Given Mean- Find missing value

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Presentation transcript:

Given Mean- Find missing value

Arithmetic mean for ungrouped data The arithmetic mean is the ratio of the sum of all the observations to the total number of observations. Arithmetic mean for ungrouped data To calculate arithmetic mean for ungrouped data we use the following formula. In Mathematics, the symbol in Greek letter Σ , is called Sigma This notation is used to represent the summation Σx With this symbol, the sum of x1, x2, x3, …… xn or simply as Then we have Note: Arithmetic mean is also known as Average or Mean.

More about notation: Σ

Example 1: The marks obtained by 10 students in a test are 15, 75, 33, 67, 76, 54, 39, 12, 78, 11. Find the arithmetic mean. Solution: Given:-Here, the number of observations, n = 10 To Find: Arithmetic mean (A.M.) Ans:- Arithmetic mean is 46

Example 2: If the average of the values 9, 6, 7, 8, 5 and x is 8 Example 2: If the average of the values 9, 6, 7, 8, 5 and x is 8. Find the value of x. Solution: Given:-Here, the given values are 9, 6, 7, 8, 5 and average=8 and n = 6 To find: Value of x By formula ie., 35 + x = 48 x = 48 – 35 = 13 Ans:- x = 13

Example 3:-The average height of 10 students in a class was calculated as 166 cm. On verification it was found that one reading was wrongly recorded as 160 cm instead of 150 cm. Find the correct mean height. Solution Given:-Here average = 166cm and n=10 The incorrect Σx = 1660 The correct Σ x = incorrect Σ x – the wrong value + correct value = 1660 – 160 + 150 = 1650 Hence, the correct A.M Ans:- Correct mean height is 165cm

Try These If the average of the values 18, 41, x , 36, 31, 24, 37, 35, 27, 36, is 31. Find the value of x. The average height of 20 students in a class was calculated as 160 cm. On verification it was found that one reading was wrongly recorded as 132 cm instead of 152 cm. Find the correct mean height.