The mean of 20 observations is 12 if each observation is increased by 5 then find the new mean

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The mean of 20 observations is 12 if each observation is increased by 5 then find the new mean

Solution:

(i) Increased by = 3

Observed mean = 32

If increased by 3, resulting mean = 32 + 3 = 35

(ii) Observed mean = 32

Decreased by = 7, resulting mean = 32 – 7 = 25

(iii) Observed mean = 32

Multiplied by = 2, resulting mean = 32\times2=64

(iv) Observed mean = 32

Divided by = 0.5, resulting mean = \frac{32}{0.5}=64

(v) Observed mean = 32

Increased by = 60%, resulting mean = 32+\left(\frac{60}{100}\right)

=\frac{3200+60}{100}=\frac{3260}{100}=32.6

(vi) Observed mean = 32

Decreased by = 20%, resulting mean = 32-\frac{20}{100}

=\frac{3200-20}{100}=\frac{3180}{100}=31.8

Video transcript

"Hello guys, hoping all of you doing. Well. This is the don't you tell me how jungus and today we will be taking up this Matt's question with says the mean of a certain number of observation is 32. Okay, so we have been given meaning of certain values certain observations. So which is 32. Okay. Now we have to find like find the resulting mean if each of Salvation is we have to find the as in the new mean. If every observation in these set of certain number of values as in observations each observation is increased by three then we have to find the new melamine and if it is decreased by 7, then again, we have to find the new mean and if the in like for the same set of observations, like if they all of them are Wide by 2 then what will be the new mean? And again if the same set of observation is divided by 0.5. What will be the new mean and similarly so on and so forth for increased by 60% and stick raised by 20% right? So now starting from like the first parts for subpart. So here we can see like what is the in like increased by 3 right the all the The patients are increased by 3. And what was our observed mean observe mean Wills 32 so if increased by three resulting mean see if all the observations are increased by certain value, then mean also will increase the mean will also get increased by that value. So if our result mean was all 32, then new mean will become 32 plus 3, but make sure Make sure each observation like each observation should have been increased. So here we can see this like this condition is being followed. That's why we are applying this 32 plus that value by which each term is being increased. Okay, so this will come out to be 35. Right? So our first answer is 35 now again, we have observed. Me to be 32 now. Like we are decreasing is each value by seven. Right? So like resulting mean will be in this case. If each value like it's each observation in a set of observation is decreased by a number that mean also gets decreased by that same number. So here it is decreased. It is being decreased by 7. So resulting mean will be decreasing. Even from our previous mean that is 32 minus 7, we will obtain 25, right? So the answer Part II subpart turns out to be 25. Okay now moving towards the third sub part. So now what we are doing is we are multiplying the each term by 2 in the set of observations. So observe mean again, we have already it is 32 So what we will do is if yeah x 2 not 3 it is multiplied by 2. Yeah, so if we are multiplying it by 2 that deserting mean again, like what happens is if each term in a set of observation is the X certain numbers, then you're mean also get increased by like that times that many times. Okay, so here again. Then the resulting mean will be 32 since it is the oyster Ms. Multiplying getting x 2 hence at mean also will get multiplied by 2. It will be 2 times the previous mean that is 32 into 264. Now coming on to the fourth subpart we have over here. We are like dividing the mean like observe mean is again 32. We are dividing it by 0.5. So What happens is if we? Divide each term by certain value then I mean also get decree like / that value. Okay. So like let us now we have resulting mean will be previous mean / the Value by which all the terms in the observation are being divided. So 32 by 5 will give you Again, if we see what head 32 by 1005 in the 552 the can by canceling the like common factors five in the 552 the 1032 2064. Hence our answer in this case with will be what 64, okay. All right. Now moving on to the next sub part. That is V 1 now here. What is happening is we are like increasing by some posit? Okay. So in the first one we are increasing by what 60% so what will be the resulting mean see if we are increasing each term by 60% then our resulting mean will also get will be resulting mean Be equal to the previous need like it being increased by 60% Okay, whatever like if we are increasing all the terms by 60% then the mean will also get increased by 60% Okay, so we are increasing by 50% hair previous mean was 32 and adding 60% since we're in like the new mean will be 60% more than The initial means so 32 plus 60 percent of 32. Okay, so this will be equal to 32 + 60 percent of 32. Six ten times a hundred ten 616 so we have 6 by 10 then if we further like follow it what could be a it would be The answer here will be I can see 32 6 R32 six eyes. Like we can calculate over here 1260 site-19, right? So we have here 32 plus 192 by 10, right or we can say equal to we have 32 Plus. 32 by 1 plus 1/9 19.2 safe 190 with 2 by 10 will give out to be 19.2 right? This will be a this will be equivalent to 30 to 40 to 50 51 Point. Okay? So this will be equal to your 51.2 okay. Great now moving on to the fourth part. Now we are if each value in this set of observation is decreased by 32 then like the resulting mean will also get decreased by 32 percent. Okay. So here what we are doing is we are decreasing each observation. It was first of all observed mean will be 32 and then let us first he could Efficient. Okay so head what we are doing is we are here to create like observe mean Wills 32 and here we are decreasing by what percent we are decreasing by 20% Okay, so there will be a decrease like of 20% in our resulting mean as well. So we have to Two minus 20% of 32 so we have over here. To 32 to 64 32 minus 64 by 10 which will be equal to. 32 minus 6.4 which will be equal to what now you can see we have 25.6. Great 32 minus 6 is what 26 and - point for 25.6. So yes, this is your answer now if still any doubt possess you can mention that in the comment section below and I would love to help you out. Thank you. Have a wonderful day ahead. "

The mean of 20 observations is 24, if 3 is added to each number find the new mean.

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