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Statistics question

2015 · Shift 0 · Q24
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Statistics question

2015 · Shift 0 · Q24

JEE MainMathematicsStatisticsMCQ+4 / −1
The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :
  1. A
    15.8
  2. B
    14.0
  3. C
    16.8
  4. D
    16.0
View written solutionFree

Correct answer: B

  1. Find the original total sum

The data set has 161616 observations and mean 161616.

Using

Mean=Sum of observationsNumber of observations,\text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}},Mean=Number of observationsSum of observations​,

we get

Original sum=16×16=256.\text{Original sum} = 16 \times 16 = 256.Original sum=16×16=256.
  1. Delete one observation of value 161616

So the new sum becomes

256−16=240.256 - 16 = 240.256−16=240.

The number of observations becomes

16−1=15.16 - 1 = 15.16−1=15.
  1. Add three new observations: 3,4,53, 4, 53,4,5

Their sum is

3+4+5=12.3+4+5=12.3+4+5=12.

So the resultant sum becomes

240+12=252.240+12=252.240+12=252.

The new number of observations becomes

15+3=18.15+3=18.15+3=18.
  1. Compute the new mean
New mean=25218=14.\text{New mean} = \frac{252}{18} = 14.New mean=18252​=14.
  1. Match with the options

14.014.014.0 corresponds to Option B.

Final Answer

14.0\boxed{14.0}14.0​
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