Quantitative Aptitude

Statistics

606 Questions
All Ungrouped data dispersion and consistency 209 Unknown terms from given average 124 Grouped data central tendencies 101 Merging means and variances of groups 53 Replacement change in average 27 Alligation and weighted average 21 Data interpretation from tables and charts 20 Net successive percentage change 19 Grouped data variance via step deviation 18 Combination of multiple ratios 1

Statistics Questions

Multiple choice range and mean deviation statistics and probability maths coefficient of variance variance and standard deviation

The coefficient of mean deviation from median of observations  $40, 62, 54, 90, 68, 76$  is

  1. $2.16$
  2. $0.2$
  3. $5$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Arrange the given observations in ascending order
$40,54,62,68,76,90$
Here, number of terms $n=6 (even) $
$\displaystyle \therefore $ Median (M) $\displaystyle =\frac{\left ( \frac{n}{2} \right )th:term+\left ( \frac{n}{2}+1 \right )th:term}{2}=\frac{62+68}{2}=65$

$\Sigma \left | x _{i}-M \right |=25+11+3+3+11+25=78$
Mean deviation from median $\displaystyle =\frac{\Sigma \left | x _{i}-M \right |}{n}=\frac{78}{6}=13 $
$\therefore $ Coefficient of M.D.=$\displaystyle =\frac{M.D.}{median}=\frac{13}{65}=0.2$

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

Mean deviation of $7,10,10,15,10,8,8,7,3,2,10$ through mean is

  1. $3.14$
  2. $8$
  3. $\dfrac {4}{5}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

mean $=\dfrac{\sum {x _1}}{n}=\dfrac{90}{11}\approx 8.18$

derivation through mean = $|x _i-\bar x|$
& mean of it is $=\dfrac{\sum|{x _i-\bar x}|}{n}$
$=\dfrac{(1.18+1.82+1.82+6.82+8.18+0.18+0.18+1.18+5.18+6.18+1.82)}{11}$
$=\dfrac{34.54}{11}=3.14$

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

If a constant value $40$ is subtracted from each observation of a set, the mean of the set is __________.

  1. increased by $40$
  2. decreased by $40$

  3. is not affected

  4. zero
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If a constant is subtracted from every observation in a set, the mean of the set is also decreased by that same constant.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

The mode of the following observations is $10, 19, 22, 16, 15, 18, 20, 18, 14, 18, 23$

  1. $17.55$
  2. $18$
  3. $15$
  4. $16.5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The mode is the value that appears most frequently. In the set 10, 19, 22, 16, 15, 18, 20, 18, 14, 18, 23, the number 18 appears three times, which is more than any other number.

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

If there are two groups containing $30$ and $20$ observations and having $50$ and $60$ as arithmetic means, then the combined arithmetic mean is ________.

  1. $55$
  2. $56$
  3. $54$
  4. $52$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Combined mean = (n1*x1 + n2*x2) / (n1 + n2). Calculation: (30*50 + 20*60) / (30 + 20) = (1500 + 1200) / 50 = 2700 / 50 = 54.

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

What is the value of mean for the following data.

Class interval Frequency
$350-369$ $15$
$370-389$ $27$
$390-409$ $31$
$410-429$ $19$
$430-449$ $13$
$450-469$ $6$
  1. $400$
  2. $400.58$
  3. $394$
  4. $394.50$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Class Intervals Mid-values(x) Frequency(f) fx
$350-369$ $359.5$ $15$ $5,392.5$
$370.389$ $379.5$ $27$ $10,246.5$
$390-409$ $399.5$ $31$ $12,384.5$
$410-429$ $419.5$ $19$ $7,970.5$
$430-449$ $439.5$ $13$ $5,713.5$
$450-469$ $459.5$ $6$ $2,757$
$\displaystyle\sum f=111$ $\displaystyle\sum fx=44,464.5$

Arithmetic mean $=44,464.5/111=400.58$.

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

Consider the following frequency distribution.

Class Intervals $0-10$ $10-20$ $20-30$ $30-40$
Frequency $8$ $10$ $12$ $15$

Arithmetic mean $=$?

  1. $39.65$
  2. $22.55$
  3. $32.55$
  4. $23.56$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Class Intervals Mid-values(x) Frequency(f) fx
$01-0$ $5$ $8$ $40$
$10-20$ $15$ $10$ $150$
$20-30$ $25$ $12$ $300$
$30-40$ $35$ $15$ $525$
$\displaystyle\sum f=45$ $\displaystyle\sum fx =1,015$

Arithmetic mean $=1,015/45=22.55$.

