Interpretation of Data Questions and Answers

Q: Arithmetic mean of 12 observations is 40. The smallest and the largest observations are 20 and 60 respectively. If we ignore the smallest and the largest observations then the arithmetic mean of the remaining observations ....................... .

The mean will not change.\[ \begin{aligned} \text{total} &= 12 \times 40 = 480 \\ \text{removed} &= 20 + 60 = 80 \\ \text{new mean} &= \frac{480 - 80}{10} = 40 \end{aligned} \]The two values removed average exactly 40, the same as the overall mean, so taking them out leaves the mean unchanged. The data are sufficient, because only the total is needed, not each observation.

Q: If a frequency distribution has some extreme scores, then appropriate measure of variability will be .........

The appropriate measure is the quartile deviation.The quartile deviation is half the distance between the first and third quartiles, so it depends only on the middle 50% of the scores and is not affected by extreme values at either end.The range is decided entirely by the two extreme scores, and the average deviation and standard deviation use every score, so extreme values distort all three.For the same reason the median, rather than the mean, is the preferred average for such skewed data.

Q: ............. is commonly used in the context of analysis of variance (ANOVA).

The F-test is used in ANOVA.Analysis of variance tests whether the means of three or more groups differ. It compares the variance between the group means with the variance within the groups, and their ratio is the F statistic, with \(s^{2}\) standing for each variance:\[ F = \frac{s^{2}_{\text{between}}}{s^{2}_{\text{within}}} \]A large F shows that the groups differ more than chance would allow. The t-test and Z-test compare two means at a time, and the chi-square test is used for frequency data, testing association or goodness of fit, not for comparing means through variance.

Q: Type-I error in research occurs when :

A Type-I error occurs when the null hypothesis is rejected even if it is true.In hypothesis testing, a Type I error is a false positive: the researcher concludes there is an effect or difference when there is none. Its probability is the significance level, alpha, usually set at 0.05.Accepting a false null hypothesis is the other mistake, a Type II error (a false negative), whose probability is beta. The options about rejecting the alternative hypothesis, or both hypotheses together, do not describe either standard error.

Q: From statistical point of view which measurement scale is of lowest level scale ?

The lowest level scale is the nominal scale.Stevens's four levels of measurement, from lowest to highest, are nominal, ordinal, interval and ratio. A nominal scale only names or classifies, such as gender, religion or blood group. The numbers attached have no order or size, so only counting and the mode can be used.The ordinal scale adds rank order, the interval scale (printed 'Internal scale') adds equal distances between values, and the ratio scale adds a true zero, which makes it the highest level.

Q: A test of statistical significance indicates how confident the researcher is about :

It indicates confidence about generalizing their finding from the sample to the population.A test of significance asks how likely it is that a result found in the sample, such as a difference or correlation, arose by chance from sampling. A significant result, for example at the 5 per cent level, lets the researcher infer with stated confidence that the result holds in the population from which the sample was drawn.Inter-coder reliability is measured with agreement statistics such as Cohen's kappa, and understanding bivariate and multivariate analysis is a matter of method, not of testing. Passing the driving test is an unrelated distractor.

Q: Mean, Median and Mode are :

Mean, median and mode are measures of central tendency.Each gives a single typical value around which the data cluster. The mean is the arithmetic average, the median is the middle value when the data are arranged in order, and the mode is the most frequent value.Measures of deviation (dispersion), such as range, standard deviation and variance, describe the spread of data. Measures of association, such as correlation coefficients, describe the relationship between two variables, and ways of sampling, such as random or stratified sampling, are methods of selecting cases, not summary statistics.

Q: The following (X, Y) points are plotted on X-Y plane and the adjacent points are joined by smooth curve :XY160230320415512What will be the nature of curve ?

The curve is a Hyperbola.For every point the product XY is the same: 1 x 60 = 2 x 30 = 3 x 20 = 4 x 15 = 5 x 12 = 60. So the points lie on XY = 60, that is \(Y = \frac{60}{X}\), a rectangular hyperbola: Y is inversely proportional to X.A straight line needs equal changes in Y for equal steps in X (here they are 30, 10, 5, 3). Y falls but not by a constant ratio (30/60 = 0.5, 20/30 = 0.67), so it is not exponential, and a parabola would turn upward again.

Q: Birth rates and Death rates per thousand :YearBirth rateDeath rate19619020197188181981821719917816200175142011701220216010From the above table in which years do you see the difference between Birth rate and Death rate the same ?

The difference is the same in 1961 and 1971.Subtract the death rate from the birth rate for each year: 1961: 90 - 20 = 70; 1971: 88 - 18 = 70; 1981: 82 - 17 = 65; 1991: 78 - 16 = 62; 2001: 75 - 14 = 61; 2011: 70 - 12 = 58; 2021: 60 - 10 = 50.Only 1961 and 1971 share a difference, 70 per thousand. The pairs 2011-2021 (58, 50), 2001-2011 (61, 58) and 1971-1981 (70, 65) all differ.

41.

Arithmetic mean of 12 observations is 40. The smallest and the largest observations are 20 and 60 respectively. If we ignore the smallest and the largest observations then the arithmetic mean of the remaining observations ....................... .

A.will increase
B.will decrease
C.will not change
D.cannot be obtained due to insufficient data

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: C

The mean will not change.

\[ \begin{aligned} \text{total} &= 12 \times 40 = 480 \\ \text{removed} &= 20 + 60 = 80 \\ \text{new mean} &= \frac{480 - 80}{10} = 40 \end{aligned} \]

The two values removed average exactly 40, the same as the overall mean, so taking them out leaves the mean unchanged. The data are sufficient, because only the total is needed, not each observation.

Discuss in Forum

42.

If a frequency distribution has some extreme scores, then appropriate measure of variability will be .........

