Interpretation of Data Questions and Answers

Q: What is the possible maximum number of students in Division B, who passed in all the four subjects ?

The possible maximum is 30.A student who passed in all four subjects is counted in every one of the four columns for Division B: 34 in English, 32 in Hindi, 36 in Marathi and 30 in History. The number who passed all four can therefore be no larger than the smallest of these counts, the 30 who passed History, and it can equal 30 if every History passer also passed the other three.34 and 36 are the English and Marathi counts and would require more students to pass all four than passed History. 26 is a possible value but not the maximum.

Q: The maximum possible number of students who passed in both Hindi and Marathi in three divisions combined is :

The maximum possible number is 93.In each division, the number passing both Hindi and Marathi can be at most the smaller of the two counts. The maximum for the three divisions combined is the sum of these:\[ \begin{aligned} A &: \min(30, 38) = 30 \\ B &: \min(32, 36) = 32 \\ C &: \min(34, 31) = 31 \\ \text{Total} &= 30 + 32 + 31 = 93 \end{aligned} \]96 is the total of the Hindi column (30 + 32 + 34), but division C has only 31 Marathi passers, so all 34 Hindi passers there cannot have passed Marathi. 105 is the Marathi total and 111 adds larger figures still, both impossible for the same reason.

Q: A ........................... is used to show exact values.

A table is used to show exact values.A table presents data in rows and columns as actual figures, so the reader can see each value exactly and look up precise numbers.Pie charts, bar diagrams and dot plots are graphical displays. They are good for showing proportions, comparisons and distributions at a glance, but the reader judges values from the size of slices, the height of bars or the position of dots, which gives only approximate values. When exact values matter, a table is the right choice.

Q: The following table presents the number of families in a village earning a certain level of monthly income from their factory job in the nearby town :Number of FamiliesIncome band (in Rupees)425,000-9,9994010,000-14,9993615,000-19,9991820,000-24,999525,000-30,000Which of the following statements are correct ?(i) Approximately 54% of the families earn between Rs. 10,000 and Rs. 20,000.(ii) There are 70% families who earn more than Rs. 10,000.(iii) A family with highest income earns Rs. 29,500.(iv) Median income is between Rs. 10,000 and Rs. 14,999.

The correct statements are (i), (ii) and (iv).The total number of families is 42 + 40 + 36 + 18 + 5 = 141.\[ \begin{aligned} \text{(i)}\ \frac{40 + 36}{141} &= \frac{76}{141} \approx 53.9\% \\ \text{(ii)}\ \frac{40 + 36 + 18 + 5}{141} &= \frac{99}{141} \approx 70.2\% \end{aligned} \]So (i), about 54 per cent between Rs. 10,000 and Rs. 20,000, and (ii), 70 per cent earning more than Rs. 10,000, are both correct. For (iv), the median is the 71st family in order of income; the first band holds 42 families and the first two hold 82, so the 71st falls in the band Rs. 10,000-14,999, and (iv) is correct.Statement (iii) cannot be known: the table says only that the highest band runs from Rs. 25,000 to Rs. 30,000, not what the richest family earns. Every code containing (iii) is therefore wrong.

Q: The following are the number of cases filed under Sec. 498A of Domestic Violence Act during the month of December, 2013, 2014 and 2015 at three cities, namely Pune, Hyderabad and Jaipur :YearPuneHyderabadJaipur201340503020145055502015506080Which of the following statements are true ?(i) Maximum increase occurred in Jaipur from 2014 to 2015.(ii) Minimum increase occurred in Hyderabad from 2013 to 2014.(iii) Average increase for the period together is lowest in the case of Hyderabad.(iv) Minimum increase has occurred in the case of Pune from 2014 to 2015.

The key gives (i), (ii) and (iv).The year-on-year increases are:City2013 to 20142014 to 2015Pune100Hyderabad55Jaipur2030(i) The largest increase in the table is Jaipur's 30, from 2014 to 2015: true. (ii) In the period 2013 to 2014, the smallest increase is Hyderabad's 5: true. (iv) In the period 2014 to 2015, the smallest increase is Pune's 0: true. Read period by period, as the key does, (ii) and (iv) each name the minimum for their own period.(iii) is not true: the average increase over the two periods is 5 for Pune ((10 + 0)/2) and also 5 for Hyderabad, so Hyderabad is not uniquely the lowest. Every code that contains (iii) is therefore wrong.

Q: Pass percentage of a school for six consecutive years starting from 2003 to 2008 are 45, 56, 42, 61, 55 and 52. If the ratio of students who appeared for the exam in the years 2003 to 2008 are 2 : 3 : 4 : 3 : 2 : 3, then the pass percentage of the school in six years together is :

The overall pass percentage is 51.5%.Because different numbers of students appeared each year, the yearly percentages must be weighted by the ratio of candidates, 2 : 3 : 4 : 3 : 2 : 3 (total 17 parts):\[ \begin{aligned} &2(45) + 3(56) + 4(42) + 3(61) + 2(55) + 3(52) \\ &= 90 + 168 + 168 + 183 + 110 + 156 = 875 \\ &\frac{875}{17} \approx 51.47\% \approx 51.5\% \end{aligned} \]The simple average of the six percentages, 311 / 6, is about 51.8%, close but not the right method, and it is not an option either. 47.5%, 55% and 42.5% come from no consistent weighting of the data.

