Question

The mean of a group of data is 60. If the data are 85, 62, 36, 48, 72, X, 75 and 30. Find the value of X

Answer 1

Given: The mean of ungrouped data 85, 62, 36, 48, 72, X, 75 and 30 is 60.

To find: The value of x

Solution:

We know that mean of certain observation is obtained by the following formula:

$\boxed{\overline{x} = \dfrac{x_1 + x_2 + x_3 + ...+ x_n} {n} = \dfrac{\sum x_i}{N}}$

Here in the formula, terms used are:

• $\overline{x}$ = Mean
• N = number of observations

Therefore, using this formula, we get:

${\implies \overline{x} = \dfrac{85 + 62 + 36 + 48 + 72 + x + 75 +30}{8}}$

$\implies 60 = \dfrac{408 + x}{8}$

$\implies (60)8 = 408 + x$

$\implies 480 = 408 + x$

$\implies 480 -408 = x$

$\implies 72 = x$

Hence the required observation 'x' is 72.

Additional information:

Mean

Mean is the average of certain observations. Inorder  to find mean of data, we use the method of dividing sum of all the observations with number of observations.

Median

Median is the mid value of given data. In order to find the median of data, firstly we arrange data in ascending order and then we use the method of dividing (n + 1) with 2 where n is the number of observations.

Mode

Mode is the most frequent value occured in our observations. To find the mode of data, we can just manually see the data and can conclude which value has highest frequency in the case of individual and discreate series.

Mean, median and mode are called Measure of central tendency.

Answer 2

Answer:

Required value of x is 72.

Step-by-step explanation:

Given,mean of a group of data is 60.

Now question is what is mean?

Mean = $\frac{total \: sum \: of \: all \: data}{number \: of \: data}$

For example,

We are taking five numbers are 50,60,70,90,100.

So, mean of 50,60,70,90,100

$= \frac{50 + 60 + 70 + 90 + 100}{5} \\ = \frac{370}{5} \\ = 74$

Here given all data 85, 62, 36, 48, 72, X, 75 and 30.

So mean of 85, 62, 36, 48, 72, X, 75 and 30

$= \frac{85+62 +36 +48 + 72 + X + 75 + 30}{8} \\ = \frac{408 + x}{8}$

According to question,

$\frac{408 + x}{8} = 60$

By cross multiplication,

$408 + x = 60 \times 8 \\ 408 + x = 480 \\ x = 480 - 408 \\ x = 72$

So, required value of x is 72.

Mean related two more questions:

https://brainly.in/question/42931457

https://brainly.in/question/31558651

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