Applied Mathematics for Electrical Engineering (3130908)

Basic Statistics

BE | Semester 3 Unit : Basic Statistics

Q5 (a) Winter-2019 Define mean, median and mode for the ungrouped data.

Unit : Basic Statistics

Q5 (b) Winter-2019 Find the first four moments about mean $x = 5, 10, 8, 13, 4 .$

Unit : Basic Statistics

Q5 (c ( i )) Winter-2019 Attempt the following. In a distribution of two different groups the variances are 15 and 27. Whereas the third central moments are 32.4 and 67.56 respectively. Compare the skewness of two groups.

Unit : Basic Statistics

Q5 (c ( ii )) Winter-2019
Two automatic filling machines A and B are used to fill mixture of cement, concrete and beam. A random sample of beam on each machine showed following results.

$A$ $32$ $28$ $47$ $63$ $71$ $39$ $10$ $60$ $96$ $14$

$B$ $19$ $31$ $48$ $53$ $67$ $90$ $10$ $62$ $40$ $80$

Find standard deviation of each machine and also comment on the performance of the two machine.

Unit : Basic Statistics

Q5 (a) Winter-2019
The pH solution is measured eight times using the same instrument and data obtained are as follows:

$7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.16, 7.18$

Calculate the mean, variance and standard deviation.

Unit : Basic Statistics

Q5 (b) Winter-2019
In environmental geology computer simulation was employed to estimate how far a block from a collapsing rock wall bounce down a soil slope. Based on the depth, location and angle of block soil impact marks left on the slope of the actual rock fall, the following 10 rebounds lengths (meters) were estimated. Compute mean and standard deviation of the rebounds.
$10.2, 9.5, 8.3, 9.7, 9.5, 11.1, 7.8, 8.8, 9.5, 10 .$

Unit : Basic Statistics

Q5 (c ( i )) Winter-2019
Attempt the following.

Find the coefficient of quartile deviation for the following data: $6, 8, 10, 4, 20, 18, 16, 14, 12, 10 .$ .

Unit : Basic Statistics

Q5 (c ( ii )) Winter-2019
State the formula for coefficient of skewness based on central moments and find it for the following frequency distribution.

Class 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75

y 8 10 15 17 8

Unit : Basic Statistics