MTH302 Practice Questions Lectures 23-40 Updated

Lecture#23

1. What are the main methods of presentation of data? 2. Differentiate between line graph and sector graph.

Lecture#24

1. Calculate the mean , median and mode for the following data 13, 18, 13, 14, 13, 16, 14, 21, 13.

Answer: Mean=15, median=14, mode=13.

2. Calculate the range, class width, frequency and relative frequency for the following data 36, 48, 54, 92, 57, 63, 66, 76, 66, 80.

Answer: Range=56, class width=10.

Lecture#25

1. Calculate the arithmetic mean of the following grouped data Distance 1-10 11-20 21-30 31-40 Number of persons

Answer: Arithmetic mean=24.5

2. A die is thrown 20 times and the following scores are recorded 6, 3, 2, 4, 5, 5, 6, 1, 3, 3, 5, 6, 6, 1, 3, 3, 5, 6, 6, 2. Find its arithmetic mean.

Answer: Arithmetic mean=4.05

3. Calculate the frequency for the following data using MS Excel. 80, 75, 90, 69, 83, 55, 79, 93, 58, 94, 89.

Lecture#26

1. Find the mean using the empirical relationship if median=15 and mode=22.

Answer: Mean=11.5

2. Find the geometric mean and harmonic mean of 80, 85, 90, 95, 100.

Answer: Geometric mean=89.72 and Harmonic mean=89.44

3. Check whether the following data set is symmetric, positively skewed or negatively skewed. 27, 28, 30, 32, 34, 38, 41, 42, 44, 44, 46, 53, 56, 62.

Answer: Positively skewed.

Lecture#27

1. Find all the quartiles for the following data set 18, 20, 23, 20, 23, 27, 24, 23, 29.

Answer: Q1=20, Q2=23 and Q3=25.5

2. Calculate the mid hinge and quartile deviation for the following data set 4, 17, 7, 14, 18, 12, 3, 16, 10, 4, 4, 11.

Answer: Mid hinge=9.75 and Quartile deviation=5.75

3. Find the range and midrange of the data set 14, 10, 17, 5, 9, 20, 8, 24, 22.

Answer: Range=19, midrange=14.5

Lecture#28

1. Calculate the standard deviation of first ten natural numbers (1-10).

Answer: 2.872

2. Marks obtained by few students in a quiz are 5, 6, 2, 3, 1, 7, 4, 8. Find the variance and coefficient of variance of the sample.

Answer: Variance=5.25 and coefficient of variance=51%.

3. Team A scored the following number of goals in their last 20 matches: 3, 0, 1, 5, 4, 3, 2, 6, 4, 2, 3, 3, 0, 7, 1, 1, 2, 3, 4, 6. Calculate the mean deviation about the mean.

Answer: Mean deviation=1.5

Lecture#29

1. Calculate the correlation coefficient for the following data X y

Answer: 0.268

2. Find the value of cov(x,y), if var(x)=100, var(y)=25 and correlation coefficient r=0.5.

Answer: cov(x,y)=25

Lecture#30

1. Find the least square regression line y=a+bx for the following data X y

Answer: y=2.2+0.9x

2. Calculate the intercept of regression line y=a+bx, if its slope is 0.55 associated with following data X y

Answer: 1.25

3. Find the slope of the regression line y=a+bx for the following data X y

Answer: 0.15

Lecture # 31 · Question: · Given  · 400, · 5, · 4, · 4, · 3,

X Y

XY · X · Y · S · S · n · . Compute the coefficient of correlation · Solution: · = 0.55 · r · Question:

Determine whether two variables 𝑋 and 𝑌 are correlated or uncorrelated by using the following

table · 𝑋 · 𝑌 · Solution: · =− 1 · r · Question:

the line is 0.5. Determine whether 𝑌 intercept is positive or negative.

𝑋 · 𝑌 · Solution: · 5.73 · a = · Question:

Using the following table find 𝑌 intercept, slope and equation of regression line.

𝑋 · 𝑌 · Solution: · Intercept = 4 · Slope = 0.5 · Y = 4 + 0.5 X