Standard Deviation about mean
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Let be ten observations of a random variable . If where , then the standard deviation of these observations is
The standard deviation of 4 consecutive numbers which are in A.P is √5. The common difference (d) of this A.P is
±√5
±2√5
±2
±√2
A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 gm and a standard deviaiton of 2 gm. Later, it was found that the measuring scale was misaligned and always under-reported every fish weight by 2gm. The correct mean and standard deviation (in gm) of fishes are respectively:
32, 2
32, 4
28, 2
28, 4
The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?
a=0, b=7
a=5, b=2
a=1, b=6
a=3, b=4
Standard deviation for x1, x2, .....xn about mean can be expressed as √1n∑ni=1(xi−¯x)2.
True
False
For a frequency distribution consisting of 18 observations, the mean and the standard deviation were found to be 7 and 4 respectively. But on comparison with the original data, it was found that a figure 12 was miscopied as 21 in calculations. Find the correct mean and standard deviation.
- 2
- 6
- 8
- 16
In a series of 2n observations, half of them equal a and remaining half equal −a. If the standard deviation of the observations is 2, then |a| equals.
√2n
√2
2
1n
Which of the following are true statements.
Variance gives a better picture of dispersion or scatter compared to mean deviation
For given n observation x1, x2, ... xn, with mean variance will be ∑ni=1 (xi−¯x)2
Variance can be zero even if all observations are not equal.
Variance can be a negative quantity if all the observations are negative
The standard deviation of the first n natural numbers is
√n(n+1)2
√n2−112
none of these
n+12
The standard deviation of a variate x is σ. Then the standard deviation of the variate ax+bc where a, b, c are constants, is
(ac)σ
∣∣ac∣∣σ
(a2c2)σ
none of these