Advertisements
Advertisements
Find variance and S.D. for the following set of numbers.
25, 21, 23, 29, 27, 22, 28, 23, 27, 25
(Given `sqrt(6.6)` = 2.57)
Concept: undefined >> undefined
Following data gives no. of goals scored by a team in 100 matches:
| No. of goals scored | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of matches | 15 | 20 | 25 | 15 | 20 | 5 |
Compute the variance and standard deviation for the above data.
Concept: undefined >> undefined
Advertisements
The value of the machine depreciates at the rate of 15% p.a. It was purchased 2 years ago. Its present value is Rs. 7225. What was the purchase price of the machine?
Concept: undefined >> undefined
A tree increases annually by 1/8 of its height. By how much will it increase after 2½ years. If its length today is 8 m.?
Concept: undefined >> undefined
A building worth Rs. 121000 is constructed on land worth Rs. 81000. After how many years will the value of both be the same if land appreciates at 10% pa. and buildings depreciate at 10% p.a.
Concept: undefined >> undefined
Following data gives the coded price (X) and demand (Y) of a commodity.
| Price | 5 | 7 | 9 | 8 | 10 | 7 | 9 | 8 | 5 | 11 | 11 | 10 | 2 | 3 | 9 |
| Demand | 9 | 15 | 13 | 15 | 14 | 10 | 11 | 14 | 10 | 14 | 6 | 14 | 15 | 11 | 12 |
| Price | 2 | 4 | 3 | 14 | 6 | 10 | 7 | 15 | 8 | 6 | 5 | 6 | 11 | 14 | 15 |
| Demand | 6 | 11 | 8 | 11 | 10 | 15 | 9 | 15 | 13 | 9 | 14 | 10 | 7 | 5 | 6 |
Classify the data by taking classes 0 – 4, 5 – 9, etc. for X and 5 – 8, 9 – 12, etc. for Y. Also find conditional frequency distribution of Y when X is less than 10
Concept: undefined >> undefined
Following data gives the age in years and marks obtained by 30 students in an intelligence test.
| Age | 16 | 17 | 22 | 19 | 21 | 16 |
| Marks | 16 | 19 | 39 | 50 | 48 | 41 |
| Age | 21 | 20 | 20 | 23 | 22 | 19 |
| Marks | 59 | 44 | 42 | 62 | 37 | 67 |
| Age | 23 | 20 | 22 | 22 | 23 | 22 |
| Marks | 45 | 57 | 35 | 37 | 38 | 56 |
| Age | 17 | 18 | 16 | 21 | 19 | 20 |
| Marks | 54 | 61 | 47 | 67 | 49 | 56 |
| Age | 17 | 18 | 23 | 21 | 20 | 16 |
| Marks | 51 | 42 | 65 | 56 | 52 | 48 |
Prepare a bivariate frequency distribution by taking class intervals 16 – 18, 18 – 20, … etc. for age and 10 – 20, 20 – 30, … etc. for marks. Find conditional frequency distribution of marks obtained when the age of students is between 20 – 22.
Concept: undefined >> undefined
Following data gives Sales (in Lakh ₹) and Advertisement Expenditure (in Thousand ₹) of 20 firms. (115, 61) (120, 60) (128, 61) (121, 63) (137, 62) (139, 62) (143, 63) (117, 65) (126, 64) (141, 65) (140, 65) (153, 64) (129, 67) (130, 66) (150, 67) (148, 66) (130, 69) (138, 68) (155, 69) (172, 68) Conditional frequency distribution of Sales when the advertisement expenditure is between 64 – 66 (Thousand ₹)
Concept: undefined >> undefined
Following data gives Sales (in Lakh Rs.) and Advertisement Expenditure (in Thousand Rs.) of 20 firms.
(115, 61) (120, 60) (128, 61) (121, 63) (137, 62) (139, 62) (143, 63) (117, 65) (126, 64) (141, 65) (140, 65) (153, 64) (129, 67) (130, 66) (150, 67) (148, 66) (130, 69) (138, 68) (155, 69) (172, 68)
Conditional frequency distribution of advertisement expenditure when the sales are between 125 – 135 (lakh Rs.)
Concept: undefined >> undefined
Prepare a bivariate frequency distribution for the following data, taking class intervals for X as 35 – 45, 45 – 55, …. etc and for Y as 115 – 130, 130 – 145, … etc. where X denotes the age in years and Y denotes blood pressure for a group of 24 persons.
(55, 151) (36, 140) (72, 160) (38, 124) (65, 148) (46, 130) (58, 152) (50, 149) (38, 115) (42, 145) (41, 163) (47, 161) (69, 159) (60, 161) (58, 131) (57, 136) (43, 141) (52, 164) (59, 161) (44, 128) (35, 118) (62, 142) (67, 157) (70, 162)
Also, find Conditional frequency distribution of Y when X ≤ 45.
Concept: undefined >> undefined
Two series of x and y with 50 items each have standard deviations of 4.8 and 3.5 respectively. If the sum of products of deviations of x and y series from respective arithmetic means is 420, then find the correlation coefficient between x and y.
Concept: undefined >> undefined
Find the number of pairs of observations from the following data,
r = 0.15, `sigma_"y"` = 4, `sum("x"_"i" - bar"x")("y"_"i" - bar"y")` = 12, `sum("x"_"i" - bar"x")^2` = 40.
Concept: undefined >> undefined
Given that r = 0.4, `sigma_"y"` = 3, `sum("x"_"i" - bar"x")("y"_"i" - bar"y")` = 108, `sum("x"_"i" - bar"x")^2` = 900. Find the number of pairs of observations.
Concept: undefined >> undefined
Given the following information, `sum"x"_"i"^2` = 90, `sum"x"_"i""y"_"i"` = 60, r = 0.8, `sigma_"y"` = 2.5, where xi and yi are the deviations from their respective means, find the number of items.
Concept: undefined >> undefined
A sample of 5 items is taken from the production of a firm. Length and weight of 5 items are given below. [Given : `sqrt(0.8823)` = 0.9393]
| Length (cm) | 3 | 4 | 6 | 7 | 10 |
| Weight (gm.) | 9 | 11 | 14 | 15 | 16 |
Calculate the correlation coefficient between length and weight and interpret the result.
Concept: undefined >> undefined
If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between 2x and y
Concept: undefined >> undefined
If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between `"x"/2` and y
Concept: undefined >> undefined
If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x and 3y
Concept: undefined >> undefined
If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x – 5 and y – 3
Concept: undefined >> undefined
If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x + 7 and y + 9
Concept: undefined >> undefined
