41 questions on Statistics for data scientists & analysts Flashcards
Questions & Solution 1) Which of these measures are used to analyze the central tendency of data? A) Mean and Normal Distribution B) Mean, Median and Mode C) Mode, Alpha & Range D) Standard Deviation, Range and Mean E) Median, Range and Normal Distribution
Solution: (B) 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.
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? A) 10 B)25 C) 50 D) 0 E) None of the above
Solution: (D) The sum of deviations of the individual will always be 0.
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? A) 180 B) 130 C) 30 D) 150 E) None of the above
Solution: (A) 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
4) Which of the following measures of central tendency will always change if a single value in the data changes? A) Mean B) Median C) Mode D) All of these
Solution: (A) 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.
5) Below, we have represented six data points on a scale where vertical lines on scale represent unit. Which of the following line represents the mean of the given data points, where the scale is divided into same units? https://s3-ap-south-1.amazonaws.com/av-blog-media/wp-content/uploads/2017/02/27134903/Image_21.jpg A) A B) B C) C D) D
Solution: (C) It’s a little tricky to visualize this one by just looking at the data points. We can simply substitute values to understand the mean. Let A be 1, B be 2, C be 3 and so on. The data values as shown will become {1,1,1,4,5,6} which will have mean to be 18/6 = 3 i.e. C.
6) If a positively skewed distribution has a median of 50, which of the following statement is true?
A) Mean is greater than 50
B) Mean is less than 50
C) Mode is less than 50
D) Mode is greater than 50
E) Both A and C
F) Both B and D
Solution: (E)
Below are the distributions for Negatively, Positively and no skewed curves.
As we can see for a positively skewed curve, Mode<median>
</median>
7) Which of the following is a possible value for the median of the below distribution?
A) 32
B) 26
C) 17
D) 40
Solution: (B)
To answer this one we need to go to the basic definition of a median. Median is the value which has roughly half the values before it and half the values after. The number of values less than 25 are (36+54+69 = 159) and the number of values greater than 30 are (55+43+25+22+17= 162). So the median should lie somewhere between 25 and 30. Hence 26 is a possible value of the median.
8) Which of the following statements are true about Bessels Correction while calculating a sample standard deviation?
Bessels correction is always done when we perform any operation on a sample data.
Bessels correction is used when we are trying to estimate population standard deviation from the sample.
Bessels corrected standard deviation is less biased.
A) Only 2
B) Only 3
C) Both 2 and 3
D) Both 1 and 3
Solution: (C)
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.
9) 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?
A) Dataset is a sample
B) Dataset is a population
C) Dataset could be either a sample or a population
D) Dataset is from a census
E) None of the above
Solution: (A)
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.
When we have the actual population data we can directly divide the sum of squared differences with n instead of n-1.
13) What would be the critical values of Z for 98% confidence interval for a two-tailed test ?
A) +/- 2.33
B) +/- 1.96
C) +/- 1.64
D) +/- 2.55
Solution: (A)
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
Context for Questions 15-17
Studies show that listening to music while studying can improve your memory. To demonstrate this, a researcher obtains a sample of 36 college students and gives them a standard memory test while they listen to some background music. Under normal circumstances (without music), the mean score obtained was 25 and standard deviation is 6. The mean score for the sample after the experiment (i.e With music) is 28.
15) What is the null hypothesis in this case?
A) Listening to music while studying will not impact memory.
B) Listening to music while studying may worsen memory.
C) Listening to music while studying may improve memory.
D) Listening to music while studying will not improve memory but can make it worse.
Solution: (D)
The null hypothesis is generally assumed statement, that there is no relationship in the measured phenomena. Here the null hypothesis would be that there is no relationship between listening to music and improvement in memory.
Context for Questions 15-17
Studies show that listening to music while studying can improve your memory. To demonstrate this, a researcher obtains a sample of 36 college students and gives them a standard memory test while they listen to some background music. Under normal circumstances (without music), the mean score obtained was 25 and standard deviation is 6. The mean score for the sample after the experiment (i.e With music) is 28.