Q: A report regarding certain examination is given below :Total number of candidates appeared = 1000The number of male candidates = 550The number of candidates passed = 700The number of successful male candidates will lie between the limits ......................... .

The number of successful male candidates lies between 250 to 550.There are 550 male and 1000 - 550 = 450 female candidates, and 700 passed.\[ \begin{aligned} \text{least} &= 700 - 450 = 250 \\ \text{greatest} &= 550 \end{aligned} \]At least 250 passing candidates must be male even if every female passed, and at most all 550 males can have passed. Ranges starting at 550 or 700 exceed the number of male candidates, and 100 to 250 ignores the forced minimum.

Q: For any frequency distribution, 50th percentile and ............................ are same.

The 50th percentile is the same as the median.The pth percentile is the value below which p per cent of the observations lie. The median is the middle value of the ordered distribution, with half the observations below it and half above, so it is by definition the 50th percentile. It is also the second quartile, Q2.The mean equals the median only in a symmetrical distribution, so it is not the same for any frequency distribution. Quartile deviation and standard deviation are measures of dispersion, not positions in the distribution, so they cannot equal a percentile.

Q: The following is the information about area of states and population :StateABCDArea (in square km.)80,00050,00010,0005,000Population (in lakh)161043Which is the most thickly populated state ?

The most thickly populated state is D.Population density is population divided by area. One lakh is 100,000:\[ \begin{aligned} A &: 1{,}600{,}000 / 80{,}000 = 20 \\ B &: 1{,}000{,}000 / 50{,}000 = 20 \\ C &: 400{,}000 / 10{,}000 = 40 \\ D &: 300{,}000 / 5{,}000 = 60 \end{aligned} \]D has 60 persons per square km, the highest. A has the largest population but also by far the largest area, so it is as thinly populated as B at 20 per square km, and C is in the middle at 40.

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

The appropriate measure is the median.The mean uses the value of every score, so a few extreme scores pull it towards them. The median is the middle value of the ordered data and depends only on position, so it is unaffected by how extreme the end values are. For skewed data such as incomes it is the preferred average.The mode is the most frequent value and can be unstable or multiple, and the range is a measure of dispersion, not of central tendency.

Direction for [ Question No: 31 To 32 ] :

Direction :

In the following table, the number of students who passed in four subjects, English, Hindi, Marathi and History in divisions A, B and C of standard X of a particular school is given :

Division	English	Hindi	Marathi	History
A	29	30	38	25
B	34	32	36	30
C	26	34	31	29

31.

What is the possible maximum number of students in Division B, who passed in all the four subjects ?

A.34
B.30
C.36
D.26

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: B

The possible maximum is 30.

A student who passed in all four subjects is counted in every one of the four columns for Division B: 34 in English, 32 in Hindi, 36 in Marathi and 30 in History. The number who passed all four can therefore be no larger than the smallest of these counts, the 30 who passed History, and it can equal 30 if every History passer also passed the other three.

34 and 36 are the English and Marathi counts and would require more students to pass all four than passed History. 26 is a possible value but not the maximum.

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32.

The maximum possible number of students who passed in both Hindi and Marathi in three divisions combined is :

A.93
B.96
C.105
D.111

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: A

The maximum possible number is 93.

In each division, the number passing both Hindi and Marathi can be at most the smaller of the two counts. The maximum for the three divisions combined is the sum of these:

\[ \begin{aligned} A &: \min(30, 38) = 30 \\ B &: \min(32, 36) = 32 \\ C &: \min(34, 31) = 31 \\ \text{Total} &= 30 + 32 + 31 = 93 \end{aligned} \]

96 is the total of the Hindi column (30 + 32 + 34), but division C has only 31 Marathi passers, so all 34 Hindi passers there cannot have passed Marathi. 105 is the Marathi total and 111 adds larger figures still, both impossible for the same reason.

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33.

A ........................... is used to show exact values.

A.pie chart
B.table
C.bar diagram
D.dot plot

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: B

A table is used to show exact values.

A table presents data in rows and columns as actual figures, so the reader can see each value exactly and look up precise numbers.

Pie charts, bar diagrams and dot plots are graphical displays. They are good for showing proportions, comparisons and distributions at a glance, but the reader judges values from the size of slices, the height of bars or the position of dots, which gives only approximate values. When exact values matter, a table is the right choice.

Discuss in Forum

34.

