The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is
38
Concept:
Mean: This is the sum of all observations divided by the number of observations.
If x1, x2, x3, …., xn are the observations, then the mean is given by:
\(\bar{X'}=\frac{x_1+x_2+...+x_n}{n}\)
Calculation:
Given: Mean X̅ = 30
New mean \(\bar{X'}=28\) is.
Therefore, \(\bar{X'}=\frac{x_1+x_2+...+x_4}{4}\)
\(\Rightarrow 28=\frac{x_1+x_2+...+x_4}{4}\)
⇒112 = x1 + x2 + ⋯ + x4
Now, \(\bar{X}=\frac{x_1+x_2+...+x_5}{5}\)
\(\Rightarrow 30=\frac{x_1+x_2+...+x_5}{5}\)
⇒ 150 = x1 + x2 + ⋯ + x5
⇒ 150 = 112 + x5
⇒ 38 = x5
The extracted number is 38.
Important Questions from Measures of Central Tendency
If X̅ = 20 is the mean of 10 observations x1, x2, ... x10; then what is the value of \(\displaystyle \sum_{i=1}^{10}\left(\frac{3 x_i-4}{5}\right) ?\) ?
What is the mean of the numbers 1, 2, 3, ... 10 with frequencies 9C0, 9C1, 9C2 ..., 9C9, respectively?
Which one of the following measures of central tendency is used in construction of index numbers?
The ‘less than’ ogive curve and the ‘more than’ ogive curve intersect at
The observations 4, 1, 4, 3, 6, 2, 1, 3, 4, 5, 1, 6 are outputs of 12 dices thrown simultaneously. If m and M are means of lowest 8 observations and highest 4 observations respectively, then what is (2m + M) equal to ?
