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
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 ?
The mean of the series x 1, x 2… x nis X̅. If x 2 is replaced by λ, then what is the new mean?
The mean of a group of 100 observations was found to be 20. Later it was found that four observations were incorrect, which were recorded as 21, 21, 18 and 20. What is the mean if the incorrect observations are omitted?
A random sample of 20 people is classified in the following table according to their ages:
Age
Frequency
15 – 25
2
25 – 35
4
35 – 45
6
45 – 55
5
55 - 65
3
What is the mean age of this group of people?
