List of top Quantitative Aptitude Questions on Statistics

The average age of 100 teachers in a college in 2000 was 50 years. In 2002, 20 teachers superannuated from their jobs, whose average age was 60 years. In 2005, 40 new teachers joined the college whose average age was 38 years. What was the average age of all the teachers in 2008?
The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
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 \( ab \).
The mean of \(50\) observations is \(28\). Later it was found that the value \(70\) had been recorded as \(7\) and the value \(24\) had been recorded as \(42\). Find the correct average.
The mean of \(50\) observations was \(36\). It was found later that an observation \(48\) was wrongly taken as \(23\). The corrected new mean is?
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 \( y \)?

A cube is painted Blue on all faces and is then cut into 125 cubes of equal size. How many cubes are not painted on any face?

If Q means 'add to', J means 'multiplied by', T means 'subtract from' and K means 'divide by', then 30 K 2 Q 3 J 6 T 5 = ?

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

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