Math Problem Solver

1. Find the median and mode of the following distribution:

Class : 150-160 160-170 170-180 180-190 190-200

Frequency: 5 7 10 8 3

2. The following table is structured regarding the age distribution of the patients admitted in the AGMC. Calculate mean, median, mode and variance of the patients.

Age(in years): 20-30 30-40 40-50 50-60 60-70

No. of patients: 5 15 30 22 8

3. Find the missing frequency of the following data, where total frequency is 230, values of

median and mode are 33.5 and 34, respectively.

Class : 0-10 10-20 20-30 30-40 40-50 50-60 60-70

Frequency: 4 16 ? ? ? 6 4

4. Obtain the correlation coefficients of marks in Physics (x) and marks in Chemistry (y)

and interpret the result :

x : 74 45 80 48 92 68

y : 85 41 73 60 89 60

What will be expected score of a student in Chemistry, whose physics score is 86?

5. In a bivariate data set (X, Y ) of 25 observations the summary of some important measures

are as follows

XX = 125,

XX

2 = 650,

XY = 100,

XY

2 = 460,

XXY = 508.

Find out the correlation coefficient between X and Y .

6. The following are 12 determinants of the melting point of a compound (in degree Celsius)

made by analyst.

Determinants: 104.4, 99.7, 103.9, 102.1, 100.9, 100.8, 101.4, 102.2, 98.5, 103.4, 102.9, 97.7

The true melting point is 1020C. Would you conclude from these data that his determinants

are free from bias by considering two following cases?

(a) for known population variance 1.35,

(b) for unknown population variance.

(Given τ0.025 = 1.96, t0.025,11 = 2.201).

7. In the population, the average IQ is 100 with a standard deviation of 15. A team of

scientists want to test a new medication to see if it has either a positive or negative effect on

intelligence, or not effect at all. A sample of 30 participants who have taken the medication

has a mean of 140. Did the medication affect intelligence?

8. A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random form the call an given a math proficiency test.

The professor wants the class to be able to score above 70 on the test. The six students get

the following scores: 62, 92, 75, 68, 83, 95. (Given t0.1,5 = 2.1328)

9. (a) In 2007, there will be three candidates for the position of principal - Dr. Singh, Dr.

Reddy and Dr. Chatterjii , whose chances of getting appointment are in 2:3:4, respectively.

The probability that Dr. Singh if selected would introduce co-education in this college is

0.75. The probabilities of Dr. Reddy and Dr. Chatterjii doing the same are respectively 0.3

and 0.2.

(i) What is th probability that there will be co-education in 2003?

(ii) If there is co-education in 2003, what is the probability that Dr. Chatterjii is the principal?

10. The following four different treatments are applied to the patients of a certain disease

and also noted that the number of days, corresponding to each patient takes to recover.

Check whether the mean effects of the treatments are significantly differ at the level 0.05.

Given F0.05; 3,8 = 8.85

T reatment A : 10 12 13

T reatment B : 13 15 15

T reatment C : 16 17 20

T reatment D : 15 17 16