Statistics · NDA previous year questions

What is the geometric mean of the data 2, 4, 8, 16, 32?

1. A.2
2. B.4
3. C.8
4. D.16

What is the cumulative frequency curve of statistical data commonly called?

1. A.Cartogram
2. B.Histogram
3. C.Ogive
4. D.Pictogram

If the values of a set are measured in cm, what will be the unit of variance?

1. A.cm
2. B.$\mathrm{c}{\mathrm{m}}^2$
3. C.$\mathrm{c}{\mathrm{m}}^3$
4. D.No unit

$$\begin{array}{lcccc}\text{Class Interval}& 1\text{-}5& 6\text{-}10& 11\text{-}15& 16\text{-}20\\ \text{Frequency}& 3& 7& 6& 5\end{array}$$ Consider the following statements in respect of the above frequency distribution : 1. The median is contained in the modal class. 2. The distribution is bell-shaped. Which of the above statements is/are correct?

1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2

For the next two (2) items that follow : The following table gives the continuous frequency distribution of a continuous variable $X$ : $$\begin{array}{lccccc}\text{Class Interval}& 0\text{-}10& 10\text{-}20& 20\text{-}30& 30\text{-}40& 40\text{-}50\\ \text{Frequency}& 5& 10& 20& 5& 10\end{array}$$ What is the median of the above frequency distribution?

1. A.23
2. B.24
3. C.25
4. D.26

For the next two (2) items that follow : The following table gives the continuous frequency distribution of a continuous variable $X$ : $$\begin{array}{lccccc}\text{Class Interval}& 0\text{-}10& 10\text{-}20& 20\text{-}30& 30\text{-}40& 40\text{-}50\\ \text{Frequency}& 5& 10& 20& 5& 10\end{array}$$ What is the mean of the above frequency distribution?

1. A.25
2. B.26
3. C.27
4. D.28

The arithmetic mean of two numbers exceeds their geometric mean by 2 and the geometric mean exceeds their harmonic mean by 1.6. What are the two numbers?

1. A.16, 4
2. B.81, 9
3. C.256, 16
4. D.625, 25

What is the conjugate of ${\left(\frac{1+2i}{2+i}\right)}^2$?

1. A.$\frac{7}{25}+i\frac{24}{25}$
2. B.$-\frac{7}{25}-i\frac{24}{25}$
3. C.$-\frac{7}{25}+i\frac{24}{25}$
4. D.$\frac{7}{25}-i\frac{24}{25}$

If the equations $x^2+kx+64=0$ and $x^2-8x+k=0$ have real roots, then what is the value of $k$?

1. A.4
2. B.8
3. C.12
4. D.16

What is ${\left(\frac{\sqrt{3}+i}{\sqrt{3}-i}\right)}^6$ equal to?

1. A.-1
2. B.0
3. C.1
4. D.2

If $A=\left[\begin{array}{cc}0& 1\\ -1& 0\end{array}\right]$, $B=\left[\begin{array}{cc}i& 0\\ 0& -i\end{array}\right]$, $C=\left[\begin{array}{cc}0& -i\\ -i& 0\end{array}\right]$, then which one of the following is not correct?

1. A.$A^2=B^2$
2. B.$B^2=C^2$
3. C.$AB=C$
4. D.$AB=BA$

If ${\log }_3[{\log }_3[{\log }_{3}x]]={\log }_{3}3$, then what is the value of $x$?

1. A.3
2. B.27
3. C.$3^9$
4. D.$3^{27}$

What is the mean deviation of the data $2,9,9,3,6,9,4$ ?

1. A.$2.23$
2. B.$2.57$
3. C.$3.23$
4. D.$3.57$

A set of $n$ values $x_1,x_2,\dots ,x_n$ has standard deviation $\sigma$. What is the standard deviation of $n$ values $x_1+k,x_2+k,\dots ,x_n+k$ ?

1. A.$\sigma$
2. B.$\sigma +k$
3. C.$\sigma -k$
4. D.$k\sigma$

The two lines of regression are $8x-10y=66$ and $40x-18y=214$, and variance of $x$ series is $9$. What is the standard deviation of $y$ series?

1. A.$3$
2. B.$4$
3. C.$6$
4. D.$8$

The standard deviation of some consecutive integers is found to be $2$. Which of the following statements best describes the nature of the consecutive integers?

