DESCRIPTIVE STATISTICS — DU B.Sc (hons) Statistics Previous Year Question Papers

Descriptive Statistics B.Sc. (Hons.) Statistics (NEP-UGCF) 2. Attempt 6 questions in all. 4. Attempt 5 more questions selecting at least2 questions from each section. 1. (a) Fill in the blanks .(i) An Ogive curve helps in determining the value of (iii) The sum of 10 items is 12 and sum of their squares is 16.9. Then variance is (iv) If the kurtosis of a distribution is 3, it is called distribution (v) For a symmetrical distribution Qi=25 and Q3=45, the median is (vi) For # attributes, the total class frequencies are and the total number of ultimate class frequencies are (vii) If rot, Y) = 0.2, then r(2X + 3, -3Y + 4) = (viii) If both the regression lines are perpendicular to each other, then we say that there is correlation between x and Y. (ix) If one of the regression coefficients is greater than unity, the other must be (b) Forthe series A and series 8 of observations X and Y respectively, 3 = 18, cr; = 9 , P = 10 and a-: = 4 . Which series is more consistent? Give reason. (c)Given(A)=(a)=(B)=(P)=¥,Showthat(AB)=(GP). (d) The following data pertain to the marks in subjects A and 8 in certain examination. and r = 0.42. Find the two regression lines. Give the estimate marks of B for candidate who secured 50 marks in A. (1x9, 2x3) 2.(a) Explain four types of measurement scales with one example of each. (b) Show that in a discrete series if deviations are small compared with mean M so that (* / A4).1 and higher powers of (x / A4) are neglected, we have where A4 is the arithmetic mean, G.is the geometric mean, H is the harmonic mean and a is the standard deviation of the distribution. (7,8) 3.(a) For a group of 200 candidates, the mean and standard deviation of scores were found to be 40 and 15 respectively. Later on, it was discovered that the scores 47 and 3 I were misread as 74 and 13 respectively. Find the correct mean and standard deviation corresponding to the correct figures. (b) If J7],J22 are the sizes, fi, *2the means, and a:1, ol2 the standard deviations of two series, then prove that standard deviation ` c7 ' of the combined series of size #, + #2 is given by: where dL = r] - r , c72 = F2 - F and f ="I f, + „2 f2 is the mean of the combined series. 4.(a) Define moments about origin and moments about mean of a frequency distribution. Establish the relationship between moments about mean in terms of moments about origin for first three moments. (b) In a series of measurements we obtain ffl, values of magnitude x„ "2values of magnitude x2 , and so on. If 5 is the mean value of all the measurements, prove that the standard deviation is where r = fr + a and 4 is any constant. 5.(a) Explain the following (i) order of a class (ii) Ultimate Classes (iii) Dichotomy. Find the total number of class frequencies of all orders for n attributes. (b) Given the following.positive frequencies, obtain all the ultimate class frequencies. 6.(a) Define Yule's coefficient of association (Q) and coefflcient of colligation (Y), Show that' g - 2y