The frequency distribution of the marks obtained by the 25 students each of the two sections is given as follows:
| Marks: | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Section A: | 2 | 5 | 10 | 5 | 3 |
| Section B: | 3 | 7 | 8 | 5 | 2 |
Find which section is more consistent.
To determine which section is more consistent, we can calculate the measures of dispersion for each section. One commonly used measure of dispersion is the standard deviation. A smaller standard deviation indicates less variability and thus greater consistency.
Let's calculate the standard deviation for both sections:
For Section A:
Mean = (2*15 + 5*25 + 10*35 + 5*45 + 3*55) / 25
= (30 + 125 + 350 + 225 + 165) / 25
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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
.
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)
The frequency distribution of the marks obtained by the 25 students each of the two sections is given as follows:
| Marks: | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Section A: | 2 | 5 | 10 | 5 | 3 |
| Section B: | 3 | 7 | 8 | 5 | 2 |
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 | |
State whether the following statements are True or False and also give the reason in support of your answer.
a) If standard deviation of x is 5, standard deviation of y = 2x–3 is 7.
b) Mean deviation is least when calculated from the median.
c) The correlation coefficient between x and (a – x) is –1.
d) The regression coefficients byx and bxy of a data are 1.2 and 0.8, respectively.
e) If (AB) = 10, (αB) = 15, (Aβ) = 20 and (αβ) = 30 then A and B are associated.
Board of Directors of Labour Union wishes to sample the opinion of its members before submitting a change in its contribution at a forthcoming annual meeting. Questionnaires are sent to a random sample of 200 members in three union locals. The results of the survey are as follows:
| Union Locals | |||||||||||||
| Reaction | A | B | C | Total | |||||||||
| Favour Change | 35 | 45 | 20 | 100 | |||||||||
| Against Change | 15 | 25 | 16 | 56 | |||||||||
| No Response | 10 | 10 | 24 | 44 | |||||||||
| Total | 60 | 80 | 60 | 200 | |||||||||