If mean of a variable is $10$ and the coefficient of variation is $60\%$. What is the variance of the variable ?
- A$6$
- ✓$36$
- C$60$
- D$50$
Answer: B.
View full solution →Question types
Measures of dispersion question types
229 questions across 6 question groups — pick any mix to generate a Statistics paper with step-by-step answer keys.
229
Questions
6
Question groups
5
Question types
01
MCQ
12 Q→021 Marks Each
55 Q→032 Mark Each
61 Q→043 Marks Each
48 Q→054 Marks Each
32 Q→065 Mark Each
21 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.
What is the value of any measure of dispersion for the observations $5, 5, 5, 5, 5 ?$
- A$1$
- B$5$
- ✓$0$
- D$25$
Answer: C.
View full solution →If the first quartile and the third quartile of a data are 30 and 50 respectively then what is the value of coefficient of quartile deviation ?
- ✓$0.25$
- B$50$
- C$4$
- D$20$
Answer: A.
View full solution →The weight (in kg) for $10$ students are $53, 47, 60, 55, 71, 65, 61, 68, 63, 70$. What is the range of the data ?
- A$17\ kg$
- B$23\ kg$
- ✓$24\ kg$
- D$18kg$
Answer: C.
View full solution →The coefficient of variation of group $A$ is less than the coefficient of variation of group $B$. Which group is more consistent with respect to variability ?
- ✓$A$
- B$B $
- CBoth
- DNone of these
Answer: A.
View full solution →Find the mean deviation for the observations $-1, 0, 4.$
View full solution →Seven students of a group get $20,20, 20, 20, 20, 20, 20$ marks in a test of $25$ marks. What is the standard deviation of their marks ?
View full solution →The $25$th and $75$th percentiles of a frequency distribution are $72.18$ and $103.99$ respectively. Find the quartile deviation.
View full solution →For a company making pipes, the following information of diameter (in cm) of Pipes is obtained. Find the range of the diameter of the pipes.
View full solution →| Diameter (cm) | $20 – 40$ | $40 – 60$ | $60 – 80$ | $80 – 100$ | $100 – 120$ |
| No. of pipes | $15$ | $40$ | $75$ | $20$ | $11$ |
If the data of heights of $10$ students are given in centimeter, what is the unit of its variance ?
View full solution →Find the range and the coefficient of range of the marks from the following frequency distribution of marks scored by $50$ students of a school in a certain examination.
View full solution →The range and standard deviation of marks obtained out of $100$ in the first test by the students of a school are $80$ marks and $20$ marks respectively. These marks are divided by $4$ for the calculation of the internal marks. Find the range and standard deviation of the marks so obtained.
View full solution →The items produced in a factory are packed into different boxes according to their weight. Using the following information, find the range and the relative range of weight of boxes :
View full solution →| Weight (kg) | Oct$-15$ | $15-20$ | $20-25$ | $25-30$ | $30-35$ |
| No. of boxes | $8$ | $15$ | $26$ | $47$ | $4$ |
The demand function of a commodity is $d=15-2 p$, where $p=$ price (in ₹) per unit and $d=$ demand (units). From the closing price of each month of the last year, it is known that for the price, range is $₹ 5$, mean deviation is $₹ 2$ and variance is $9(₹)^{2}$. Find range, mean deviation and variance of the demand from it.
View full solution →The range, quartile deviation mean deviation and standard deviation for a variable $x$ are $10, 2, 3$ and $5$ respectively. Ify $= 5x + 3$ find the range, quartile deviation, mean deviation and standard deviation for the variable $y.$
View full solution →Calculate mean deviation and coefficient of mean deviation of typing time from the following information of time (in minutes) taken to type a report by 32 typists.
The measurements of weight (in kg) of $8$ students of a class of a school are given below :
$46, 58, 60, 43, 75, 66, 51, 81$
Find the mean deviation and coefficient of mean deviation of weights of the students.
View full solution →$46, 58, 60, 43, 75, 66, 51, 81$
Find the mean deviation and coefficient of mean deviation of weights of the students.
The time (in minutes) taken to solve a puzzle by $5$ students are $5, 8, 3, 6, 10.$
Compute the standard deviation of the time taken to solve the puzzle.
View full solution →Compute the standard deviation of the time taken to solve the puzzle.
The runs scored by a batsman in his last $7$ matches are given below :
$52, 58, 40, 60, 54, 38, 48$
Find the variance of the runs of the batsman. Also find the standard deviation.
View full solution →$52, 58, 40, 60, 54, 38, 48$
Find the variance of the runs of the batsman. Also find the standard deviation.
$20$ children are selected for a district level spelling test. The distribution of their marks out of $50$ marks is given below :
Find the mean deviation of the marks obtained by the children from this data.
View full solution →Find the mean deviation of the marks obtained by the children from this data.
The information regarding time (in minutes) taken to solve a puzzle by $50$ students is given below. Find the quartile deviation and the coefficient of quartile deviation of the time taken to solve a puzzle by the children from it.
View full solution →A bus operator gets the following number of passengers in $10$ trips on a day. Find the quartile deviation and the coefficient of quartile deviation of number of passengers from the following data :
$19, 25, 35, 10, 24, 8, 12, 5, 20, 30$
View full solution →$19, 25, 35, 10, 24, 8, 12, 5, 20, 30$
The mean number of units produced by $100$ workers of a factory per day is $60$ units and its standard deviation is $10$ units. Later on, it was noticed that two workers have actually produced $30$ and $20$ units respectively but it was registered as $5$ and $45$ units respectively. By considering this, find corrected mean and corrected standard deviation of the number of units produced by the workers.
View full solution →The information of number of accidents in $10$ days on a particular road is given below. Find the mean and standard deviation of number of accidents per day. Find the percentage of days having the number of accidents lying between the limits $\bar{x} \perp s$.
View full solution →Calculate the standard deviation from the following frequency distribution of marks obtained by $200$ students of a school in an examination :
View full solution →Using the following distribution of income of $1000$ persons of a city, calculate the quartile deviation and coefficient of quartile deviation of income of the persons :
View full solution →The information of number of roses on $30$ rose plants in a nursery is given below. Find range, coefficient of range, quartile deviation, coefficient of quartile deviation, mean deviation and coefficient of mean deviation of the number of roses from it.
View full solution →The following results are obtained on the basis of daily wages (in ?) paid to workers of two firms $A$ and $B$ :
Answer the following questions using the above information.
$1.$ Which firm is paying more total daily wages to their workers ?
$2.$ Determine which firm shows more relative variation in wages paid to its workers.
$3.$ Find the combined mean and combined standard deviation for the two firms.
View full solution →Answer the following questions using the above information.
$1.$ Which firm is paying more total daily wages to their workers ?
$2.$ Determine which firm shows more relative variation in wages paid to its workers.
$3.$ Find the combined mean and combined standard deviation for the two firms.
A factory manufactures certain items in two shifts. The information regarding the time taken by workers to manufacture the items is given below. Using the following information, find the combined standard deviation :
Five observations in each of two groups $G1$ and $G2$ are given below :
Group $G1 :1, 3, 5, 7, 9$
Group $ G2 :2, 4, 6, 8, 10$
Find the mean and variance of both the groups.
Hence obtain the combined standard deviation from it.
View full solution →Group $G1 :1, 3, 5, 7, 9$
Group $ G2 :2, 4, 6, 8, 10$
Find the mean and variance of both the groups.
Hence obtain the combined standard deviation from it.
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