Question

mean of twenty observations is 15. if two observations 3and14 are replaced by 8and9, then the new mean will be....​

Answer 1

Answer:

• New mean will also be 15

Explanation:

Given that, mean of twenty observations is 15

therefore,

• mean = 15

• no. of observation = 20

• and, Let Sum of all observations be x

So,

using formula ;

• mean = sum of all observations / total number of observations

→ 15 = x / 20

→ x = 300

Now, as given that, 3 and 14 are replaced by 8 and 9

therefore,

→ New mean = [ x - ( 3 + 14 ) + ( 8 + 9 ) ] / 20

→ new mean = [ x - 17 + 17 ] / 20

→ new mean = [ 300 ] / 20

→ New mean = 15

therefore,

• New mean of twenty observations, when 3 and 14 are replaced by 8 and 9 will also be 15 .

Answer 2

$\huge{\mathcal{\underline{\green{SOLUTION}}}} </p><p></p><p>$

Mean of twenty observations is 15

So the sum = $20 \times 15 = 300$

Now two observations 3 & 14 are replaced by 8 & 9

So the new sum

$= 300 - (3 + 14) + (8 + 9) = 300$

Since the sum remains the same as before

Hence the required mean is same as before & it is = $\frac{300}{20} = 15$

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