New Update Question Bank of Ag. Statistics (210)

Question Bank of Statistics (210).https://cststudy.blogspot.com/


Question Bank of Statistics (210)


(1) (a) Define statistics. (15, 10)
(b) Write down the scopes of statistics in agriculture. (15, 10)
(c) How can you construct a frequency distribution from raw data? (15)
(d) Define following in connection with a frequency table; (14)
  (i) Class interval, (ii) Class mid value, (iii) Class limits, iv) Class frequency
(e) What are the various types of charts and diagram used in presenting statistical data? Briefly discuss any two of them. (14)
(f) Describe frequency curve and describe its usual forms. (13)
(g) Distinguish between histogram and bar diagram. (13)
(h) What are the graphical methods of representing statistical data? Discuss any two of them. (12)
(i) How will you construct a grouped frequency distribution from raw data on a discrete variable? (12)
(j) Define frequency distribution. What is the purpose of constructing a frequency distribution? (10)
(k) How can you construct a frequency distribution from raw data? (10)
(l) Define variable. Describe different types of variables with examples. (11)             
(m) What is graphical representation of frequency distribution? Describe the different forms of frequency curves. (11)                                                     

(2) (a) Define following terms;
     (i) Arithmetic mean. (15, 14)
     (ii) Geometric mean. (15)
     (iii) Harmonic mean. (15)
     (iv) Median. (14)
     (v) Mode. (14)
(b) What is central tendency? States its various measures and discuss their merits and demerits. (13)
(b) What is central tendency and what are the measures thereof? (11)         (c) Find the mean of the first ‘n’ natural numbers. (11)
(c) Find the arithmetic mean of the first ‘n’ natural numbers. (13)
(d) Show that arithmetic mean is dependent on change of origin and scale. (12)
(e) The frequency distribution of profit per share of 20 companies are given below; (15)
Profit per share (Tk)
0-5
5-10
10-15
15-20
20-25
No. of companies
2
4
8
4
2
(f) Calculate arithmetic mean, median and mode of the values 1, -1, 0, 3, 2 and 2. (14, 11)
(g) For two non-zero positive observations, prove that (i) A≥G≥H,(10) (ii) AH=G², Where A, G and H are usual symbol. (14, 12)
(h) What do you mean by central tendency? (12, 10)
(i) What is mode and median? Describe how mode and median can be determined graphically? (10)

(3) (a) What is dispersion? (15, 12)
(b) What are its different measures? (15, 12)
(c) What are the characteristics of an ideal measure of dispersion? (10)
(d) Calculate mean and standard deviation from the following data; (15)
Weight of tomato (gm)
 No. of tomato
80-90
4
90-100
7
100-110
12
110-120
15
120-130
11
130-140
5
(e) Define standard deviation and coefficient of variation with their merits and demerits. (14, 11)

(f) Calculate standard deviation and coefficient of variation from the following data; (14, 12)
Weight of mango (gm)
No. of mangoes
100-120
8
120-140
15
140-160
18
160-180
30
180-200
12
200-220
10
220-240
7
(f) The profit (in taka thousand) earned by 6 farmers in current year are shown below;
Profits
No. of farmers
10-20
4
20-30
8
30-40
18
40-50
15
50-60
8
60-70
7
Calculate: (i) Standard deviation and (ii) Co-efficient of variation. (11)

(g) Define moment. Describe relationship between the first four central moments and raw moments. (13)
(h) Define standard deviation and mean deviation. Write the important properties of standard deviation. (10)
(i) In a certain distribution, the first four raw moments about the point 4 are 2, 20, 40 and 50. Calculate mean and variance. (13)
(j) Obtain standard deviation in the following cases; (10)
    (i) -2 and 2, (ii) 3, 3 and 3.

