Let the observations be x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, and x_{6}.

It is given that mean is 8 and standard deviation is 4

\( Mean,\overline X=\dfrac{x_1+ x_2+x_3+ x_4+ x_5+x_6}{6}\)

If each observation is multiplied by 3 and the resulting observations are y_{i} , then

y_{i }= 3x_{i}

\( Mean,\overline y=\dfrac{y_1+ y_2+y_3+ y_4+ y_5+y_6}{6}\)

\( =\dfrac{3(x_1+ x_2+x_3+ x_4+ x_5+x_6)}{6}\)

= \( 3\times 8 =24\)

We know that,

Standard deviation,σ =

\( \sqrt{\dfrac{1}{n} \displaystyle\sum_{i=1}^{6} (X_i - \overline X})^2\)

By squaring both sides,

\( (4)^2={\dfrac{1}{6} \displaystyle\sum_{i=1}^{6} (X_i-\overline {X})^2}\)

\( \displaystyle\sum_{i=1}^{6} (X_i-\overline {X})^2=96\)

From (1) and (2), it can be observed that

\( \overline{y}=3\overline{x}\)

Substituting the values of x_{1} and \( \overline{x}\) in (2), we obtain

\( \displaystyle\sum_{i=1}^{6}(\dfrac{1}{3}y_i-\dfrac{1}{a}\overline{y})^2 =96\)

\(\displaystyle\sum_{i=1}^{6}(y_i-\overline{y})^2=864\)

Therefore, variance of new observations =

\( \dfrac{1}{6}\times 864\) = 144

Hence, the standard deviation of new observations is

\( \sqrt{144}=12\)

Answered by Pragya Singh | 11 months agoFind the mean deviation from the mean and from a median of the following distribution:

Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

No. of students | 5 | 8 | 15 | 16 | 6 |

The age distribution of 100 life-insurance policy holders is as follows

Age (on nearest birthday) | 17-19.5 | 20-25.5 | 26-35.5 | 36-40.5 | 41-50.5 | 51-55.5 | 56-60.5 | 61-70.5 |

No. of persons | 5 | 16 | 12 | 26 | 14 | 12 | 6 | 5 |

Compute mean deviation from mean of the following distribution:

Marks | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 |

No. of students | 8 | 10 | 15 | 25 | 20 | 18 | 9 | 5 |

Find the mean deviation from the mean for the following data:

Classes | 95-105 | 105-115 | 115-125 | 125-135 | 135-145 | 145-155 |

Frequencies | 9 | 13 | 16 | 26 | 30 | 12 |

Find the mean deviation from the mean for the following data:

Classes | 0-100 | 100-200 | 200-300 | 300-400 | 400-500 | 500-600 | 600-700 | 700-800 |

Frequencies | 4 | 8 | 9 | 10 | 7 | 5 | 4 | 3 |