The formula of standard deviation is based on which of the following ?
- ✓$\bar{x}$
- B$M$
- C$M_{ o }$
- D$Q_3$
Answer: A.
View full solution →Question types
Measures of dispersion question types
71 questions across 6 question groups — pick any mix to generate a Statistics paper with step-by-step answer keys.
71
Questions
6
Question groups
5
Question types
01
MCQ
15 Q→021 Marks Each
13 Q→032 Mark Each
17 Q→043 Marks Each
14 Q→054 Marks Each
7 Q→065 Mark Each
5 Q→Sample Questions
Measures of dispersion questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
For a data, $75 \%$ observations are more than $38$ and $25 \%$ observations are more than $50$ . Find a suitable measure of dispersion using the information.
- A$12$
- B$88$
- ✓$6$
- D$-6$
Answer: C.
View full solution →$730,824,594,638,912,1152$ and $2194$ persons visited a shopping mall on different days respectively during the last week. Find the range of this data.
- A$1164$
- ✓$1600$
- C$558$
- D$1042$
Answer: B.
View full solution →What is the standard deviation of the observations $-7,-7,-7,-7,-7,-7,-7 ?$
- A$-7$
- B$7$
- ✓$0$
- D$1$
Answer: C.
View full solution →Give the popular name of semi-inter quartile range.
- ✓Quartile deviation
- BStandard deviation
- CRange
- DVariance
Answer: A.
View full solution →The variance of $10$ observations is $81$ . If each observation is multiplied by $(-3)$, what will be the standard deviation of the resulting data ?
View full solution →The standard deviation of a data is $12$ . What is the value of the standard deviation if all observations of the data are divided by $3$ ?
View full solution →The average rainfall of last five years in Ahmedabad is $25$ inches. What is the standard deviation, if the coefficient of variation of this data is $20 \%$ ?
View full solution →The sum of squares of deviations taken from the mean for $25$ observations is $400$ . What is its standard deviation?
View full solution →The standard deviations of the weights and heights of students of a class are $2 \ kg$ and $4 \ cms$ respectively. So, the standard deviation of height is double the standard deviation of weight. Check the validity of this statement.
View full solution → If the quartile deviation of $x$ is 12 and $3 x+4 y-20=0$, find the quartile deviation of $y$.
View full solution → What is the variance of $(12-3 x)$ if the standard deviation of $x$ is 2 ?
View full solution →If the standard deviation of $x$ is $k$, find the the standard deviation of $\left(\frac{x-5}{k}\right)$.
View full solution →Find the standard deviation of $y$ if $2 x+3 y=10$ and the standard deviation of $x$ is 15 .
View full solution →Find the standard deviation of $y$ if $y=3 x+2$ and the variance of $x$ is 25 .
View full solution →Which series is more consistent among the following ?
View full solution →| Particulars | Series A | Series B |
| No. of observations | $40$ | $50$ |
| Average | $25$ | $30$ |
| The sum of squares of deviations taken from mean | $640$ | $1800$ |
The number of challans issued to the vehicle owners by traffic police in a city for violating the traffic ules in the last ten days are $20,42,55,60,48,80,95,70,10$ and $50$ .
Find the coefficient of variation of challans received by the vehicle owners.
View full solution →Find the coefficient of variation of challans received by the vehicle owners.
The distribution of time spent daily on social media by $20$ students of a school is given below.
Find the mean deviation.
View full solution →| Time spent on social media (minute) | $30$ | $50$ | $100$ | $120$ | $150$ |
| No. of students | $4$ | $7$ | $6$ | $2$ | $1$ |
Find the mean deviation.
Find the coefficient of quartile deviation for seven observations $12,-3,0,18,9,-5,21$.
View full solution →The mean and standard deviation of the marks obtained by $100$ students in the test of $60$ marks are $40$ and $5.1$ respectively. Later on, it was known that one of the students scored $40$ Marks of but by mistake it was taken as $50$. Find the correct marks value of the standard deviation of the marks.
View full solution →The number of students who scored $85$ or more marks out of $100$ marks in the subject of Statistics in the $12th$ board exam for last ten years in two schools are given below.
Find the coefficients of variation of the number of students of both the schools and compare them.
View full solution →| Year | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
| School $A$ | $17$ | $13$ | $14$ | $26$ | $53$ | $29$ | $79$ | $36$ | $49$ | $84$ |
| School $B$ | $22$ | $37$ | $10$ | $20$ | $56$ | $52$ | $37$ | $14$ | $48$ | $4$ |
Find the coefficients of variation of the number of students of both the schools and compare them.
The mean and standard deviation of a sample of size $15$ are $3.5$ and $3$ respectively and that of another sample of size $22$ are $4.7$ and $4$ respectively.
Obtain the combined standard deviation from this information.
View full solution →Obtain the combined standard deviation from this information.
A transport company has $100$ trucks. These trucks are inspected for maintenance purpose and the following distribution is obtained for the number of defects in the trucks.
Find the range, coefficient of range, quartile deviation, mean deviation and coefficient of mean deviation for the number of defects per truck.
View full solution →| No. of Defects | $0$ | $1$ | $2$ | $3-4$ | $5-8$ | $9-14$ | $15-25$ |
| No. of trucks | $8$ | $12$ | $18$ | $24$ | $18$ | $12$ | $8$ |
Find the range, coefficient of range, quartile deviation, mean deviation and coefficient of mean deviation for the number of defects per truck.
$20$ workers of a factory get bonus from $₹ 1000$ to $₹ 5000$ as per their performance. Its distribution is as follows.
Obtain coefficient of range, quartile deviation and standard deviation for the bonus.
View full solution →| Bonus (₹) | $1000$ | $2000$ | $3000$ | $4000$ | $5000$ |
| No. of workers | $3$ | $5$ | $6$ | $4$ | $2$ |
Obtain coefficient of range, quartile deviation and standard deviation for the bonus.
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