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Answer Keys Senior & Junior Investigator Paper
Answer Keys Senior & Junior Investigator Paper
1.
Find the mode and median of the 9 consecutive number
12,7,8,14,21,23,27,7,11
(A)
12,9
(B)
7,9
(C)
7,12
(D)
11,9
Answer: “7,12”
2.
When the Mean of a number is 18, what is the Mean of the sampling
distribuƟon?
(A)
21
(B)
18
(C)
27
(D)
23
Answer: “18”
3.
If the probability of hiƫng an object is 0.8, find the variance
(A)
0.18
(B)
0.16
(C)
0.14
(D)
0.12
Answer: “0.16”
4.
Find the variance of the given data set: 3,9,5,6,7
(A)
1
(B)
2
(C)
3
(D)
4
Answer: “4”
5.
Find the mean, mode and median of the given sets of data: 5,8,12,17,12,14,6,8,
12, and 10
(A)
11,12,10
(B)
10,12,13
(C)
11,12,13
(D)
10,12,11
Answer: “10,12,11”
6.
Find the mean mode and median of the messages received on 7 consecuƟve
days 7,13,5,9,6,5,10
(A)
7,8,9
(B)
8,9,9
(C)
8,8,9
(D)
6,8,9
Answer: “8,9,9”
7.
Which of the following measures of central tendency is affected by extreme
values in the data set?
(A)
Mean
(B)
Median
(C)
Mode
(D)
Range
Answer: “Mean”
8.
The interquarƟle range (IQR) is a measure of:
(A)
Variability
(B)
Central tendency
(C)
Skewness
(D)
Spread of data
Answer: “Spread of data”
9.
Mode is the value of x where f(x) is a maximum if X is conƟnuous.
(A)
TRUE
(B)
FALSE
(C)
True and False
(D)
none
Answer: “TRUE”
10.
E (XY)=E (X)E (Y) if x and y are independent.
(A)
TRUE
(B)
FALSE
(C)
TRUE AND FALSE
(D)
none
Answer: “TRUE”
11.
The random variables X and Y have variances 0.2 and 0.5 respecƟvely.Let Z= 5X2Y. The variance of Z is?
(A)
3
(B)
4
(C)
5
(D)
7
Answer: “7”
12.
In a dice roll, what is the probability of geƫng an even number?
(A)
44958
(B)
44986
(C)
45078
(D)
44987
Answer: “45078”
13.
The number of students present in a classroom is an example of a:
(A)
ConƟnuous random variable
(B)
Discrete random variable
(C)
DeterminisƟc variable
(D)
Constant variable
Answer: “Discrete random variable”
14.
The probability distribuƟon funcƟon (PDF) gives the probability of a random
variable:
(A)
Taking on a specific value
(B)
Being greater than a specific value
(C)
Being less than or equal to a specific value
(D)
Falling within a specific range
Answer: “Taking on a specific value”
15.
The kurtosis of a random variable measures its:
(A)
Symmetry
(B)
Dispersion
(C)
Skewness
(D)
Shape of the distribuƟon
Answer: “Shape of the distribuƟon”
16.
Which of the following is true about a leptokurƟc distribuƟon?
(A)
It has a high peak and heavy tails
(B)
It has a low peak and light tails
(C)
It has a symmetric distribuƟon
(D)
It has a mean of zero
Answer: “It has a high peak and heavy tails”
17.
Which of the following is an example of compressed data:
(A)
Histogram
(B)
Ungrouped data
(C)
Frequency distribuƟon
(D)
TabulaƟon
Answer: “Frequency distribuƟon”
18.
Which of the following represents the number of Ɵmes an observaƟon occurs
in a data set?
(A)
Frequency
(B)
Mean
(C)
Median
(D)
Mode
Answer: “Frequency”
19.
A frequency distribuƟon is used to:
(A)
Represent data in a tabular form
(B)
Calculate the mean of a data set
(C)
Find the range of a data set
(D)
Determine the standard deviaƟon of a data set
Answer: “Represent data in a tabular form”
20.
In a cumulaƟve frequency distribuƟon, each entry represents:
(A)
The sum of the frequencies up to that class
(B)
The mean of the data in that class
(C)
The median of the data in that class
(D)
The mode of the data in that class
Answer: “The sum of the frequencies up to that class”
21.
