The mean of 5 numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is
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We are given the following information:
– The mean of 5 numbers is 30.
– When one number is excluded, the mean of the remaining 4 numbers becomes 28.
Calculate the total sum of the 5 numbers.
The formula for the mean is:
Mean = (Sum of all observations) / (Number of observations).
For the 5 numbers:
Mean = 30,
Number of observations = 5.
Substitute into the formula:
30 = (Sum of all 5 numbers) / 5.
Multiply through by 5:
Sum of all 5 numbers = 30 × 5 = 150.
Calculate the total sum of the remaining 4 numbers.
When one number is excluded, the mean of the remaining 4 numbers is 28. Using the same formula:
Mean = (Sum of remaining 4 numbers) / (Number of observations).
For the 4 numbers:
Mean = 28,
Number of observations = 4.
Substitute into the formula:
28 = (Sum of remaining 4 numbers) / 4.
Multiply through by 4:
Sum of remaining 4 numbers = 28 × 4 = 112.
Find the excluded number.
The excluded number is the difference between the total sum of the 5 numbers and the sum of the remaining 4 numbers:
Excluded number = (Sum of all 5 numbers) – (Sum of remaining 4 numbers).
Substitute the values:
Excluded number = 150 – 112 = 38.
This question related to Chapter 12 Mathematics Class 9th NCERT. From the Chapter 12 Statistics. Probability. Give answer according to your understanding.
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