Question

The sum of deviations measured from 4 is 72 of and the sum of deviations of the
same data set measured from 7 is -3. Find the number of observations and the mean
of the data set. ?

Answer 1

Answer:

Solution: Let 'n' be the number of observations whose mean = 40. ... Therefore, the number of items in the original data = 15. Example The sum of deviations of a certain numbers of observations measured from 4 is 72 and the sum of deviations of observations measured from 7 is -3.

Answer 2

Answer:

The number of observations are 25.

Mean of the data set is 6.88

Step-by-step explanation:

Given the sum of deviations measured from $4$ is $72$.

The sum of deviations of the same data set measured from $7$ is $-3$.

Remember the formula,

deviation = |data value-mean|.

Let n be the number of required observations.

Let $x_i$ be the data set.

Given, $\sum (x_i-4)=72$,

therefore, $\sum x_i-4n=72$.

Note $\sum 4=4n$ and $\sum(x_i-7)=-3$,

therefore, $\sum x_i-7n=-3$

Subtracting the two equations, we get

$\sum x_i-4n-(\sum x_i-7n)=72-(-3)$

$\sum x_i-4n-\sum x_i+7n=72+3$

$3n=75$

$n=25$

Therefore, the number of observations are $n=25$.

Putting $n=25$ in $\sum x_i-4n=72$, we get

$\sum x_i-4(25)=72$

$\sum x_i=72+100$

$\sum x_i=172$.

Now use the formula for mean,

Mean, $\bar x=\frac{\sum x_i}{n}$

$\bar x=\frac{172}{25}$

$\bar x=6.88$

So the mean of the data set is $6.88$