Monday, 13 December 2021

MOMENTS, SKEWNESS, KURTOSIS

SKEWNESS:
Karl Pearson: (Mn - Mod)/S. D
                      : 3(Mn - Med)/S. D
            : (Q₃+ Q₁ - 2 Med)/(Q₃ - Q₁)

1) Find the coefficient of skewness from the following:
a) Value: 6  12  18  24  30  36  42

       F:      4    7    9   18  15  10  5.                                                       +0.139

b) variable         frequency

   20.5 - 23.5          17

   23.5 - 26.5        193 

   26.5 - 29.5        399

   29.5 - 32.5        194

   32.5 - 35.5          27

   35.5 - 38.5         10       

With the help of mode.           0.068

c) Marks          No. Of students
Above  0               150
    ,,      10               140
    ,,      20               100
    ,,      30                 80
    ,,      40                 80
    ,,      50                 70
    ,,      60                 30
    ,,      70                 14
    ,,      80                   0     
With the help of Median        - 0.754

d) Marks          No. Of students
Below  80               12
    ,,       90                30
    ,,      100              65
    ,,      110             107
    ,,      120             157
    ,,      130             202
    ,,      140             222
    ,,      150             330           - 0.332

e) Variable         Frequency
    10 - 20               358
    20 - 30              2417
    30 - 40               976
    40 - 50               129
    50 - 60                 62
    60 - 70                 18
    70 - 80                 10
With the help of Quartiles.      0.131

f) Convert the following into an ordinary frequency table and obtain the values of Quartiles Deviation and Coefficient of Skewness.
Marks below.    No of students
    80                         240
    70                         190
    60                         125
    50                           95
    40                           75
    30                           60
    20                           40
    10                           25         -0.473

2) In a certain distribution the following results were obtained:
Mean = 45.00
Median= 48.00
Coefficient of skewness= - 0.4. find the standard deviation.             22.5

3) For a moderately skewed data, the arithmetic mean is 100, the coefficient of variation is 35 and the Karl Pearson's coefficient of Skewness is 0.2. find the mode and the median.                                97.7

4) Karl Pearson's coefficient of Skewness of a distribution is +0.40. Its standard deviations is 8 and mean is 30. Find the mode and median of the distribution.       26.8, 28.93

5) For a group of 10 items, ∑x= 452,  ∑x² =24270, Mode= 43.7. Find the Pearson's coefficient of skewness.
A) +0.08 B) 0.80 C) -0.08 D) -0.80

6) For a moderately skewed distribution, mean= 160, Mode=157, S. D= 50. What is the value of coefficient of variation?
A) 31.52 B) 31.25 C) 31.35 D) 31.58

7) For a moderately skewed distribution, mean= 160,  mode= 157, SD= 50. What is the value of Pearson coefficient of skewness.
A) -0.06 B)0.06 C)+0.60 D)+0.60

8) For a moderately skewed distribution, mean =160, Mode= 157, S D= 50. what is the value of Median ?
A) 195 B)159 C)169 D) 191

9) For a moderately skewed distribution, mean= 172, median= 167, SD= 60. what is the value of coefficient of skewness ?
A) -0.25 B) 0.52 C) -0.52 D)0.25

10) For a moderately skewed distribution, mean=172, median= 167, SD= 60. What is value of mode ?
A) 175 B)157 C)159 D) 169

11) The Karl Pearson's coefficient of skewness of a distribution is 0.32. its SD is 6.5, and the mean is 29.6. find the mode.
A)27.25 B)27.45 C)27.54 D) 27.52

12) the Karl Pearson's coefficient of skewness of a distribution is 0.32. Its SD is 6.5, and the mean is 29.6. find the median.
A) 28.9 B)25.9 C)29.8 D) 29.2

13) Given the coefficient of skewness= -0.475, mean= 64,  median= 66; find the value of standard deviation.
A)12.36 B)12.53 C)12.63 D) 12.68

14) the measure of skewness for a certain distribution is -0.8. if the lower and upper quartiles are 44.1 and 56.6 respectively, find the median.
A) 55.35 B) 55.53 C) 55.85 D) 55.58

15) For a moderately skewed distribution, the mean is 100, the coefficient of variation is 35, and Karl Pearson Coefficient of Skewness is 0.2. find the mode.
A) 91 B) 93 C) 92 D) 94

16) For a moderately skewed distribution, the mean is 100, the coefficient of variation is 35, and Karl Pearson's coefficient of skewness is 0.2. Find the median.
A) 97.27 B) 97.77 C) 97.57 D) 97.67

17) In a certain distribution mean = 45, median =48, coefficient of skewness = - 0.4. what is the value of standard deviation ?
A) 22.3 B) 22.7 C) 22.5 D) 22.9

18) For a frequency distribution with coefficient of variation= 5, standard deviations= 2, Karl Pearson's coefficient of skewness =0.5. find the mean and standard deviation.
A) 39,40  B) 38, 40 C) 40, 39 D) 40, 42

19) the median, mode and coefficient of skewness for a certain distribution are respectively 17.4 ,15.3, 0.35. Calculate the coefficient of variation.

A) 47 B) 49. C) 48 D) 50

 

*** For a particular distribution, let mean= 50, Coefficient of Vari6= 40%, Coefficient of skewness =- 0.4 find 

20) Find the Variance

A) 399 B)400. C) 401 D) 402

21) find the median.

A) 52.76 B)53.76 C) 53.67 D)52.67.

22) find the mode 

A) 58. B) 59 C) 60 D) 61

 

23) Find the coefficient of variation of a frequency distribution, given that its mean is 120, Mode= 123, coefficient of skewness= - 0.3.

A)8.33%. B)8.53% C)8.34% D)8.53% 

24) The median, mode and the coefficient of skewness for a certain distribution are respectively 17.4, 15.3 and 0.35. Find the value of coefficient of variation.

A) 47 B) 49  C) 51.  D) 53 


** It is given that mean, median and coefficient variation of a set of variable are 45, 42 and 40 respectively.

25) find the mode.

A) 33 B) 34 C) 35 D) 36.

26) find SD 

A) 17 B) 19. C) 18 D) 20

27) find the coefficient of skewness

A) 0.3  B) 0.4 C) 0.5. D) 0.6


28) The measure of skewness for a certain distribution is - 0.8. if the lower and upper quartiles are 44.1, and 56.6 respectively. find the median.

A) 56.35             B) 55.36

C) 56.56             D) 55.35.

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