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Question
The mean of three numbers is 10. The mean of other four numbers is 12. Find the mean of all the numbers.
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Solution
Mean of three numbers = `"Sum of three numbers"/3`
⇒ `10 = "Sum of three numbers"/3` ...[∵ Mean of three numbers = 10, given]
Here, sum of three numbers = 30
Mean of other four numbers = `"Sum of other four numbers"/4`
⇒ `12 = "Sum of other four numbers"/4` ...`[(∵ "Mean of other four"),("numbers" = 12"," "given")]`
Hence, sum of other four numbers = 48
∴ Mean of all the numbers = `"Sum of all the numbers"/"Total numbers"`
= `(["Sum of first three numbers" + "Sum of other four numbers"])/7`
= `(30 + 48)/7`
= `78/7`
= 11.14
Hence, mean of all the numbers is 11.14.
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