Solve for the descret data below

What are the desiderata (requirements) of a good average? Compare the mean,

the median and the mode in the light of these desiderata? Why averages are

called measures of central tendency?

2. "Every average has its own peculiar characteristics. It is difficult to say which

average is the best." Explain with examples.

3. What do you understand .by 'Central Tendency'? Under what conditions is the

median more suitable than other measures of central tendency?

4. The average monthly salary paid to all employees in a company was Rs 8,000.

The average monthly salaries paid to male and female employees of the

company were Rs 10,600 and Rs 7,500 respectively. Find out the percentages

of males and females employed by the company.

5. Calculate the arithmetic mean from the following data:

Class 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89

Frequency 2 4 9 11 12 6 4 2

6. Calculate the mean, median and mode from the following data:

Height in Inches Number of Persons

62-63 2

63-64 6

64-65 14

65-66 16

66-67 8

67-68 3

68-69 1

Total 50

7. A number of particular articles have been classified according to their weights.

After drying for two weeks, the same articles have again been weighed and

similarly classified. It is known that the median weight in the first weighing 53

was 20.83 gm while in the second weighing it was 17.35 gm. Some

frequencies a and b in the first weighing and x and y in the second are missing.

It is known that a = 1/3x and b = 1/2 y. Find out the values of the missing

frequencies.

Class Frequencies

First Weighing Second Weighing

0- 5 a z

5-10 b y

10-15 11 40

15-20 52 50

20-25 75 30

25-30 22 28

8 Cities A, Band C are equidistant from each other. A motorist travels from A to

B at 30 km/h; from B to C at 40 km/h and from C to A at 50 km/h. Determine

his average speed for the entire trip.

9 Calculate the harmonic mean from the following data:

Class-Interval 2-4 4-6 6-8 8-10

Frequency 20 40 30 10

10 A vehicle when climbing up a gradient, consumes petrol @ 8 km per litre.

While coming down it runs 12 km per litre. Find its average consumption for

to and fro travel between two places situated at the two ends of 25 Ian long

gradient.

[3] A chip manufacturing company manufactures chips independently. Each manufactured chip is either good or defective. Based on the company's data, with probability 0.18, one out of every two manufactured chips is defective. It is also known that the probability of a defective chip is smaller than 0.5. Find the probability that (a) [9 pts] more than two chips are defective out of 100 manufactured chips (b) [8 pts] the 34" chip and one other chip is defective out of the first 100 manufactured chips (c) [8 pts] 2 chips among the first 50 manufactured chips and I chip among the second 50 manufactured chips are defective.an19 Problem 4 (10 marks) The screens used for certain type of cell phone are manufactured by three companies, A, B, and C. The proportions of screens supplied by A, B, and C are 0.5, 0.3, and 0.2, respectively. and their screens are defective with probabilities 0.01, 0.02 and 0.03, respectively. Given that the screen on a randomly selected phone is defective, what is the probability that Company A manufactured it?There is about 80% chance that a randomly selected person aged 20 will still be alive at age 65, according to the U.S. National Center for Health Statistics. Suppose that you randomly select forty 20-year-olds. [a] What is the probability that at least 35 of the 40 persons are still alive at age 65? Math formula: (Write the mathematical formula, with standard notation, for the probability.) Excel commands: Numerical answer: [b] What is the probability that between 10 and 25 (both inclusive) persons are alive at age 65? Math formula: (Write the mathematical formula, with standard notation, for the probability.) Excel commands: Numerical answer:Problem 4 Each year, ratings are compiled concerning the performance of new cars during the first 90 days of use. Suppose that the cars have been categorized according to whether the car needs warranty-related repair (yes or no) and the country in which the company manufacturing the car is based (United States or not United States). Based on the data collected, the probability that the new car needs a warranty repair is 0.04, the probability that it was manufactured by a U.S-based company is 0.60, and the probability that the new car needs a warranty repair and was manufactured by a U.S. - based company is 0.025. a. Suppose you know that a company based in the United States manufactures a particular car. What is the probability that the car needs warranty repair