The cumulaƟve frequency curve is obtained by ploƫng the cumulaƟve
frequencies against the:
(A)
Lower boundaries of the classes
(B)
Upper boundaries of the classes
(C)
Midpoints of the classes
(D)
RelaƟve frequencies of the classes
Answer: “Upper boundaries of the classes”
22.
The frequency curve is obtained by smoothing the:
(A)
Histogram
(B)
Frequency polygon
(C)
Bar diagram
(D)
Line diagram
Answer: “Frequency polygon”
23.
The cumulaƟve frequency curve is a graphical representaƟon of the:
(A)
CumulaƟve frequency distribuƟon
(B)
Frequency distribuƟon of ungrouped data
(C)
RelaƟve frequency distribuƟon of grouped data
(D)
Median of the data set
Answer: “CumulaƟve frequency distribuƟon”
24.
The point where the cumulaƟve frequency curve ends is equal to the:
(A)
Sum of all frequencies in the data set
(B)
Mean of the data set
(C)
Median of the data set
(D)
Mode of the data set
Answer: “Sum of all frequencies in the data set”
25.
Which of the following is not a disadvantage of using mean?
(A)
It is affected by extreme values
(B)
It cannot be computed in grouped data with open-ended class intervals
(C)
It does not possess the desired algebraic property
(D)
None of these
Answer: “It does not possess the desired algebraic property”
26.
The two methods of finding mode in a discrete series are .
(A)
Grouping method and ascending method
(B)
Table method and midpoint method
(C)
Grouping method and inspecƟng method
(D)
Grouping and not inspecƟng method
Answer: “Grouping method and inspecƟng method”
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27.
When the values in a series do not have equal importance, we calculate the
.
(A)
Mode
(B)
Weighted mean
(C)
ArithmeƟc mean
(D)
CalculaƟng arithmeƟc mode
Answer: “Weighted mean”
28.
Which one of the following statements best describes the mode measure?
(A)
It gives us the most common score in a data set, which will change if you
rearrange the scores in any order.
(B)
It gives us the most common score in a data set, which will not change if you
rearrange the scores in any order.
(C)
It is always greater than or equal to the mean of a data set.
(D)
None of these
Answer: “It is always greater than or equal to the mean of a data set”
29.
Which one of the following statements best describes the range measure?
(A)
It gives us the highest and lowest scores in a data set.
(B)
It gives us the lowest and highest scores in a data set.
(C)
It is always greater than or equal to the mean of a data set.
(D)
cant say
Answer: “It gives us the lowest and highest scores in a data set”
30.
The mean is calculated by:
(A)
Adding all the values and dividing by the number of values
(B)
Finding the middle value of the data set
(C)
CounƟng the number of Ɵmes each value occurs in the data set
(D)
SubtracƟng the smallest value from the largest value
Answer: “Adding all the values and dividing by the number of values”
31.
Which of the following measures is most affected by extreme values in a data
set?
(A)
Mean
(B)
Median
(C)
Mode
(D)
Range
Answer: “Mean”
32.
The mode is the value that:
(A)
Appears most frequently in the data set
(B)
Divides the data set into two equal halves
(C)
Represents the middle value in the data set
(D)
Is the difference between the largest and smallest values
Answer: “Appears most frequently in the data set”
33.
“Regression analysis was applied to return rates of sparrowhawk colonies.
Regression analysis was used to study the relaƟonship between return rate (x:
% of birds that return to the colony in a given year) and immigraƟon rate (y: %
of new adults that join the colony per year).
The following regression equaƟon was obtained.
! = 31.9 – 0.34x Based on the above esƟmated regression equaƟon, if the
return rate were to decrease by 10% the rate of immigraƟon to the colony
would:”
(A)
increase by 34%
(B)
increase by 3.4%
(C)
decrease by 0.34%
(D)
decrease by 3.4%
Answer: “increase by 3.4%”
34.
“In least squares regression, which of the following is not a required
assumpƟon about the error term ε?”
(A)
The expected value of the error term is one.
(B)
The variance of the error term is the same for all values of x.
