The coefficient of ___________ is a measure of the shape of a distribution.
- ASkewness
- BKurtosis
- ✓Both (a) and (b)
- DNone
Answer: C.
View full solution →Question types
Data Interpretation question types
87 questions across 7 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.
87
Questions
7
Question groups
5
Question types
01
MCQ
15 Q→022 Marks Questions
14 Q→033 Marks Question
12 Q→045 Marks Questions
12 Q→05Fill in the blanks.
14 Q→064 Marks Questions
16 Q→07Match the following.
4 Q→Sample Questions
Data Interpretation questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The degree of peakness or flatness of a unimodal distribution is called
- ASkewness
- BSymmetry
- CDispersion
- ✓Kurtosis
Answer: D.
View full solution →In a symmetrical distribution the coefficien skewness will be :
- ✓$0$
- B$Q_1$
- C$Q_3$
- D$1$
Answer: A.
View full solution →Departure from symmetry is called
- ASecond moment
- BKurtosis
- ✓Skewness
- DVariation
Answer: C.
View full solution →The standard deviation of some temperature data in ${ }^{\circ} C$ is 5 . If the data were converted into ${ }^{\circ} F$, then the variance would be
- ✓81
- B57
- C36
- D25
Answer: A.
View full solution →For some symmetrical distribution, $Q_1=36$ and $Q_3$ $=63$. Using Bowely's measures of skewness, find the median.
View full solution →Compute $S_k$ if
(i) Mean $=108$, Mode $=99, \sigma=5$
(ii) $\sigma=4$, Mean $=20.5$, Mode $=22$
Also, mention type of skewness.
View full solution →(i) Mean $=108$, Mode $=99, \sigma=5$
(ii) $\sigma=4$, Mean $=20.5$, Mode $=22$
Also, mention type of skewness.
If the central moments $\mu_1, \mu_2, \mu_3$ and $\mu_4$ are $0,6,31$ and 108, respectively. Find coefficient of kurtosis.
View full solution →Karl Pearson's coefficient of skewness is 1.28 , its mean is 164 and mode 100, find standard deviation.
If $Q_1=26, Q_2=46$ and $Q_3=76$, find coefficient of skewness.
View full solution →For a certain frequency distribution $\mu_1^{\prime}=2, \mu_2^{\prime}=18$ and $\mu_3^{\prime}=100$, find $S_k$.
View full solution →For a frequency distribution the Bowley's coefficient of skewness is 1.2. If the sum of 1st and 3 rd quartile is 200 and median is 76 , then find the value of third quartile.
Co-efficient of variation of two distributions are 60 and 70, and their standard deviations are 21 and 16 respectively. What are their arithmetic mean?
Find the variance of first $n$ natural numbers.
View full solution →Find the mean and variance for the following data :
$
6,7,10,12,13,4,8,12 .
$
View full solution →$
6,7,10,12,13,4,8,12 .
$
The following are the marks of 150 students in an examination. Calculate Karl Pearson's coefficient of skewness.
Calculate the first four moments about the arbitrary origin and then calculate the first four moments about mean.
| x | 10-13 | 13-16 | 16-19 | 19-22 | 22-25 | 25-28 |
| f | 2 | 4 | 26 | 47 | 15 | 6 |
For the following distribution, find central moments, $\beta_1$ and $\beta_2$.
View full solution →| Class | 1.5 - 2.5 | 2.5 - 3.5 | 3.5 - 4.5 | 4.5 - 5.5 | 5.5 - 6.5 |
| Frequency | 1 | 3 | 7 | 3 | 1 |
The mean and standard deviation of 20 observations are found to be 10 and 2 , respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases :
(i) If wrong item is omitted.
(ii) If it is replaced by 12 .
(i) If wrong item is omitted.
(ii) If it is replaced by 12 .
An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results :
(i) Which firm A or B pays larger amounts as monthly wages ?
(ii) Which firm A or B shows greater variability in individual wages ?
| Particular | Firm A | Firm B |
| No. of wage earners | 586 | 648 |
| Mean of monthly wages | ₹ 5,253 | ₹ 5,253 |
| Variance of the distribution of wages | 100 | 121 |
(ii) Which firm A or B shows greater variability in individual wages ?
In symmetric distribution, the third quartile and first quartile of data in distribution must be at ____________ distance.
When the frequency curve is more peaked than normal curve it is called __________
In case of negatively skewed distribution, the extreme value lies in ___________
For a positively skewed distribution mean is always ___________
The sum of square of the deviations of values of variables is ___________ , when taken about their arithmetic mean.
For a certain distribution, $\Sigma x_i=20, \Sigma x_i^2=100$ and $\Sigma x_i^3$ $=1500$, and $n=10$, find coefficient of skewness.
View full solution →Find the first four moments about zero for the set of the number $1,3,5,7$.
View full solution →The first four raw moments of a distribution are $2,136,320$ and 40000 . Find out coefficient of skewness and kurtosis.
View full solution →Find the mean and standard deviation using short-cut method.
View full solution →| $x_i$ | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 |
| $f_i$ | 2 | 1 | 12 | 29 | 25 | 12 | 10 | 4 | 5 |
If $\bar{x}$ is the mean and $\sigma^2$ is the variance of $n$ observations $x_1, x_2, x_3, \ldots, x_n$, then prove that the mean and variance of the observations $a x_1, a x_2, \ldots$, $a x_n$ are $a \bar{x}$ and $a^2 \sigma^2$ respectively $(a \neq 0)$.
View full solution →| Column-I | Column-II |
| (a) Moments about mean are called | (i) raw moments |
| (b) Moments about origin are called | (ii) Platykurtic |
| (c) If $\beta_2<3$, then curve is | (iii) leptokurtic |
| (d) If $\beta_2>3$, then curve is | (iv) central moments |
| Column 1 | Column 2 |
| (a) The square of standard deviation is known as | (i) absolute measure |
| (b) Coefficient of variation is | (ii) Mean |
| (c) The standard deviation is always taken from | (iii) Variance |
| (d) Standard Deviation is | (iv) Relative Measure |
| Column 1 | Column 2 |
| (a) $\sum_{i=1}^n \frac{\left|x_i-\bar{x}\right|}{n}$ | (i) Mean Deviation about median |
| (b) $\sum_{i=1}^n \frac{\left|x_i-M_d\right|}{n}$ | (ii) Mean deviation for discrete frequency distribution |
| (c) $\sum_{i=1}^n \frac{f_i\left|x_i-A\right|}{N}$ | (iii) Mean deviation about mean |
| (d) $\frac{\Sigma f_i x_i}{N}$ | (iv) Mean |
| Column 1 | Column 2 |
| (a) Third Quartile $\left(Q_3\right)$ | (i) $23.4$ |
| (b) Sixth Decile $\left(D_6\right)$ | (ii) 20 |
| (c) $70^{\text {th }}$ Percentile $\left(P_{70}\right)$ | (iii) $26.25$ |
| (d) Median $(m d)$ | (iv) $25.7$ |
Generate a Data Interpretation paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.