A.Range
B.Quartile Deviation
C.Average Deviation
D.Standard Deviation

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: B

The appropriate measure is the quartile deviation.

The quartile deviation is half the distance between the first and third quartiles, so it depends only on the middle 50% of the scores and is not affected by extreme values at either end.

The range is decided entirely by the two extreme scores, and the average deviation and standard deviation use every score, so extreme values distort all three.

For the same reason the median, rather than the mean, is the preferred average for such skewed data.

Discuss in Forum

43.

............. is commonly used in the context of analysis of variance (ANOVA).

A.F-test
B.Z-test
C.Chi-square test
D.t-test

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: A

The F-test is used in ANOVA.

Analysis of variance tests whether the means of three or more groups differ. It compares the variance between the group means with the variance within the groups, and their ratio is the F statistic, with \(s^{2}\) standing for each variance:

\[ F = \frac{s^{2}_{\text{between}}}{s^{2}_{\text{within}}} \]

A large F shows that the groups differ more than chance would allow. The t-test and Z-test compare two means at a time, and the chi-square test is used for frequency data, testing association or goodness of fit, not for comparing means through variance.

Discuss in Forum

44.

Type-I error in research occurs when :

A.Null hypothesis is rejected even if it is true
B.Null hypothesis is accepted even if it is false
C.Alternative hypothesis is rejected
D.Both the null and alternative hypothesis are rejected

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: A

A Type-I error occurs when the null hypothesis is rejected even if it is true.

In hypothesis testing, a Type I error is a false positive: the researcher concludes there is an effect or difference when there is none. Its probability is the significance level, alpha, usually set at 0.05.

Accepting a false null hypothesis is the other mistake, a Type II error (a false negative), whose probability is beta. The options about rejecting the alternative hypothesis, or both hypotheses together, do not describe either standard error.

Discuss in Forum

45.

From statistical point of view which measurement scale is of lowest level scale ?

A.Ratio scale
B.Ordinal scale
C.Nominal scale
D.Internal scale

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: C

The lowest level scale is the nominal scale.

Stevens's four levels of measurement, from lowest to highest, are nominal, ordinal, interval and ratio. A nominal scale only names or classifies, such as gender, religion or blood group. The numbers attached have no order or size, so only counting and the mode can be used.

The ordinal scale adds rank order, the interval scale (printed 'Internal scale') adds equal distances between values, and the ratio scale adds a true zero, which makes it the highest level.

Discuss in Forum

46.

A test of statistical significance indicates how confident the researcher is about :

A.the inter coder reliability of their structured interview schedule
B.Passing the driving test
C.Understanding the differences between bi-variate and multivariate analysis
D.Generalizing their finding from the sample to the population

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: D

It indicates confidence about generalizing their finding from the sample to the population.

A test of significance asks how likely it is that a result found in the sample, such as a difference or correlation, arose by chance from sampling. A significant result, for example at the 5 per cent level, lets the researcher infer with stated confidence that the result holds in the population from which the sample was drawn.

Inter-coder reliability is measured with agreement statistics such as Cohen's kappa, and understanding bivariate and multivariate analysis is a matter of method, not of testing. Passing the driving test is an unrelated distractor.

Discuss in Forum

47.

Mean, Median and Mode are :

A.Measures of deviation
B.Ways of sampling
C.Measures of association
D.Measures of central tendency

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: D

Mean, median and mode are measures of central tendency.

Each gives a single typical value around which the data cluster. The mean is the arithmetic average, the median is the middle value when the data are arranged in order, and the mode is the most frequent value.

Measures of deviation (dispersion), such as range, standard deviation and variance, describe the spread of data. Measures of association, such as correlation coefficients, describe the relationship between two variables, and ways of sampling, such as random or stratified sampling, are methods of selecting cases, not summary statistics.

Discuss in Forum

48.

The following (X, Y) points are plotted on X-Y plane and the adjacent points are joined by smooth curve :

X	Y
1	60
2	30
3	20
4	15
5	12

What will be the nature of curve ?

A.Straight line
B.Parabola
C.Hyperbola
D.Exponential curve

Exam Year(s)

MH SET - 2024, SET Exam - 2024,

Answer: C

The curve is a Hyperbola.

For every point the product XY is the same: 1 x 60 = 2 x 30 = 3 x 20 = 4 x 15 = 5 x 12 = 60. So the points lie on XY = 60, that is \(Y = \frac{60}{X}\), a rectangular hyperbola: Y is inversely proportional to X.

A straight line needs equal changes in Y for equal steps in X (here they are 30, 10, 5, 3). Y falls but not by a constant ratio (30/60 = 0.5, 20/30 = 0.67), so it is not exponential, and a parabola would turn upward again.

Discuss in Forum

49.

Birth rates and Death rates per thousand :

Year	Birth rate	Death rate
1961	90	20
1971	88	18
1981	82	17
1991	78	16
2001	75	14
2011	70	12
2021	60	10

From the above table in which years do you see the difference between Birth rate and Death rate the same ?

A.2011, 2021
B.2001, 2011
C.1971, 1981
D.1961, 1971

Exam Year(s)

MH SET - 2025, SET Exam - 2025,

Answer: D

The difference is the same in 1961 and 1971.

Subtract the death rate from the birth rate for each year: 1961: 90 - 20 = 70; 1971: 88 - 18 = 70; 1981: 82 - 17 = 65; 1991: 78 - 16 = 62; 2001: 75 - 14 = 61; 2011: 70 - 12 = 58; 2021: 60 - 10 = 50.

Only 1961 and 1971 share a difference, 70 per thousand. The pairs 2011-2021 (58, 50), 2001-2011 (61, 58) and 1971-1981 (70, 65) all differ.

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