Which of the following statements Is true for a symmetric distribution ?
- ✓$Q_3=2 M-Q_1$
- B$Q_2-Q_3=Q_2-Q_1$
- C$Q_3+Q_1>2 M$
- D$Q_3+Q_1<2 M$
Answer: A.
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Skewness of frequency distribution question types
135 questions across 6 question groups — pick any mix to generate a Statistics paper with step-by-step answer keys.
135
Questions
6
Question groups
5
Question types
01
MCQ
14 Q→021 Marks Each
25 Q→032 Mark Each
34 Q→043 Marks Each
23 Q→054 Marks Each
13 Q→065 Mark Each
26 Q→Sample Questions
Skewness of frequency distribution questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Which of the following statements is false for a negatively skewed frequency distribution ?
- AValue of mean is less than median and mode.
- BThe distance between the third quartile and median is less than the distance between median and the first quartile.
- CThe left tall of the frequency curve of the distribution is more clongated.
- ✓The distance between the third quartile and median is more than the distance between median and the first quartile.
Answer: D.
View full solution →In a moderately skewed distribution. $($mean - mode$)$ will be how many times $($mean – median$)\ ?$
- A$3$
- B$- 1$
- ✓$\frac{1}{3}$
- D$0$
Answer: C.
View full solution →If $Q_3+Q_1=60$ and $M=30$ for a frequency distribution, which of the following statements about its skewness is true?
- ADistribution is highly skewed.
- BDistribution is less skewed.
- CDistribution has lack of symmetry.
- ✓Distribution is symmetric.
Answer: D.
View full solution →Mode of a frequency distribution exceeds its mean by $2$. What type of distribution is it ?
- ✓Negatively skewed
- Bsymmetric
- Cpositively skewed
- Dnothing can be said
Answer: A.
View full solution →Which method gives more reliable value of coefficient of skewness ?
State the basic assumption of obtaining Bowley’s measure of skewness.
Which measures are used to obtain Karl Pearson’s measure of skewness ?
What is coefficient of skewness ? State the range for its value.
Explain how to determine the skewness using a frequency curve.
Mode of a symmetric frequency distribution is $84$. If the first quartile is $68$, find the third quartile.
View full solution →For a frequency distribution of monthly overtime (in hours) of employees of a company, the difference between the two extreme quartiles is $50$ and their sum is $218$. If the median is $112$, find the coefficient of skewness.
View full solution →The median of the distribution of marks in statistics obtained by students of a school is $72$ and its mean is $75$. Find the skewness for the marks obtained by the students from these data and state the type of skewness.
View full solution →If a frequency distribution has $Q_3-Q_2=2\left(Q_2-Q_1\right)$, find $j$.
View full solution →The mean of a skewed distribution exceeds its median by $3.$ If its coefficient of skewness is $0.75$, find standard deviation.
View full solution →The following information is available about marks in a subject obtained by the students of a school in the annual examination. $25\%$ students have scored less than $28$ marks whereas,$75\%$ students have scored less than $47$ marks. If the coefficient of skewness for marks is $0.4$, find the median.
View full solution →What are the main objectives of studying skewness ?
Find coefficient of skewness from the following data :
$n = 20$, $= 640$, $= 20,800$ and $M = 32.2$
If coefficient of variation is $25 \%, \overline{ x }=32$ and $M _0=32.2$ for a set of data, find its coefficient of skewness.
View full solution →Third quartile is at a distance of $12.8$ from the median in a frequency distribution and its first quartile is at a distance of $11.2$ from the median. Find skewness and its coefficient.
View full solution →The data about the number of runs scored by two cricketers in $10$ matches are as follows. Use this information to determine which cricketer’s game is more skewed.
View full solution →| Details | Cricketer $A$ | Cricketer $B$ |
| Mean $ \bar{x}$ | $50$ | $35$ |
| Mode $M_0$ | $56$ | $31$ |
| Standard deviation $s$ | $14.4$ | $5.2$ |
The following figures are given to describe the changes in the market prices of shares of a company before and after their general body meeting. Take them into consideration to comment whether the proceedings of this meeting have affected the market pries of shares by computing coefficient of skewness.
From the following measures obtained for the frequency distributions of sales (in lakh Rs.) of potatoes by two merchants in a month, determine which distribution is more close to symmetry.
For the frequency distribution of a set of data, $n=200, \Sigma f ( x - 2 4 0 )=0, \Sigma f ( x - 2 4 0 )^2=11,250$ and median $= 246$ , find coefficient of skewness and state the type of skewness:
View full solution →The following information is available about defective staplers after testing $50$ packets of $500$ staplers each. Find coefficient of skewness using Karl Pearson’s method.
View full solution →| No. of defective staplers | $19$ | $20$ | $21$ | $22$ | $23$ | $24$ | $25$ | $26$ |
| No. of packets | $5$ | $18$ | $10$ | $8$ | $4$ | $2$ | $2$ | $1$ |
The frequency distribution of hourly wages paid to $600$ workers is given below. Find the Karl Pearson’s coefficient of skewness from this distribution.
View full solution →The following information is about the annual advertisement cost (in lakh $?$) of $30$ companies. Find skewness and coefficient of skewness using it.
View full solution →The following information is obtained for life (in complete hours) of $400$ electric bulbs. Find the skewness and the coefficient of skewness by Karl Pearson’s method.
View full solution →The average monthly transportation cost of $200$ families in a city in the year $2014$ is as follows. Find skewness and coefficient of skewness using Karl Pearson’s method.
View full solution →A factory has $100$ machines for production. The following data are obtained about rejected items during the production process. Find the skewness and its coefficient using Karl Pearson’s method from these data.
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