List of top Quantitative Aptitude Questions on Statistics asked in NPAT

If the median of a set consisting of \( n \) consecutive odd positive integers is an even integer, the sum of the mean and the range of the set is an odd integer.
Two sets of numbers having medians \( p \) and \( q \) respectively are combined to form a new set. If \( p>q \), then the median \( m \) of the new set satisfies \( q<m<p \).
Given: \( a \) and \( b \) are positive integers and \( a>b \). The median of a set consisting of 5 terms: \( a^2, ab, b^2, (a - b)^2 \) and \( (a + b)^2 \) is \( ab \).
If the standard deviation of \( x_1, x_2, x_3, \dots, x_n \) is \( k \), then what will be the standard deviation of \( \frac{10x_1 - 7}{2} \), \( \frac{10x_2 - 7}{2} \), ......., \( \frac{10x_n - 7}{2} \)?
What is the variance of the following data? \( 9, 10, 13, 14, 6, 11, 8, 7, 4, 18 \)
Let \( x \) be the median of the data: 13, 17, 52, 56, 65, 35, 77, 39, 15, 37. If 35 is replaced by 53 in the data, then the median of the new data will be \( y \). What is the difference between \( x \) and \( y \)?
The mean deviation (correct to one decimal place) of the numbers 3, 10, 6, 11, 14, 17, 9, 8, 12 about the mean is:
If the mean of the following distribution is 22, then what will be the value of x?
ClassFrequency
0 – 1012
10 – 2016
20 – 306
30 – 40x
40 – 509
The marks obtained by seven students in a test are: 36, 46, 70, 60, 20, 18, 30. What is the mean deviation of the data from the mean?
The variance of the ten integers 11, 12, 13,........ 20 is:
The scores of a batsman in 10 different test matches were 42, 38, 48, 70, 46, 63, 55, 34, 54, and 44. What is the mean deviation about the median of these scores?
The mean of the following distribution is 25. \[ \begin{array}{|c|c|} \hline \text{Class} & \text{Frequency} \\ \hline 0-10 & 14 \\ 10-20 & p \\ 20-30 & 27 \\ 30-40 & 21 \\ 40-50 & 15 \\ \hline \end{array} \]
What is the median of the following distribution? \[ \begin{array}{|c|c|} \hline x_i & f_i \\ \hline 8 & 4 \\ 9 & 6 \\ 10 & 2 \\ 11 & 3 \\ 12 & 7 \\ 13 & 6 \\ 14 & 4 \\ \hline \end{array} \]
In a class of 100 students, 55 students passed in Mathematics and 65 passed in English. Five students failed in both subjects. Let \( n \) be the number of students who passed in exactly one of the two subjects and \( m \) be the number of students who failed in at least one subject, then what is the value of \( (m - n) \)?
When 3 is subtracted from each of the given 'n' numbers, then the sum of the numbers so obtained is 84. When 8 is added to each of the given 'n' numbers, then the sum of the resulting numbers is 216. The mean of the given 'n' numbers is:

The mean of five observations is 4.4 and their variance is 8.24. If three of the five observations are 1, 4 and 9, then the product of other two observations is:
The heights (in cm) of 8 students are recorded as 162, 163, 160, 164, 160, 170, 161, 164. The standard deviation of the data is closest to:

What is the median of the following distribution? \[ \begin{array}{|c|c|} \hline x_i & f_i \\ \hline 8 & 4 \\ 9 & 6 \\ 10 & 2 \\ 11 & 3 \\ 12 & 7 \\ 13 & 6 \\ 14 & 4 \\ \hline \end{array} \] 

Calculate the variance of: 2, 4, 5, 6, 8, 17.

Let \( x \) be the median of the data: \[ \{20, 50, 60, 53, 77, 88, 90, 40, 30, 70, 25, 45, 64, 72, 8, 15, 85, 60, 55, 28\} \] If \( y \) is the median of the same dataset when 25 and 28 are replaced by 52 and 82 respectively, then what is the value of \( |x - y| \)?
The mean of the following distribution is 25. \[ \begin{array}{|c|c|} \hline \text{Class} & \text{Frequency} \\ \hline 0-10 & 14 \\ 10-20 & p \\ 20-30 & 27 \\ 30-40 & 21 \\ 40-50 & 15 \\ \hline \end{array} \]
The heights (in cm) of 8 students are recorded as 162, 163, 160, 164, 160, 170, 161, 164. The standard deviation of the data is closest to:
Let \( x \) be the median of the data: 23, 17, 19, 11, 7, 3, 13, 2, 5, 29. Let \( y \) be the median of the same data set obtained by replacing 2 by 21 and 13 by 31. What is the value of \( |x - y| \)?

What is the standard deviation of the given data set: 25, 50, 45, 30, 70, 42, 36, 48, 34, 60 (correct to two decimal places).
Consider the following distribution:
mean of the distribution is 8.84 years. 
The mean of the distribution is 8.84 years. The value of x is: