SYIT Semester 4 Theory Revision Questions

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11 Questions

What is the median for the given data?

7

Calculate Q₁ and Q₃ from the provided data.

Q₁ = 15, Q₃ = 20

Determine the standard deviation of the heights of 10 students.

3.16

Create a Venn diagram and find the probability of a viewer watching all three games and exactly one of the three games.

a) 0.02, b) 0.18

What is the hypothesis being tested in the given data?

The hypothesis being tested is that the presence or absence of hypertension is independent of smoking habits.

What statistical test would you use to test the hypothesis in the given data?

Chi-square test for independence.

What type of distribution would you fit to the given data in question 18?

Poisson distribution.

Explain the concept of Karl Pearson's measure of skewness.

Karl Pearson's measure of skewness is a statistic that measures the asymmetry of a distribution. It indicates whether a distribution is symmetric, negatively skewed, or positively skewed.

What is the purpose of hypothesis testing and what are the types of hypotheses?

Hypothesis testing is a statistical method used to make inferences about a population using sample data. The two types of hypotheses are null hypothesis (H0) and alternative hypothesis (H1).

Explain the difference between one-tailed and two-tailed tests.

In a one-tailed test, the critical region is located in only one tail of the distribution, while in a two-tailed test, the critical region is split between both tails of the distribution.

How are raw moments related to central moments?

Raw moments are used to calculate central moments. Central moments are calculated based on deviations from the mean, while raw moments are calculated without considering the mean.

Study Notes

Descriptive Statistics

  • Median is a measure of central tendency that separates the upper half from the lower half of the data.

Quartiles

  • Q₁ (First Quartile or Lower Quartile) is the median of the lower half of the data.
  • Q₃ (Third Quartile or Upper Quartile) is the median of the upper half of the data.

Measures of Dispersion

  • Standard deviation is a measure of dispersion that indicates how much the data deviates from the mean.

Probability

  • A Venn diagram is a visual representation of events and their probabilities.
  • Probability of an event is the number of favorable outcomes divided by the total number of outcomes.

Hypothesis Testing

  • A hypothesis is a statement about a population parameter.
  • A statistical test is used to test a hypothesis.

Distribution Fitting

  • The type of distribution to fit to the data depends on the characteristics of the data.

Skewness

  • Karl Pearson's measure of skewness is a quantitative measure of skewness in a distribution.

Hypothesis Testing

  • The purpose of hypothesis testing is to make a decision about a population parameter based on a sample of data.
  • There are two types of hypotheses: null hypothesis and alternative hypothesis.

Types of Tests

  • One-tailed tests are used when the alternative hypothesis specifies a direction of difference.
  • Two-tailed tests are used when the alternative hypothesis does not specify a direction of difference.

Moments

  • Raw moments are summations of powers of values in a distribution.
  • Central moments are summations of powers of deviations from the mean in a distribution.

Prepare for the SYIT Semester 4 Regular Exam with this theory revision quiz. Topics covered include calculating median, Q1, Q3, class limits, and percentiles from given data sets. Test your understanding of statistical concepts with practice questions.

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