The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to .

Question

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

We have Variance =( displaystyle∑ r =115 x r 2/15)-(( displaystyle∑ r =115 x r /15))2 Now, as per information given in equation ( displaystyle∑ x r 2/15)-82=32 ⇒ displaystyle∑ x r 2= log 5 Now, the new displaystyle∑ x r 2= log 5-52+202=1470 And, new displaystyle∑ x r =(15 × 8)-5+(20)=135 ∴ Variance =(1470/15)-((135/15))2=98-81=17

Q. The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to ______.

We have Variance =15r=1∑15​xr2​​−⎝⎛​15r=1∑15​xr​​⎠⎞​2 Now, as per information given in equation 15∑xr2​​−82=32⇒∑xr2​=log5 Now, the new ∑xr2​=log5−52+202=1470 And, new ∑xr​=(15×8)−5+(20)=135 ∴ Variance =151470​−(15135​)2=98−81=17

Q. The mean and standard deviation of $15$ observations are found to be $8$ and $3$ respectively. On rechecking it was found that, in the observations, $20$ was misread as $5$ . Then, the correct variance is equal to ______.