Statistics Questions

MathematicsStatistics25 Questions Found

MathematicsMeasures of DispersionJEE Advanced 1979Easy

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In calculating the mean and variance of 10 readings, a student wrongly used the figure 52 for the correct figure of 25. He obtained the mean and variance as 45.0 and 16.0 respectively. Determine the correct mean and variance.

Answer:Correct mean 42.3 ; Correct variance 43.81

MathematicsVariance and Standard DeviationJEE Advanced 1981Moderate

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The mean square deviations of a set of observations $x_{1}, x_{2}, \dots, x_{n}$ about a point $c$ is defined to be $\frac{1}{n} \sum_{i = 1}^{n} (x_{i} - c)^{2}$ . The mean square deviations about $- 1$ and $+ 1$ of a set of observations are 7 and 3 respectively. Find the standard deviation of this set of observations.

Answer:

3

MathematicsVariance and Standard DeviationJEE Advanced 1982Moderate

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The marks obtained by 40 students are grouped in a frequency table in class intervals of 10 marks each. The mean and the variance obtained from this distribution are found to be 40 and 49 respectively. It was later discovered that two observations belonging to the class interval (21-30) were included in the class interval (31-40) by mistake. Find the mean and the variance after correcting the error.

Answer:new mean = 39.5, new variance = 49.25

MathematicsMeasures of Central Tendency (Mean, Median, Mode)JEE Advanced 1982Moderate

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A variable takes value $x$ with frequency $^{n + x - 1} C_{x}$ , $x = 0, 1, 2, \dots, n$ . The mode of the variable is .........

Answer:

n

MathematicsVariance and Standard DeviationJEE Advanced 1980Easy

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The standard deviation of 17 numbers is zero. Then

(A)

the numbers are in geometric progression with common ratio not equal to one.

(B)

eight numbers are positive, eight are negative and one is zero.

(C)

either (a) or (b)

(D)

none of these

Answer:D

MathematicsMeasures of DispersionJEE Advanced 1980Easy

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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

(A)

s

(B)

cs

(C)

s c

(D)

none of these

Answer:B

MathematicsMeasures of DispersionJEE Advanced 1981Easy

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Consider any set of 201 observations $x_{1}, x_{2}, \dots, x_{200}, x_{201}$ . It is given that $x_{1} < x_{2} < \dots < x_{200} < x_{201}$ . Then the mean deviation of this set of observations about a point $k$ is minimum when $k$ equals

(A)

(x_{1} + x_{2} + \dots + x_{200} + x_{201}) /201

(B)

x_{1}

(C)

x_{101}

(D)

x_{201}

Answer:C

MathematicsMeasures of Central Tendency (Mean, Median, Mode)JEE Main 2002Easy

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In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls?

(A)

(B)

(C)

(D)

Answer:B

MathematicsMeasures of DispersionJEE Main 2003Easy

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In an experiment with 15 observations on x, the following results were available: $\sum x^{2} = 2830, \sum x = 170$ . One observation that was 20 was found to be wrong and was replaced by the correct value 30. The corrected variance is

(A)

8.33

(B)

78.00

(C)

188.66

(D)

177.33

Answer:B

MathematicsMeasures of Central Tendency (Mean, Median, Mode)JEE Main 2003Easy

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The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

(A)

remains the same as that of the original set

(B)

is increased by 2

(C)

is decreased by 2

(D)

is two times the original median.

Answer:A

In calculating the mean and variance of 10 readings, a student wrongly used the figure 52 for the correct figure of 25. He obtained the mean and variance as 45.0 and 16.0 respectively. Determine the correct mean and variance.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A variable takes value x with frequency n+x−1Cx​, x=0,1,2,…,n. The mode of the variable is .........

The standard deviation of 17 numbers is zero. Then

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls?

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

In calculating the mean and variance of 10 readings, a student wrongly used the figure 52 for the correct figure of 25. He obtained the mean and variance as 45.0 and 16.0 respectively. Determine the correct mean and variance.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A variable takes value x with frequency n+x−1Cx​, x=0,1,2,…,n. The mode of the variable is .........

The standard deviation of 17 numbers is zero. Then

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls?

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set

A variable takes value $x$ with frequency $^{n + x - 1} C_{x}$ , $x = 0, 1, 2, \dots, n$ . The mode of the variable is .........

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

A variable takes value $x$ with frequency $^{n + x - 1} C_{x}$ , $x = 0, 1, 2, \dots, n$ . The mode of the variable is .........

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