600 candidates were appeared in an examination. The boys outnumbered girls by 15% of all candidates. Number of passed exceeded the number of failed candidates by 300. Boys failing in the examination numbered 80. Determine the coefficient of association.
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A statistician wanted to compare two methods A and B of teaching. He selected a random sample of 22 students. He grouped them into 11 pairs so that the students in pair have approximately equal scores on an intelligence test. In each pair one student was taught by method A and the other by method B and examined after the course. The marks obtained by both methods are given as:
| Methods | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |
| Method A | 24 | 29 | 19 | 14 | 30 | 19 | 27 | 30 | 20 | 28 | 11 | |
| Method B | 37 | 35 | 16 | 26 | 23 | 27 | 19 | 20 | 16 | 11 | 21 | |
The equations of two regression lines are given as follows:
Calculate (i) regression coefficients, and
; (ii) correlation coefficient r(x, y); (iii) Mean of X and Y; and (iv) the value of
if
.
Find the missing information from the following data:
| Group I | Group II | Group III | Combined | ||
| Number | 50 | ? | 90 | 200 | |
| Standard Deviation | 6 | 7 | ? | 7.746 | |
| Mean | 113 | ? | 115 | 116 | |
Calculate the first, second and third quartile for the following data:
| Class: | Below 30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80 and above | |||||||
| Frequency: | 69 | 167 | 207 | 65 | 58 | 27 | 10 | |||||||
A researcher collects the following information for two variables x and y: n = 20, r = 0.5, mean (x) = 15, mean (y) = 20, and
Later it was found that one pair of values (x, y) has been wrongly taken as (16, 30) whereas the correct values were (26, 35). Find the correct value of r(x, y)
Mean and Standard deviation of 18 observations are found to be 7 and 4, respectively. On comparing the original data, it was found that an observation 12 was miscopied as 21 in the calculations. Calculate correct mean and standard deviation.
If a, b, c, d are constants, then show that the coefficient of correlation between ax+b and cy+d is numerically equal to that between x and y.