Question

The mean of the 8 smallest numbers from a group is 17, while the mean of all the numbers of the group taken together is 20. If the mean of the umbers leaving the smallest eight out is 22, how many numbers were present in the group in all?​

Answer 1

Answer:

Total 20 numbers were present in the group in all.

Step-by-step explanation:

• If there are n observation, having values x1, x2, x3, ..., xn, then mean of thses observation is defined as

$mean = \frac{x1 + x2 + x3 + ... + xn}{n}$

Given that :

• Mean of 8 smaller numbers = 17
• Mean of all numbers = 20
• Mean of all numbers except 8 smallest = 22

To find :

• Total numbers in the group

Solution :

• Let, there are n numbers in the group.
• Since, mean of 8 smallest number is 17.
• Sum of 8 smallest number = 8 x 17
• Mean of all n numbers is 20.
• Sum of all n numbers = n x 20
• Mean of all numbers except 8 smallest is 22
• Sum of all numbers except 8 smallest = 22 x (n - 8)
• Sum of all numbers in group= Sum of 8 smallest numbers + Sum of all numbers except 8 smallest.
• This gives,
• 20 x n = (8 x 17) + 22 x (n - 8)

⇒20n = (8 x 17) + 22n -(22 x 8)

⇒2n = (5 x 8)

⇒2n = 40

⇒n = 20

• Hence, total numbers in group is 20.

Answer 2

Answer:

There are 20 numbers in the group in all.

Step-by-step explanation:

Let the numbers in the group be x

According to the statement of the question,

8 X 17 + (x - 8) x 22= 20x

136 + 22x - 176 = 20x

22x - 20x - 40 = 0

2x - 40 = 0

2x = 40

x = 40/2

x = 20

Formula

mean  ={sum of the terms} / {number of terms}

$\xbar$X = ∑x / N

Example:

Consider the following number set: 3, 4, 6, 6, 8, 9, 11.

The mean is calculated in the following manner:

Mean = 3 + 4 + 6 + 6 + 8 + 9 + 11 / 7

Mean  = 47/7

Mean = 6.71 (approximately)

We can find the mean, or average, of a data set in two simple steps:

• Find the sum of the values by adding them all up.
• Divide the sum by the number of values in the data set.