Standard Deviation
Trending Questions
For what value of n, an+1+bn+1an+bn is the arithmetic mean of a and b?
Let be eighteen observations such that and , where are distinct real numbers.
If the standard deviation of these observations is , then the value of is
IQ of a person is given by the gormula IQ=MACA×100 where MA is mental age and CA is chronological age. If 80≤IQ≤140 for a group of 12 years old childern, find the range of their mental age.
For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectivley. The variance of the combined data set is
112
132
52
6
Let be a positive number such that the arithmetic mean of and exceeds their geometric mean by .Then, the value of is
- none of these
- 40
- 45
- 40+2125
If the arithmetic mean of two numbers be and the geometric mean be , then the numbers will be:
Complete the mean and standard deviation of the following observations of marks of 5 students of a tutorial group: Marks out of
None of these
- 3
- 1
- 4
- 2
Let S be the standard deviation of n observations. Each of the n observations is multiplied by a constant C. Then the standard deviation of the resulting number is
S
CS
S√C
none of these
The standard deviation of 17 numbers is zero. Then
the numbers are in geometric progression with common ratio not equal to one.
eight numbers are positive, eight are negative and one is zero.
either (a) or (b)
none of these
standard deviation is
- 4
Suppose a population A has 100 observations 101, 102, . . . . 200 and another population B has 100 observations 151, 152, . . . . 250. If VA and VB represent the variances of the two populations, respectively then VAVB is
94
49
23
1
If a, b, c are positive and in Harmonic progression, then ax + cx < 2bx, where x ∈ (0, 1)
True
False
A golfer recorded the following scores for each of four rounds of golf: .
The mean of the scores is .
What is the sum of the squared deviations of the scores from the mean?
- 0.25
- 0.50
- 1
- 2
- 4
The harmonic mean of 2 numbers is 4. Their arithmetic mean A and geometric mean G satisfy the relation 2A + G2 = 27. The sum of the numbers is
For two data sets, each of size , the variance is given to be and and the corresponding means are given to be and , respectively. The variance of the combined data set is
In a random sample of teenagers, the average number of texts handled in a day is . The confidence interval for the mean number of texts handled by teens daily is given as to
a) What is the standard deviation of the sample?
b) If the number of samples were doubled, by what factor would the confidence interval change? (keeping the same confidence level)
Let x1, x2, ⋯⋅xn be n observations, and let ¯x be their arithmetic mean and σ2 be their variance.
Statement 1: Variance of 2x1, 2x2, …, 2xn is 4σ2.
- Statement 1 is false, Statement 2 is true,
- Statement 1 is true, Statement 2 is false.
- Statement 1 is true, Statement 2 is true, Statament 2 is a correct explanation for Statement 1
- Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
- 14.98, 39.95
- 39.95, 14.98
- 39.95, 224.5
- None the these
- False
- True
Let x1, x2, ⋯, xn be n observations, and let ¯x be their arithmetic mean and σ2 be the variance.
Statement – 1: Variance of 2x1, 2x2, ⋯, 2xn is 4σ2
Statement – 2: Arithmetic mean 2x1, 2x2, ⋯, 2xn is 4¯x
Statement – 1 is true, statement – 2 is true; statement – 2 is a correct explanation for Statement – 1.
Statement – 1 is true, statement – 2 is true; statement – 2 is not a correct explanation for Statement – 1.
Statement – 1 is false, Statement – 2 is true
Statement – 1 is true, statement – 2 is false.
- 2√6
- 2√103
- 4√53
- √6
ValueFrequency412202−22−41
- 6
- 3
- 5
- \N
Let x1, x2, ⋯, xn be n observations, and let ¯x be their arithmetic mean and σ2 be the variance.
Statement – 1: Variance of 2x1, 2x2, ⋯, 2xn is 4σ2
Statement – 2: Arithmetic mean 2x1, 2x2, ⋯, 2xn is 4¯x
Statement – 1 is false, Statement – 2 is true
Statement – 1 is true, statement – 2 is true; statement – 2 is a correct explanation for Statement – 1.
Statement – 1 is true, statement – 2 is true; statement – 2 is not a correct explanation for Statement – 1.
Statement – 1 is true, statement – 2 is false.
- 6
- 7
- 8
- 9
If VA and VB represent the variances of the two populations, respectively, then VAVB is
- 1
- 49
- 94
- 13
- 98
- 2
- 78
- 1