Statistics and Dispersion

If the mean of 5 values is 21, then total sum = 21 × 5 = 105. Sum of four given values = 12 + 29 + 32 + 18 = 91. Fifth value = 105 - 91 = 14.

Mean = Sum of values / Count. Sum = 28 + 14 + 39 + 42 + 27 = 150. Count = 5. Mean = 150/5 = 30.

Yes, it is correct. The formula to find out error in the individual measurement values is - Δ a₁ = a _mean – a₁,          Δ a₂ = a _mean – a_2,          Δ a₃ = a _mean – a_3,       -------------------------      -------------------------      

For data 221, 118, 141, 389, 260, 480, 291, 460, 260, 227, 290, 302, 347, 260: Mean = 4046/14 = 289, Median = (275+275)/2 = 275, Mode = 260 (appears 3 times), Range = 480-118 = 362. Option C matches these calculations.

Range = Highest - Lowest = 35 - 15 = 20

The Quadratic Mean (QM) is calculated as the square root of the mean of squares, which is literally 'root-mean-square'. It's used in physics for RMS voltage and in statistics. Other means have different formulas: Harmonic Mean = n / sum(1/xi), Geometric Mean = (product of xi)^(1/n), Combined Mean is a weighted average of multiple datasets.

Let the average of the remaining 3 quantities be x.

Then, as per the question,

Average of 9 quantities is 21.

So, 21 = (6 * 22 + 3 * x)/9

189 = 132 + 3x

x = 57/3

x = 19

So, required average = 19

Average of 15 numbers = 26.2

Then, sum of all 15 numbers = 26.2 * 15

= 393 

Now, average of first 8 numbers = 27.875 

So, sum of first 8 numbers = 27.875 * 8

= 223

And average of last 8 numbers = 25.125 

Then, sum of last 8 numbers = 25.125 * 8

= 201 

So, 8^th number = 203 + 201 - 393

= 424 - 393

= 31

Let the first number be x.

Then, second number = x/16 and third number = x/4 

Now, average of 3 numbers = 28

(x + x/16 + x/4)/3 = 28

x = 64

So, the first number is 64.

Then, second number = 64/16 = 4

The average of x, y, z and w is a.

So, a = (x + y + z + w)/4    --------------(1)

Now, average of x, y and a = (x + y + a)/3

On putting the value of (x + y) from equation (1) 

= (4a - z - w + a)/3

= [5a - (z + w)]/3

Mean deviation is the average of difference of the values of items from some average of the series. Such a difference is technically described as deviation. In calculating mean deviation we ignore the minus sign of deviations while taking their total for obtaining the mean deviation.

It is correct answer.Sum of 15 results =(15*60) = 900Sum of First 8 results=(8*59) = 472Sum of Last 8 results= (8*63) = 504It is quite obvious that the 8th result is included twice.Therefore,value of the 8th result = Sum of 1^st eight results + Sum of last eight results - Sum of 15 results                                                            =  472 + 504 - 900 = 76

Median can be determined from Ogive.

The sum of the squares of the deviations will be the least when they are taken from their arithmetic mean.

Geometric mean alongwith arithmetic mean and harmonic mean is a mathematical average.