Let the remaining two observations be x and y.

The observations are 2, 4, 10, 12, 14, x, y.

\( Mean,\overline{X}=\dfrac{2+4+10+12+14+x+y}{7}\)

= 8

= 56 + 42 + x + y

= x + y =14 ….............(1)

Variance = \( \dfrac{1}{n} \displaystyle\sum_{i=1}^{n} f_i (x_i-\overline {x} )^2 \)

16 = \( \dfrac{1}{7}[(-6)^2 + (-4)^2+(2)^2+(4)^2+(6)^2+x^2\)

\(+y^2 -2\times 8(x+y)+2\times (8)^2]\)

By using equation (i) substiute 14 instead of (x+y)

16=\( \dfrac{1}{7}[36 + 16+4+(16)+36+x+y\)

\( -16(14)+2(64)]\)

16 = \( \dfrac{1}{7}[12+x^2+y^2]\)

= x^{2}+y^{2} = 112 - 12

= x^{2}+y^{2} = 100 ....................(2)

From (1), we obtain

x^{2}+y^{2} +2xy = 196 ....................(3)

From (2) and (3), we obtain

2xy = 196 – 100

2xy = 96 ............................(4)

Subtracting (4) from (2), we obtain

x^{2}+y^{2}-2xy = 100-96

= (x-y)^{2} = 4

= x-y = ± 2 ......................(5)

Therefore, from (1) and (5), we obtain

x = 8 and y = 6 when x – y = 2

x = 6 and y = 8 when x – y = – 2

Thus, the remaining observations are 6 and 8.

Answered by Pragya Singh | 1 year 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 |