16) What would be the Type I error?
A) Concluding that listening to music while studying improves memory, and it’s right.
B) Concluding that listening to music while studying improves memory when it actually doesn’t.
C) Concluding that listening to music while studying does not improve memory but it does.
Solution: (B)
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.
Context for Questions 15-17
Studies show that listening to music while studying can improve your memory. To demonstrate this, a researcher obtains a sample of 36 college students and gives them a standard memory test while they listen to some background music. Under normal circumstances (without music), the mean score obtained was 25 and standard deviation is 6. The mean score for the sample after the experiment (i.e With music) is 28.
17) After performing the Z-test, what can we conclude ____ ?
A) Listening to music does not improve memory.
B)Listening to music significantly improves memory at p
C) The information is insufficient for any conclusion.
D) None of the above
Solution: (B)
Let’s perform the Z test on the given case. We know that the null hypothesis is that listening to music does not improve memory.
Alternate hypothesis is that listening to music does improve memory.
In this case the standard error i.e.
The Z score for a sample mean of 28 from this population is
Z critical value for α = 0.05 (one tailed) would be 1.65 as seen from the z table.
Therefore since the Z value observed is greater than the Z critical value, we can reject the null hypothesis and say that listening to music does improve the memory with 95% confidence.
18) A researcher concludes from his analysis that a placebo cures AIDS. What type of error is he making?
A) Type 1 error
B) Type 2 error
C) None of these. The researcher is not making an error.
D) Cannot be determined
Solution: (D)
By definition, type 1 error is rejecting the null hypothesis when its actually true and type 2 error is accepting the null hypothesis when its actually false. In this case to define the error, we need to first define the null and alternate hypothesis.
19) What happens to the confidence interval when we introduce some outliers to the data?
A) Confidence interval is robust to outliers
B) Confidence interval will increase with the introduction of outliers.
C) Confidence interval will decrease with the introduction of outliers.
D) We cannot determine the confidence interval in this case.
Solution: (B)
We know that confidence interval depends on the standard deviation of the data. If we introduce outliers into the data, the standard deviation increases, and hence the confidence interval also increases.
Question Context 23-25
A researcher is trying to examine the effects of two different teaching methods. He divides 20 students into two groups of 10 each. For group 1, the teaching method is using fun examples. Where as for group 2 the teaching method is using software to help students learn. After a 20 minutes lecture of both groups, a test is conducted for all the students.
We want to calculate if there is a significant difference in the scores of both the groups.
It is given that:
Alpha=0.05, two tailed.
Mean test score for group 1 = 10
Mean test score for group 2 = 7
Standard error = 0.94
25) What percentage of variability in scores is explained by the method of teaching?
A) 36.13
B) 45.21
C) 40.33
D) 32.97
Solution: (A)
The % variability in scores is given by the R2 value. The formula for R2 given by
R2 =
The degrees of freedom in this case would be 10+10 -2 since there are two groups with size 10 each. The degree of freedom is 18.
R2 = = 36.13
26) [True or False] F statistic cannot be negative.
A) TRUE
B) FALSE
Solution: (A)
F statistic is the value we receive when we run an ANOVA test on different groups to understand the differences between them. The F statistic is given by the ratio of between group variability to within group variability
Below is the formula for f Statistic.
Since both the numerator and denominator possess square terms, F statistic cannot be negative.
28) Correlation between two variables (Var1 and Var2) is 0.65. Now, after adding numeric 2 to all the values of Var1, the correlation co-efficient will_______ ?
A) Increase
B) Decrease
C) None of the above
Solution: (C)
If a constant value is added or subtracted to either variable, the correlation coefficient would be unchanged. It is easy to understand if we look at the formula for calculating the correlation.
If we add a constant value to all the values of x, the xi and will change by the same number, and the differences will remain the same. Hence, there is no change in the correlation coefficient.
