Free Measures of Dispersion 03 Practice Test - 11th Grade - Commerce
Question 1
The square root of
SOLUTION
Solution : Standard deviation is the square root of variance.
Question 2
The distribution of weights of 50 students in a class is as follows.
Weight (kg)40−4545−5050−5555−6060−6565−70No. of students371112107
Calculate the standard deviation using the step deviation method.
SOLUTION
Solution : D
Let the assumed mean be 52.5 i.e. A = 52.5 and the dividing factor (c) be 5.
XFDD′=DcFD′FD′242.53−10−2−61247.57−5−1−7752.511000057.51251121262.510102204067.571532163∑F=50∑FD′=40∑FD′2=134
σ=√∑FD′2∑F−(∑FD′∑F)2×c=√13450−(4050)2×5=√2.68−0.64×5=√2.04×5=1.428×5=7.14
Question 3
Relative measures of dispersion have the same units as that of the observations in the data. State true or false.
SOLUTION
Solution : B
Relative measures are ratios and have no units.
Question 4
Find the coefficient of mean deviation about median for the following cumulative frequency distribution:
xfrequencyCumulative frequency221134233925458135482156930684347843884240
0.187
0.203
0.215
0.224
SOLUTION
Solution : A
Here, the sum of frequencies, n = 40, which is even.
So, the median terms will be the n2th and the (n2+1)th observations, i.e. the 20th and the 21st observations.
Both the 20th and the 21st observations are 54.
So, the median term, M= 54.
Deviations from the median are tabulated below
XFD=|X−M|FD22132323422040392153045897254800569218684145678424968423060 ∑F=40∑FD=404
M.D(M)=40440=10.1
Coefficient of M.D(M)=M.D(M)Median=10.154=0.187
Question 5
The following are the scores of Adil and Kratu in 5 subjects. Adil's scores are out of 10 and Kratu's are out of 50.
Adil: 7, 9, 6, 8, 4
Kratu: 36, 44, 49, 41, 25
Compare the variability in scores using the coefficient of variation.
SOLUTION
Solution : A
MeanA=7+9+6+8+45=6.8
MeanK=36+44+49+41+255=39
σA=√0.22+2.22+0.82+1.22+2.825=√2.96=1.72
σK=√32+52+102+22+1425=√66.8=8.17
C.O.VA=1.726.8×100=25.29%
C.O.VK=8.1739×100=20.95%
Hence, Adil's scores have higher variability
Question 6
Inter-quartile range =
SOLUTION
Solution : C
Inter−quartile range=Q3−Q1
Question 7
Number of goals scored by Ronaldo in champions league for past 10 years are as follows. {1, 3, 8, 4, 7, 6, 10, 12, 17, 10} Find the mean deviation about the mean.
3
3.6
4
4.4
SOLUTION
Solution : B
Mean=1+3+8+4+7+6+10+12+17+1010
¯X=7810=7.8
∑|X−7.8|=6.8+4.8+0.2+3.8 +0.8+1.8+2.2+4.2+9.2+2.2=36
∴ Mean deviation=3610=3.6
Question 8
If the coefficient of variation and standard deviation of a distribution are 2 and 0.4 respectively, then mean of the distribution is
40
20
10
8
SOLUTION
Solution : B
C.V=2;σ=0.4(given)C.V=100×s.dmean2=100×0.4meanMean=402=20
Question 9
If the S.D of a set of observations is 4 and if each observation is divided by 4, the S.D of the new set of observations will be
4
3
2
1
SOLUTION
Solution : D
We know that if we multiply all numbers of a set by a constant "k" then the mean of these numbers will also be a multiple of the old mean.
And the variance of these numbers will be multiple of "k2".
Since standard deviation is nothing but the square root of variance, s.d will be multiple of "k" of the old standard deviation.
We are given the s.d was 4.
So after multiplying each observation by (1/4), the s.d will also be multiplied by (1/4), thus giving the value = 4×14 = 1
Question 10
The coefficient of variation of a distribution is
100×σ¯X
100ׯXσ
100×σ2¯X
σ¯X
SOLUTION
Solution : A
C.V. is given byC.V=100×σ¯X