Question 1

Any measure indicating the centre of a set of data, arranged in an increasing or decreasing order of magnitude, is called a measure of
A)Skewness
B)Symmetry
C)Central tendency
D)Dispersion

Accepted Answer

Measures of central tendency (mean, median, mode) describe the center point of a data set, indicating where the middle value lies, which is what the question describes.

Question 2

Scores that differ greatly from the measures of central tendency are called:
A)Raw scores
B)The best scores
C)Extreme scores
D)Z-scores

Accepted Answer

Extreme scores, or outliers, are those that differ significantly from the measures of central tendency (mean, median, mode) in a data set. They can affect the overall analysis and interpretation of the data.

Question 3

The measure of central tendency listed below is:
A)The raw score
B)The mean
C)The range
D)Standard deviation

Accepted Answer

The mean is a measure of central tendency, which is a single value that attempts to describe a set of data by identifying the central position within that set of data. Other measures of central tendency include the median and mode. The range and standard deviation are measures of variability, not central tendency.

Question 4

While computing the arithmetic mean of a frequency distribution, the each value of a class is considered equal to:
A)Class mark
B)Lower limit
C)Upper limit
D)Lower class boundary

Accepted Answer

The answer of While computing the arithmetic mean of a...

Question 5

The sum of the squares fo the deviations about mean is:
A)Zero
B)Maximum
C)Minimum
D)All of the above

Accepted Answer

The sum of the squares of the deviations about the mean is minimized, which is a fundamental property of the mean in statistics. This is why the mean is often used as a measure of central tendency, as it minimizes the total squared deviation from the mean compared to any other point.

Question 6

For a certain distribution, if ?(X -20) = 25, ?(X- 25) =0, and ?(X-35) = -25, then is equal to:
A)20
B)25
C)-25
D)35

Accepted Answer

The notation ?(X - a) = b suggests a function that outputs the difference between the mean of the distribution, X, and a specific value, a, as b. Given ?(X- 25) =0, it implies that the mean of the distribution, X, is 25.

Question 7

The sum of the squares of the deviations of the values of a variable is least when the deviations are measured from
A)Harmonic mean
B)Geometric mean
C)Median
D)Arithmetic mean

Accepted Answer

The sum of the squares of the deviations of the values of a variable is least when the deviations are measured from the Arithmetic mean. This is a fundamental principle in statistics, particularly in the method of least squares.

Question 8

If X1, X2, X3, ... Xn, be n observations having arithmetic mean and if Y =4X ± 2, then is equal to:
A)4X
B)4
C)4 ± 2
D)4 ± 2.

Accepted Answer

The answer of If X1, X2, X3, ... Xn, be...

Question 9

If =100 and Y=2X - 200, then mean of Y values will be:
A)0
B)2
C)100
D)200

Accepted Answer

The mean of Y values is calculated by substituting the value of X into the equation Y = 2X - 200. Given X = 100, Y = 2(100) - 200 = 200 - 200 = 0. Therefore, the mean of Y values is 0.

Question 10

If the arithmetic mean of 20 values is 10, then sum of these 20 values is:
A)10
B)20
C)200
D)20 + 10

Accepted Answer

The arithmetic mean is calculated as the sum of all values divided by the number of values. If the mean of 20 values is 10, then the sum of these values is 20 * 10 = 200.

Question 11

Ten families have an average of 2 boys. How many boys do they have together?
A)2
B)10
C)12
D)20

Accepted Answer

The average number of boys per family is 2. With 10 families, the total number of boys is 10 families * 2 boys/family = 20 boys.

Question 12

If the arithmetic mean of the two numbers X1 and X2 is 5 if X1=3, then X2 is:
A)3
B)5
C)7
D)10

Accepted Answer

The arithmetic mean of two numbers X1 and X2 is given by (X1 + X2) / 2. If the mean is 5 and X1 is 3, then (3 + X2) / 2 = 5. Solving for X2 gives X2 = 10 - 3 = 7.

Question 13

We must arrange the data before calculating:
A)Mean
B)Median
C)Mode
D)Geometric mean

Accepted Answer

To calculate the median, the data must be arranged in order either from smallest to largest or from largest to smallest. This is because the median is the middle value of a data set, which can only be accurately identified once the data is organized. Mean, mode, and geometric mean do not require the data to be arranged in order.