1. A.The integers are any set of eight consecutive integers
2. B.The integers are any set of eight consecutive positive integers
3. C.The integers are any set of seven consecutive integers
4. D.None of the above

Consider the following data : $$\begin{array}{lll}& \text{Factory-A}& \text{Factory-B}\\ \text{Mean wage of workers}& \text{Rs }540& \text{Rs }620\\ \text{Standard deviation of wages}& \text{Rs }40.50& \text{Rs }31\end{array}$$ What is the variability in the wages of the workers in Factory-A ?

1. A.$100\%$ more than the variability in the wages of the workers in Factory-B
2. B.$50\%$ more than the variability in the wages of the workers in Factory-B
3. C.$50\%$ less than the variability in the wages of the workers in Factory-B
4. D.$150\%$ more than the variability in the wages of the workers in Factory-B

The distributions $X$ and $Y$ with total number of observations $36$ and $64$, and mean $4$ and $3$ respectively are combined. What is the mean of the resulting distribution $X+Y$ ?

1. A.$3.26$
2. B.$3.32$
3. C.$3.36$
4. D.$3.42$

Consider the following data : $$\begin{array}{cccccc}x& 5& 7& 8& 4& 6\\ y& 2& 4& 3& 2& 4\end{array}$$ What is the regression equation of $y$ on $x$?

1. A.$y=0.6+0.4x$
2. B.$y=0.7+0.3x$
3. C.$y=6+5x$
4. D.$y=4+9x$

What is the value of ${\lim }_{x\to 0}\frac{\cos (ax)-\cos (bx)}{x^2}$ ?

1. A.$a-b$
2. B.$a+b$
3. C.$\frac{b^2-a^2}{2}$
4. D.$\frac{b^2+a^2}{2}$

The frequency distribution of life of $90$ TV tubes whose median life is $17$ months is as follows : $$\begin{array}{ll}\text{Life of TV tubes (in months)}& \text{No. of TV tubes}\\ 0\text{-}5& 3\\ 5\text{-}10& 12\\ 10\text{-}15& x\\ 15\text{-}20& 35\\ 20\text{-}25& y\\ 25\text{-}30& 4\end{array}$$ What is the lower limit of the median class?

1. A.$10$
2. B.$15$
3. C.$20$
4. D.$25$

The frequency distribution of life of $90$ TV tubes whose median life is $17$ months is as follows : $$\begin{array}{ll}\text{Life of TV tubes (in months)}& \text{No. of TV tubes}\\ 0\text{-}5& 3\\ 5\text{-}10& 12\\ 10\text{-}15& x\\ 15\text{-}20& 35\\ 20\text{-}25& y\\ 25\text{-}30& 4\end{array}$$ What is the missing frequency $y$?

1. A.$20$
2. B.$16$
3. C.$15$
4. D.$12$

The frequency distribution of life of $90$ TV tubes whose median life is $17$ months is as follows : $$\begin{array}{ll}\text{Life of TV tubes (in months)}& \text{No. of TV tubes}\\ 0\text{-}5& 3\\ 5\text{-}10& 12\\ 10\text{-}15& x\\ 15\text{-}20& 35\\ 20\text{-}25& y\\ 25\text{-}30& 4\end{array}$$ What is the cumulative frequency of the modal class?

1. A.$31$
2. B.$35$
3. C.$66$
4. D.Cannot be determined as the given data is insufficient

Directions: For the next 3 (three) questions to follow: The table below gives an incomplete frequency distribution with two missing frequencies $f_1$ and $f_2$. $$\begin{array}{ll}\text{Value of X}& \text{Frequency}\\ 0& f_1\\ 1& f_2\\ 2& 4\\ 3& 4\\ 4& 3\end{array}$$ The total frequency is 18 and the arithmetic mean of X is 2. What is the value of $f_2$?

1. A.4
2. B.3
3. C.2
4. D.1

Directions: For the next 3 (three) questions to follow: The table below gives an incomplete frequency distribution with two missing frequencies $f_1$ and $f_2$. $$\begin{array}{ll}\text{Value of X}& \text{Frequency}\\ 0& f_1\\ 1& f_2\\ 2& 4\\ 3& 4\\ 4& 3\end{array}$$ The total frequency is 18 and the arithmetic mean of X is 2. What is the standard deviation?

1. A.$\frac{\sqrt{5}}{2}$
2. B.$\frac{\sqrt{5}}{3}$
3. C.$\frac{4}{3}$
4. D.$\frac{16}{9}$