Contents

## Statistical Questions

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1.Which of the following measures of central tendency will always change if a single value in the data changes?
Ans-
Mean
Solution-
The mean of the dataset would always change if we change any value of the data set. Since we are summing up all the values together to get it, every value of the data set contributes to its value. Median and mode may or may not change with altering a single value in the dataset.
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2.If the variance of a dataset is correctly computed with the formula using (n – 1) in the denominator, which of the following option is true?
Ans-
Dataset is a sample
Solution-
If the variance has n-1 in the formula, it means that the set is a sample. We try to estimate the population variance by dividing the sum of squared difference with the mean with n-1.
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When we have the actual population data we can directly divide the sum of squared differences with n instead of n-1
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3.If a positively skewed distribution has a median of 50, which of the following statement is true?
Ans-
Mean is greater than 50
Mode is less than 50
Solution-
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4.Which of the following statements are true about Bessels Correction while calculating a sample standard deviation?
Ans-
Bessels correction is used when we are trying to estimate population standard deviation from the sample.
Bessels corrected standard deviation is less biased.
Solution-
Contrary to the popular belief Bessel’s correction should not be always done. It’s basically done when we’re trying to estimate the population standard deviation using the sample standard deviation. The bias is definitely reduced as the standard deviation will now(after correction) be depicting the dispersion of the population more than that of the sample.
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5.Standard deviation is robust to outliers?
Ans-
False
Solution-
If you look at the formula for standard deviation above, a very high or a very low value would increase standard deviation as it would be very different from the mean. Hence outliers will effect standard deviation.
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6.What would be the critical values of Z for 98% confidence interval for a two-tailed test ?
Ans-
+/- 2.33
Solution-
We need to look at the z table for answering this. For a 2 tailed test, and a 98% confidence interval, we should check the area before the z value as 0.99 since 1% will be on the left side of the mean and 1% on the right side. Hence we should check for the z value for area>0.99. The value will be +/- 2.33
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## List Of Statistical Questions

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1.Which of these measures are used to analyze the central tendency of data?
Ans-
Mean, Median and Mode
Solution-
The mean, median, mode are the three statistical measures which help us to analyze the central tendency of data. We use these measures to find the central value of the data to summarize the entire data set.
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2.Five numbers are given: (5, 10, 15, 5, 15). Now, what would be the sum of deviations of individual data points from their mean?
Ans-
0
Solution-
The sum of deviations of the individual will always be 0.
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3.A test is administered annually. The test has a mean score of 150 and a standard deviation of 20. If Ravi’s z-score is 1.50, what was his score on the test?
Ans-
180
Solution-
X= μ+Zσ where μ is the mean, σ is the standard deviation and X is the score we’re calculating. Therefore X = 150+20*1.5 = 180
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4.What would be the Type I error?
Ans-
Concluding that listening to music while studying improves memory when it actually doesn’t.
Solution-
Type 1 error means that we reject the null hypothesis when its actually true. Here the null hypothesis is that music does not improve memory. Type 1 error would be that we reject it and say that music does improve memory when it actually doesn’t.
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5.On average, how old are the dogs that live on this street?
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6.What proportion of the students at your school like watermelons?
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## Good Statistical Questions Examples

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Question 1. What Is Likelihood?
Answer :
The probability of some observed outcomes given a set of parameter values is regarded as the likelihood of the set of parameter values given the observed outcomes.
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Question 2. What Is Mode?
Answer :
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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Question 3. What Is Median?
Answer :
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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Question 4. What Is Skewness?
Answer :
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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Question 5. What Is Variance?
Answer :
variance describes how far values lie from the mean.
var(x) %return 1.1429
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Question 6. What Is P-value?
Answer :
In statistical significance testing, the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. If the p-value is less than 0.05 or 0.01, corresponding respectively to a 5% or 1% chance of rejecting the null hypothesis when it is true.
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Question 7. What Is Bayesian?
Answer :
Bayesians condition on the data actually observed and consider the probability distribution on the hypotheses.
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## Basic Statistics Questions And Answers

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Question 1. What Is Frequentist?
Answer :
Frequentists condition on a hypothesis of choice and consider the probability distribution on the data, whether observed or not.
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Question 2. What Is Kurtosis?
Answer :
Kurtosis is a measure of how outlier-prone a distribution is.
kurtosis(x) % return2.3594
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Question 3. What Is Moment?
Answer :
Quantitative measure of the shape of a set of points.
moment(x, 2); %return second moment
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Question 4. What Is Covariance?
Answer :
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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Question 5. What Is One Sample T-test?
Answer :
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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Question 6. What Is Alternative Hypothesis?
Answer :
The Alternative hypothesis (denoted by H1 ) is the statement that must be true if the null hypothesis is false.
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Question 7. What Is Significance Level?
Answer :
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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## Non Statistical Questions

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How many days are in March?
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How old is your dog?
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Do you like watermelons?
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How many bricks are in this wall?
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What was the temperature at noon today at City Hall?
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