Q.No.1. Read the following passage and observe the word length of each word. Make a frequency distribution of word length. “Statistics play an intrinsic role in computer science and vice versa. Statistics is used for data mining, speech recognition, vision and image analysis, data compression, artificial intelligence, and network and traffic modeling. A statistical background is essential for understanding algorithms and statistical properties that form the backbone of computer science. Typically, statistical approach to models tends to involve stochastic (random) models with prior knowledge of the data. The computer science approach, on the other hand, leans more to algorithmic models without prior knowledge of the data. Ultimately, these come together in attempts to solve problems.” Q.No.2. Show (prove by example) that the geometric mean of any two values is equal to the geometric mean of their arithmetic mean and harmonic mean Q.No.3. All children in a number of families were together in a party. Each child was asked to state the number of children’s in his (or her) family. Two children said on child, four children said two children and twelve children said three. i. How many families were in the party? ii. Calculate the arithmetic mean of the number of children per family Q.No.4. Mean and variance of marks of BSCS Section A are 62 and 16 respectively and that of BSSE Section B are 69 and 25 respectively, while the number of students are 30 and 40. Find out the combined mean. Which section has grater absolute dispersion? Which has greater relative dispersion? Q.No.5. UIIT is giving two training programmes. Two groups from BSSE were trained for the same task. For the first group trained by programme A, it took a mean of 28.74 hours with a variance of 79.39. For the second group trained by programme B, it took a mean of 20.5 hours with a variance of 54.76. Which training program has less variability in its performance? Q.No.6. (a) In a surprise checking of passenger in a local bus, 20 passengers without ticket were caught. The sum of squares and standard deviation of that amount found in their pocket were Rs. 2000 and 6 respectively. If the total fine imposed is equal to the amount discovered from them, and fine imposed is uniform. Find amount of fine to be paid by each passenger. (b): For the given data calculate Skewness by Karl Pearson’s method Weights in Kg 118-126 127-135 136-144 145-153 154-162 Number of item 2 6 10 4 3
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Q.No.1. Read the following passage and observe the word length of each word. Make a frequency distribution of word length.
“Statistics play an intrinsic role in computer science and vice versa. Statistics is used for data mining, speech recognition, vision and image analysis, data compression, artificial intelligence, and network and traffic modeling. A statistical background is essential for understanding algorithms and statistical properties that form the backbone of computer science. Typically, statistical approach to models tends to involve stochastic (random) models with prior knowledge of the data. The computer science approach, on the other hand, leans more to algorithmic models without prior knowledge of the data. Ultimately, these come together in attempts to solve problems.”
Q.No.2. Show (prove by example) that the geometric mean of any two values is equal to the geometric mean of their arithmetic mean and harmonic mean
Q.No.3. All children in a number of families were together in a party. Each child was asked to state the number of children’s in his (or her) family. Two children said on child, four children said two children and twelve children said three.
i. How many families were in the party?
ii. Calculate the arithmetic mean of the number of children per family
Q.No.4. Mean and variance of marks of BSCS Section A are 62 and 16 respectively and that of BSSE Section B are 69 and 25 respectively, while the number of students are 30 and 40. Find out the combined mean. Which section has grater absolute dispersion? Which has greater relative dispersion?
Q.No.5. UIIT is giving two training programmes. Two groups from BSSE were trained for the same task. For the first group trained by programme A, it took a mean of 28.74 hours with a variance of 79.39. For the second group trained by programme B, it took a mean of 20.5 hours with a variance of 54.76. Which training program has less variability in its performance?
Q.No.6. (a) In a surprise checking of passenger in a local bus, 20 passengers without ticket were caught. The sum of squares and standard deviation of that amount found in their pocket were Rs. 2000 and 6 respectively. If the total fine imposed is equal to the amount discovered from them, and fine imposed is uniform. Find amount of fine to be paid by each passenger.
(b): For the given data calculate Skewness by Karl Pearson’s method
|
Weights in Kg |
118-126 |
127-135 |
136-144 |
145-153 |
154-162 |
|
Number of item |
2 |
6 |
10 |
4 |
3 |
Step by step
Solved in 3 steps
