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Solution: Total number of days = 7

Sum of the number of tickets sold = 145 + 120 + 125 + 135 + 205 + 250 + 300 = 1280
We have,

Sum of all observations
Arithmetic mean (A.M.) =
Number of observations
1280
x = = 182.86
7
Thus, the required arithmetic mean of tickets sold during the week is 182.86.

Example 10: The mean of 8, 11, 13, x, and 17 is 12. Find the value of x.
Solution: The total number of observation = 5
Sum of the observations = 8 + 11 + 13 + x + 17 = 49 + x

Since, the mean of the given observations is 12.
We have,

Sum of all observations
Arithmetic mean (A.M.) =
Number of observations

49 + x
12 =
5
⇒ 49 + x = 60
⇒ x = 60 – 49

x = 11
Thus, the value of x is 11.
Example 11: The mean of five numbers is 38. It was found later that one number 21 was wrongly
written as 12. Find the correct mean.

Solution: Since the mean of 5 numbers = 38
We have, Quick Check

Sum of all observations 1. What is the mean of first 9 whole
Mean =
Number of observations numbers?
2. What is the average weight of
Sum of all observations the students of your classroom?
38 =
5 3. What is the mean of first five
prime numbers?
Sum of observations = 38 × 5 = 190 4. What is the mean of first five

Since one observation 21 was wrongly written as 12. negative integers?
\ New sum of 5 observations = 190 – 12 + 21 = 199
199
Now, correct mean = = 39.8
5
Example 12: The mean of six numbers is 45. If one of the numbers is excluded, the mean becomes
38. Determine the excluded number.

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