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

Coefficient of variation of a distribution is $60$ and its standard deviation is $21$, then its arithmetic mean is?

  1. $36$
  2. $37$
  3. $35$
  4. $38$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The coefficient of variation (CV) is calculated as (Standard Deviation / Mean) * 100. Rearranging the formula gives Mean = (Standard Deviation / CV) * 100. Substituting the given values: Mean = (21 / 60) * 100 = 0.35 * 100 = 35.

Multiple choice maths measure of central tendency assumed mean method assumed mean method of finding mean mean and median

Sum of squares of deviation of $10$ observations measured from $5$ is $17$ and sum of squares of observations is $170$ then mean of observation is

  1. $40.3$
  2. $4.5$
  3. $4$
  4. $4.03$
  5. $4.3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$x _1,x _2,x _3,x _4...x _10\x _1^2+x _2^2+x _3^2+x _4^2+....x _10^2=17 (Given) \rightarrow (i)$

$(x _1-5)^2+(x _2-5)^2+(x _3-5)^2+....+(x _10-5)^2=17(Given)\rightarrow (i)$
$Mean (M)=\cfrac{x _1+x-2+x _3+....x _10}{10}\ \Rightarrow x _1+x _2+x _3+....+x _10=10M\rightarrow(iii)$
From equation $(ii)$ we get
$x _1^2+25-10x _1+x _2^2+25-10x _2+x _3^2+25-10x _3+...+x _10^2+25-10x _10=17\ \Rightarrow (x _1^2+x _2^2+....x _10^2)-10(x _1+x _2+x _3+....+x _10)+25\times10=17\ \Rightarrow 170-10(10M)+250=17\ \Rightarrow420-100M=17\ \Rightarrow100M=403\ \Rightarrow M=\cfrac{403}{100}=4.03$

Multiple choice chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

Two students are working on an AP Chemistry lab. Their assignment is to determine experimentally the density of a nonvolatile organic liquid, limestone. The accepted value for the density of limestone is $0.8422\ g/mL$. Each student conducts three separate density determinations, then calculates a mean (average) value for the density and the standard deviation for their three trials.

Student A Student B
Density #$1$ $0.8421 g/mL$ $0.8408 g/mL$
Density #$2$ $0.8514 g/mL$ $0.8502 g/mL$
Density #$3$ $0.8355 g/mL$ $0.8332 g/mL$
Mean Density $0.8430 g/mL$ $0.8414 g/mL$
Standard Deviation $0.0080$ $0.0085$

The results and calculations for each students are shown in the table below.
Of the four descriptions given below, which BEST interprets the accuracy and precision of Student A and Student B?

  1. Student A and Student B are equally precise, but Student B has more accurate results.

  2. Student A and Student B are equally accurate, but Student B has more precise results.

  3. Student A and Student B have equal accuracy and equal precision.

  4. Student A has more accurate and more precise results than Student B.
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

Find the mean and standard deviation of the following observations: X $=2, 5, 7, 8, 13$.

  1. $7$ & $3.63$
  2. $3.63$ & $7$
  3. $7.63$ & $3$
  4. $3$ & $7.63$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle\frac{2+5+7+8+13}{5}=7$
$\sqrt{\displaystyle\frac{4+25+49+64+169}{5}}-49=3.63$.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The mean of $100$ observations is $18.4$ and sum of sqares of deviations from mean is $1444$, the Co-efficient of variation is ______.

  1. $30.6$
  2. $35.6$
  3. $20.6$
  4. $10.6$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Standard deviation = sqrt(Sum of squared deviations / N) = sqrt(1444 / 100) = sqrt(14.44) = 3.8. Coefficient of Variation (CV) = (SD / Mean) * 100 = (3.8 / 18.4) * 100 = 20.65.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The following distribution of ages (in complete years) is obtained for the students of higher secondary.
The mode of the distribution is.

Age (in years) 15 16 17 18 19 20 21
Number of students 12 18 20 10 7 6 2





  1. $16$
  2. $17$
  3. $18$

  4. None of them
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The mode is the value with the highest frequency. Here, age 17 has the highest frequency of 20 students.

Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method to find variance and standard deviation variance and standard deviation measures of dispersion

The mean of $25$ observations is $73.408$. If one observation $64$ is removed, the revised mean is ______.

  1. $72.8$
  2. $73.8$
  3. $80.8$
  4. $76.8$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original sum = 25 * 73.408 = 1835.2. New sum = 1835.2 - 64 = 1771.2. New mean = 1771.2 / 24 = 73.8.