Mathematics · Quantitative Aptitude
Statistics and Dispersion
515 Questions
Statistics and dispersion involve the calculation of mean, standard deviation, variance, and coefficient of variation for data sets. These questions also cover probability distributions and cumulative frequency analysis. Such quantitative aptitude topics are heavily featured in banking and SSC examinations.
Standard deviationNormal distributionMean calculationCumulative frequencyCoefficient of variation
Statistics and Dispersion Questions
-
(1) 1% slower than,38% slower
-
(2) 10% slower than,4% slower
-
(3) 1% faster than,38% faster
-
(4) 10% faster than,4% faster
A
Correct answer
Explanation
According to IBM COBOL performance benchmarks, compiling with ARITH(EXTEND) is on average 1% slower than compiling with ARITH(COMPAT), with a maximum range of up to 38% slower in extreme cases.
C
Correct answer
Explanation
Total is not a standard SQL aggregate function. The correct function for summing values is SUM, not Total. COUNT, AVG, and MAX are all valid SQL aggregate functions used to perform calculations across multiple rows.
B
Correct answer
Explanation
AVG and SUM functions only work on numeric data types. They cannot be applied to text, date, or other non-numeric data types. Attempting to use them on strings or dates will result in an error.
C
Correct answer
Explanation
In Oracle SQL, the standard group (aggregate) functions are COUNT, AVG, MAX, MIN, SUM, STDDEV, VARIANCE, etc. 'Total' is NOT a valid Oracle group function, making it the correct answer to 'which is NOT a group function'. While some other databases might have a TOTAL function, Oracle does not.
C
Correct answer
Explanation
Standard SQL aggregate functions include COUNT, AVG, MAX, MIN, and SUM. TOTAL is not a valid SQL aggregate function. To sum values, use the SUM function instead.
B
Correct answer
Explanation
AVG and SUM aggregate functions ignore NULL values and return NULL if all values in the group are NULL. They don't work on 'any' numeric data because they skip NULL values entirely in their calculations.
C
Correct answer
Explanation
Standard SQL group/aggregate functions include COUNT, AVG, MAX, MIN, SUM, STDDEV, and VARIANCE. TOTAL is not a standard SQL aggregate function - the standard uses SUM for totaling values. While some databases might implement TOTAL, it's not part of core SQL group functions.
B
Correct answer
Explanation
AVG and SUM are defined only for numeric data types; they cannot operate on character or date fields. Attempting to use them on non‑numeric columns yields errors, so the statement that they work on any numeric data is false, confirming the stored answer.
A,B,D
Correct answer
Explanation
Aggregate functions perform calculations on multiple values and return a single result. SUM and AVG are standard SQL aggregate functions. Median is also an aggregate function (though not available in all SQL dialects). Trim is a string manipulation function that operates on individual values, not sets.
C
Correct answer
Explanation
Process capability (Cp) is defined as the specification width divided by 6 times the process standard deviation. This formula shows how many 6-sigma intervals fit within specification limits. A capable process typically has Cp at least 1.0, meaning 6 sigma fits within specifications. The 6 sigma relationship is fundamental to process capability analysis.
-
avg( )
-
sqrt( )
-
sum()
-
max()
-
PROC MEANS DATA= ORGANIZATION MEDIAN MEAN CLM MAXDEC=0; Label TOTREV = 'Total Billed Revenue' TOTKWH = 'Total KwH Consumption'; VAR TOTREV TOTKWH; run;
-
PROC MEANS DATA= ORGANIZATION MEDIAN MEAN UCLM ; Label TOTREV = 'Total Billed Revenue' TOTKWH = 'Total KwH Consumption'; VAR TOTREV TOTKWH; run;
-
PROC MEANS DATA= ORGANIZATION MEDIAN MEAN LCLM Label TOTREV = 'Total Billed Revenue' TOTKWH = 'Total KwH Consumption'; VAR TOTREV TOTKWH; run;
-
PROC MEANS DATA= ORGANIZATION MEDIAN SUM CLM MAXDEC=0; Label TOTREV = 'Total Billed Revenue' TOTKWH = 'Total KwH Consumption'; VAR TOTREV TOTKWH; run;
A
Correct answer
Explanation
CLM (confidence limits for the mean) generates confidence intervals around the mean. Option A correctly specifies CLM with MEDIAN and MEAN. UCLM and LCLM are separate options for upper/lower limits only - using them individually wouldn't give the full interval. Option D incorrectly uses SUM instead of CLM.
D
Correct answer
Explanation
The SET statement reads dataset A once (it has 2 observations: SEQID 1 and 2). The DO loop iterates from 1 to 10, but SET only executes once at the start. So we get 2 observations total (one from each row in A). The n variable counts iterations, ending at 2, not 10.
-
Observations =2 and Salary = 45000 at both observations
-
Observations = 2 and Salary = 45000 at first and Salary =. at second observation
-
Observation = 1 and Salary = 45000
-
Error
A
Correct answer
Explanation
The conditional IF n=1 executes only for the first iteration, setting salary. SET score reads both observations (2 rows). The salary variable is retained in the PDV, so both output observations have salary=45000. Result: 2 observations, salary=45000 for both.
-
2 observations
-
0 observations
-
1 observation
-
Error
B
Correct answer
Explanation
Dataset A has 2 observations (x=1,y=3,z=6 and x=2,y=4,z is not set). When reading into B, we compute z=x*y. For first obs: 1*3=3, but WHERE z<6 filters it out. For second obs: 2*4=8, also filtered out. Result: 0 observations meet the WHERE condition.