sum of all observations / Total number of observations
= 5010 / 100
= 50.1
Therefore, the correct mean is 50.1.
Step 4: Find the correct median
- The median is the middle value of a set of observations when they are arranged in ascending order.
- Since the misread value was the greatest observation, we need to replace it with the correct value, 110, and then find the median.
Observations arranged in ascending order: ... 50, 52, ..., 110 ...
Since there are 100 observations, the median will be the 50th observation. As the observations are arranged in ascending order, the 50th observation will be 55.
Therefore, the correct median is 55.
Final Answer:
- Correct mean = 50.1
- Correct median = 55
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