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31 Statistics Questions And Answers

1⟩ What is linear regression?

Modeling the relationship between a scalar variable y and one or more variables denoted X. In linear regression, models of the unknown parameters are estimated from the data using linear functions.

polyfit( x,y2,1) %return 2.1667 -1.3333, i.e 2.1667x-1.3333

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2⟩ What is null hypothesis?

The null hypothesis (denote by H0 ) is a statement about the value of

a population parameter (such as mean), and it must contain the condition of equality and must be written with the symbol =, ≤, or ≤.

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3⟩ Explain central limit theorem?

As the sample size increases, the sampling distribution of sample

means approaches a normal distribution

If all possible random samples of size n are selected from a population with mean μ and standard deviation σ, the mean of the sample means is denoted by μ x̄ , so

μ x̄ = μ

the standard deviation of the sample means is:

σ x̄ = σ⁄√ n

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4⟩ Explain hash table?

A hash table is a data structure used to implement an associative array, a structure that can map keys to values. A hash table uses a hash function to compute an index into an array of buckets or slots, from which the correct value can be found.

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5⟩ Do you know what is binary search?

For binary search, the array should be arranged in ascending or descending order. In each step, the algorithm compares the search key value with the key value of the middle element of the array. If the keys match, then a matching element has been found and its index, or position, is returned. Otherwise, if the search key is less than the middle element's key, then the algorithm repeats its action on the sub-array to the left of the middle element or, if the search key is greater, on the sub-array to the right.

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7⟩ What is significance level?

The probability of rejecting the null hypothesis when it is called

the significance level α , and very common choices are

α = 0.05 and α = 0.01

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8⟩ Give example of Central Limit Theorem?

Given that the population of men has normally distributed weights, with a mean of 173 lb and a standard deviation of 30 lb, find the probability that

a. if 1 man is randomly selected, his weight is greater than 180 lb.

b. if 36 different men are randomly selected, their mean weight is greater that 180 lb.

Solution: a) z = (x - μ)/ σ = (180-173)/30 = 0.23

For normal distribution P(Z>0.23) = 0.4090

b) σ x̄ = σ/√n = 20/√ 36 = 5

z= (180-173)/5 = 1.40

P(Z>1.4) = 0.0808

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10⟩ What is one sample t-test?

T-test is any statistical hypothesis test in which the test statistic follows a Student's t distribution if the null hypothesis is supported.

[h,p,ci] = ttest(y2,0)% return 1 0.0018 ci =2.6280 7.0863

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11⟩ What is covariance?

Measure of how much two variables change together

y2=[1 3 4 5 6 7 8]

cov(x,y2) %return 2*2 matrix, diagonal represents variance

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12⟩ What is moment?

Quantitative measure of the shape of a set of points.

moment(x, 2); %return second moment

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13⟩ What is kurtosis?

Kurtosis is a measure of how outlier-prone a distribution is.

kurtosis(x) % return2.3594

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14⟩ What is skewness?

Skewness is a measure of the asymmetry of the data around the sample mean. If skewness is negative, the data are spread out more to the left of the mean than to the right. If skewness is positive, the data are spread out more to the right.

Skewness(x) % return-0.5954

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16⟩ What is quartile?

► first quartile (25th percentile)

► second quartile (50th percentile)

► third quartile (75th percentile)

► kth percentile

► prctile(x, 25) % 25th percentile, return 2.25

► prctile(x, 50) % 50th percentile, return 3, i.e. median

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17⟩ What is median?

Median is described as the numeric value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one

median(x) % return 3.

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18⟩ What are sampling methods?

There are four sampling methods:

► Simple Random (purely random),

► Systematic( every kth member of population),

► Cluster (population divided into groups or clusters)

► Stratified (divided by exclusive groups or strata, sample from each group) samplings.

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19⟩ What is mode?

The mode of a data sample is the element that occurs most often in the collection.

x=[1 2 3 3 3 4 4]

mode(x) % return 3, happen most

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20⟩ What is sampling?

Sampling is that part of statistical practice concerned with the selection of an unbiased or random subset of individual observations within a population of individuals intended to yield some knowledge about the population of concern.

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