(4) (a) What do you mean by skewness? (15)
(b) Write down the different types of skewness. (15)
(c) Suppose first four raw moments are 2, 12, 25 and 60 respectively. Find out skewness and kurtosis. Also comment on the shape of the distribution. (15)
(d) What is kurtosis? When do you call a distribution mesokurtic, platykurtic and leptokurtic? (14)
(e) Show graphically the approximate position of mean, mean and mode when the distribution is (i) Negative skewed, (ii) Positively skewed and (iii) Symmetrical. (14)
(f) Define experiment, mutually exclusive event, sample space and complementary event. (13)
(g) Two dice are thrown, find the probability that the sum of the points shown on the upper faces is (i) 9, (ii) Less than 8, (iii) Neither 8 nor 9. (13)


(5) (a) Define sample space, event and probability of an event with examples. (15)
(b) State and prove the multiplicative law of probability for two events A and B. (15, 10)
(c) State and prove the addictive law of probability for both mutually exclusive and not mutually exclusive cases. (14)
(d) Three coins are tossed simultaneously set up a sample space for this experiment and obtain the probability that (i) All are heads, (ii) No heads occur, (iii) Two or more heads occur. (14)
(e) Define probability of an event. Show that the probability of an event lies between 1. (12)
(i) Define experiment, exhaustive cases, favorable cases, event and probability of an event. (11)
(f) Define event, mutually exclusive event, equally likely event, independent event and dependent event. (10)                                                                            (g) State and prove the additive law of probability for both mutually exclusive and not mutually exclusive cases. (11)
(h) A box contains 6 red and 8 black balls. One ball is drawn at random and kept a side and another ball is drawn. What is the probability that (i) the first ball will be red and the second ball will be black (ii) both balls will be same colors. (10)


(6) (a) Define binominal distribution (11). Write its important properties. (15, 13)
(b) Find mean and variance of binominal distribution. (15, 11)
(c) What are the parameters of normal distribution? Write down the density function of the normal distribution. (14)
(d) Write the important properties of normal distribution. (14)
(e) Define mathematical expectation. (13)
(f) Define Poisson distribution and state its important properties. (12, 10)
(g) What do you mean by mathematical expectation? (11)


(7) (a) Define correlation and coefficient of correlation. (15, 11)
(b) Distinguish between correlation and regression. (15)
(c) Calculate the correlation coefficient between length and number of grains of 9 panicles from the following data; (15)
Length (cm)
12
13
14
15
16
17
18
19
20
No. of grains
50
55
65
73
80
90
100
105
105

(d) Define correlation. Show that the correlation coefficient lies between -1 to +1. (14)
(e) From the data given below examine whether there exists any correlation between x and y; (11)
x
6
8
5
8
9
7
10
y
2
3
6
2
5
3
3
(e) Show that correlation co-efficient depends neither on origin nor on scale. (13)
(f) Age distribution of 10 new married couples are as below. Calculate correlation co-efficient between age of wife and husband interprets the result; (13)
Age of wife (X)
21
16
20
18
23
19
25
27
21
23
Age of Husband (Y) 
27
18
22
19
30
25
27
28
19
24

(g) How will you estimate the parameters of a regression equation like y= a + bx + c (as usual notation)? (13)
(h) The regression co-efficient of y on x is 2, 12 and the correlation co-efficient between x and y is 0.83 for a set of data. Find the regression co-efficient of x and y. (13)
(i) Find the least squares estimates of the parameters in a simple regression model. (11)
(j) State any four properties of regression of correlation. (11)

Short Notes:
(a) Variable. (15)
(b) Histogram. (15)
(c) Kurtosis. (15, 13)
(d) Probability of an event. (14, 11)
(e) Skewness. (14, 11)
(f) Poisson distribution. (14)
(g) Normal distribution. (13)
(h) Conditional probability. (13)
(i) Random variable. (13)
(j) Scatter diagram. (13, 11)
(k) Moment. (12, 10)
(l) Normal distribution. (12, 11)
(m) Standard deviation. (12)
(n) Co-efficient of variation. (12)
(o) Independent and dependent events. (12)
(p) Histogram (10) and bar diagram. (11)
(q) Additive laws of probability. (10)
(r) Uses of statistics in agriculture. (10)



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