(C)
The values of the error term are independent.
(D)
The error term is normally distributed
Answer: “The expected value of the error term is one”
35.
Larger values of r 2 (R2) imply that the observaƟons are more closely grouped
about the
(A)
average value of the independent variables
(B)
average value of the dependent variable
(C)
least squares line
(D)
origin
Answer: “least squares line”
36.
If the coefficient of determinaƟon is 0.81, the correlaƟon coefficient
(A)
is 0.6561
(B)
could be either + 0.9 or – 0.9
(C)
must be posiƟve
(D)
must be negaƟve
Answer: “could be either + 0.9 or – 0.9”
37.
“Regression analysis was applied between $ sales (y) and $ adverƟsing (x)
across all the branches of a major internaƟonal corporaƟon. The following
regression funcƟon was obtained
! = 5000 + 7.25x If the adverƟsing budgets of two branches of the corporaƟon
differ by $30,000, then what will be the predicted difference in their sales?”
(A)
$217,500
(B)
$222,500
(C)
$5000
(D)
$7.25
Answer: “$217,500”
38.
If the values of two variables move in the opposite direcƟon,
(A)
The correlaƟon is said to be linear
(B)
The correlaƟon is said to be non-linear
(C)
The correlaƟon is said to be posiƟve
(D)
The correlaƟon is said to be negaƟve
Answer: “The correlaƟon is said to be negaƟve”
39.
Which of the following statements is true about the arithmeƟc mean of two
regression coefficients?
(A)
It is less than the correlaƟon coefficient
(B)
It is equal to the correlaƟon coefficient
(C)
It is greater than or equal to the correlaƟon coefficient
(D)
It is greater than the correlaƟon coefficient
Answer: “It is greater than the correlaƟon coefficient”
40.
How many AR and MA terms should be included for the Ɵme series by looking
at the above ACF and PACF plots?
(A)
AR (1) MA(0)
(B)
AR(0)MA(1)
(C)
AR(2)MA(1)
(D)
AR(1)MA(2)
Answer: “AR(0)MA(1)”
41.
Consider the following AR(1) model with the disturbances having zero mean
and unit variance. yt = 0.4 + 0.2yt-1 + ut. The (uncondiƟonal) variance of y will
be given by ?
(A)
1.5
(B)
1.04
(C)
0.5
(D)
2
Answer: “1.04”
42.
Second differencing in Ɵme series can help to eliminate which trend?
(A)
QuadraƟc Trend
(B)
Linear Trend
(C)
All
(D)
None
Answer: “QuadraƟc Trend”
43.
BIC penalizes complex models more strongly than the AI
(A)
TRUE
(B)
FALSE
(C)
Maybe
(D)
None
Answer: “TRUE”
44.
In a Time-series forecasting problem, if the seasonal indices for quarters 1, 2,
and 3 are 0.80, 0.90, and 0.95 respectively. What can you say about the
seasonal index of quarter 4?
(A)
It will be less than 1
(B)
It will be greater than 1
(C)
It will be equal to 1
(D)
Seasonality does not exist
Answer: “It will be greater than 1”
45.
A is a sequence of observaƟons over a certain perio(D)
(A)
Theano
(B)
Scikit
(C)
Time series
(D)
Tensor
Answer: “Time series”
46.
A Time series has _ components. (A) 1 (B) 2 (C) 3 (D) 4 Answer: “4”
47. Which of the following is the square root of the mean square error?
(A) AMSQ
(B) RMSE
(C) AMSE
(D) RMES
Answer: “RMSE”
48. Mean Absolute Error is the average of absolute difference between?
(A) normal values and true values
(B) predicted values and imaginary values
(C) predicted values and true values
(D) imaginary values and true values
Answer: “predicted values and true values”
49. Noise is the error in the observaƟons added due to environmental factors.
(A) Yes (B) No
(C) Can be yes or no
(D) Cannot say Answer: “Yes”
50. Company A produces 10% defecƟve products, Company B produces 20% defecƟve products, and Company C produces 5% defecƟve products. If choosing a company is an equally likely event, then find the probability that the product chosen is defecƟve.
(A) 0.11
(B) 0.21
(C) 0.22
(D) 0.12