Question 14

The lower and upper quartiles of a symmetrical distribution are 40 and 60 respectively. The value of median is:
A)40
B)50
C)60
D)(60 - 40) / 2

Accepted Answer

In a symmetrical distribution, the median is exactly in the middle of the lower and upper quartiles. Since the lower quartile is 40 and the upper quartile is 60, the median is (40 + 60) / 2 = 50.

Question 15

If in a discrete series 75% values are greater than 50, then:
A)Q1 = 50
B)Q1 < 50
C)Q1 > 50
D)Q1 ? 50

Accepted Answer

Q1 is the first quartile, which means that 25% of the values are less than Q1. Since 75% of the values are greater than 50, this means that Q1 must be less than 50.

Question 16

Suitable average for averaging the shoe sizes for children is
A)Mean
B)Mode
C)Median
D)Geometric mean

Accepted Answer

The mode is suitable for averaging shoe sizes for children as it represents the most frequently occurring shoe size, which is useful when dealing with categorical data like shoe sizes.

Question 17

A measurement that corresponds to largest frequency in a set of data is called:
A)Mean
B)Median
C)Mode
D)Percentile

Accepted Answer

The mode is the value that appears most frequently in a data set, making it the measurement that corresponds to the largest frequency.

Question 18

Which of the following average cannot be calculated for the observations 2, 2, 4, 4, 6, 6, 8, 8, 10, 10 ?
A)Mean
B)Median
C)Mode
D)All of the above

Accepted Answer

The mode is the value that appears most frequently in a data set. In this case, all numbers appear exactly twice, so there is no single number that appears more frequently than others. This means the mode cannot be uniquely determined from the given observations, whereas the mean and median can be calculated without issue.

Question 19

What have been constructed from OR problems and methods for solving the models that are available in many cases?
A)Scientific models
B)Algorithms
C)Mathematical models
D)None of these

Accepted Answer

Mathematical models have been constructed from Operations Research (OR) problems, and various methods for solving these models are widely available. These models use mathematical expressions to represent complex real-world problems in a structured and solvable manner.

Question 20

Which of the following is not the phase of OR methodology?
A)Formulating a proble
B)Constructing a model
C)Establishing controls
D)Controlling the environment

Accepted Answer

Controlling the environment is not considered a phase of Operations Research (OR) methodology. OR typically involves formulating a problem, constructing a mathematical model to represent the problem, deriving solutions from the model, and then testing and implementing these solutions. Establishing controls may be part of the process, particularly in the implementation phase, but "controlling the environment" is not standard terminology used to describe a phase of OR methodology.

Quiz 1: Measures of Central Tendency and Operations Research

Any measure indicating the centre of a set of data, arranged in an increasing or decreasing order of magnitude, is called a measure of

Scores that differ greatly from the measures of central tendency are called:

The measure of central tendency listed below is:

While computing the arithmetic mean of a frequency distribution, the each value of a class is considered equal to:

The sum of the squares fo the deviations about mean is:

For a certain distribution, if ?(X -20) = 25, ?(X- 25) =0, and ?(X-35) = -25, then is equal to:

The sum of the squares of the deviations of the values of a variable is least when the deviations are measured from

If X1, X2, X3, ... Xn, be n observations having arithmetic mean and if Y =4X ± 2, then is equal to:

If =100 and Y=2X - 200, then mean of Y values will be:

If the arithmetic mean of 20 values is 10, then sum of these 20 values is:

Ten families have an average of 2 boys. How many boys do they have together?

If the arithmetic mean of the two numbers X1 and X2 is 5 if X1=3, then X2 is:

We must arrange the data before calculating:

The lower and upper quartiles of a symmetrical distribution are 40 and 60 respectively. The value of median is:

If in a discrete series 75% values are greater than 50, then:

Suitable average for averaging the shoe sizes for children is

A measurement that corresponds to largest frequency in a set of data is called:

Which of the following average cannot be calculated for the observations 2, 2, 4, 4, 6, 6, 8, 8, 10, 10 ?

What have been constructed from OR problems and methods for solving the models that are available in many cases?

Which of the following is not the phase of OR methodology?