Question
Download Solution PDFThe mean of a data set comprising of 10 observations is 20. If one of the observations whose value is 20 is deleted and two new observations with values 14 and 15 are added to the data, then the mean of the new data set is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation of the New Mean:
The problem involves determining the mean of a modified data set. Let us calculate step by step:
Step 1: Initial Mean and Total:
- The mean of the original data set of 10 observations is 20.
- The total sum of the observations, based on the formula Mean = Total Sum / Number of Observations, is:
Total Sum = Mean × Number of Observations = 20 × 10 = 200
Step 2: Modifications to the Data Set:
- One observation with a value of 20 is deleted. Therefore, the updated total sum becomes:
New Total Sum (after deletion) = 200 - 20 = 180
- Two new observations with values 14 and 15 are added to the data set. The updated total sum is:
New Total Sum (after addition) = 180 + 14 + 15 = 209
- The new number of observations is:
New Number of Observations = (10 - 1) + 2 = 11
Step 3: Calculation of the New Mean:
The mean of the new data set is calculated using the formula:
New Mean = New Total Sum / New Number of Observations
Substituting the values:
New Mean = 209 / 11 = 19
Therefore, the mean of the new data set is 19.
Correct Option: Option 3: 19
Last updated on May 30, 2025
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