The following table presents the number of families in a village earning a certain level of monthly income from their factory job in the nearby town :

Number of Families	Income band (in Rupees)
42	5,000-9,999
40	10,000-14,999
36	15,000-19,999
18	20,000-24,999
5	25,000-30,000

Which of the following statements are correct ?

(i) Approximately 54% of the families earn between Rs. 10,000 and Rs. 20,000.
(ii) There are 70% families who earn more than Rs. 10,000.
(iii) A family with highest income earns Rs. 29,500.
(iv) Median income is between Rs. 10,000 and Rs. 14,999.

A.(i), (ii) and (iii)
B.(ii), (iii) and (iv)
C.(i), (ii) and (iv)
D.(i), (iii) and (iv)

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: C

The correct statements are (i), (ii) and (iv).

The total number of families is 42 + 40 + 36 + 18 + 5 = 141.

\[ \begin{aligned} \text{(i)}\ \frac{40 + 36}{141} &= \frac{76}{141} \approx 53.9\% \\ \text{(ii)}\ \frac{40 + 36 + 18 + 5}{141} &= \frac{99}{141} \approx 70.2\% \end{aligned} \]

So (i), about 54 per cent between Rs. 10,000 and Rs. 20,000, and (ii), 70 per cent earning more than Rs. 10,000, are both correct. For (iv), the median is the 71st family in order of income; the first band holds 42 families and the first two hold 82, so the 71st falls in the band Rs. 10,000-14,999, and (iv) is correct.

Statement (iii) cannot be known: the table says only that the highest band runs from Rs. 25,000 to Rs. 30,000, not what the richest family earns. Every code containing (iii) is therefore wrong.

Discuss in Forum

35.

The following are the number of cases filed under Sec. 498A of Domestic Violence Act during the month of December, 2013, 2014 and 2015 at three cities, namely Pune, Hyderabad and Jaipur :

Year	Pune	Hyderabad	Jaipur
2013	40	50	30
2014	50	55	50
2015	50	60	80

Which of the following statements are true ?

(i) Maximum increase occurred in Jaipur from 2014 to 2015.
(ii) Minimum increase occurred in Hyderabad from 2013 to 2014.
(iii) Average increase for the period together is lowest in the case of Hyderabad.
(iv) Minimum increase has occurred in the case of Pune from 2014 to 2015.

A.(i), (ii) and (iii)
B.(ii), (iii) and (iv)
C.(i), (iii) and (iv)
D.(i), (ii) and (iv)

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: D

The key gives (i), (ii) and (iv).

The year-on-year increases are:

City	2013 to 2014	2014 to 2015
Pune	10	0
Hyderabad	5	5
Jaipur	20	30

(i) The largest increase in the table is Jaipur's 30, from 2014 to 2015: true. (ii) In the period 2013 to 2014, the smallest increase is Hyderabad's 5: true. (iv) In the period 2014 to 2015, the smallest increase is Pune's 0: true. Read period by period, as the key does, (ii) and (iv) each name the minimum for their own period.

(iii) is not true: the average increase over the two periods is 5 for Pune ((10 + 0)/2) and also 5 for Hyderabad, so Hyderabad is not uniquely the lowest. Every code that contains (iii) is therefore wrong.

Discuss in Forum

36.

Pass percentage of a school for six consecutive years starting from 2003 to 2008 are 45, 56, 42, 61, 55 and 52. If the ratio of students who appeared for the exam in the years 2003 to 2008 are 2 : 3 : 4 : 3 : 2 : 3, then the pass percentage of the school in six years together is :

A.51.5%
B.47.5%
C.55%
D.42.5%

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: A

The overall pass percentage is 51.5%.

Because different numbers of students appeared each year, the yearly percentages must be weighted by the ratio of candidates, 2 : 3 : 4 : 3 : 2 : 3 (total 17 parts):

\[ \begin{aligned} &2(45) + 3(56) + 4(42) + 3(61) + 2(55) + 3(52) \\ &= 90 + 168 + 168 + 183 + 110 + 156 = 875 \\ &\frac{875}{17} \approx 51.47\% \approx 51.5\% \end{aligned} \]

The simple average of the six percentages, 311 / 6, is about 51.8%, close but not the right method, and it is not an option either. 47.5%, 55% and 42.5% come from no consistent weighting of the data.

Discuss in Forum

37.

A report regarding certain examination is given below :

Total number of candidates appeared = 1000
The number of male candidates = 550
The number of candidates passed = 700

The number of successful male candidates will lie between the limits ......................... .

A.100 to 250
B.250 to 550
C.550 to 700
D.700 to 1000

Exam Year(s)

MH SET - 2019, SET Exam - 2019,

Answer: B

The number of successful male candidates lies between 250 to 550.

There are 550 male and 1000 - 550 = 450 female candidates, and 700 passed.

\[ \begin{aligned} \text{least} &= 700 - 450 = 250 \\ \text{greatest} &= 550 \end{aligned} \]

At least 250 passing candidates must be male even if every female passed, and at most all 550 males can have passed. Ranges starting at 550 or 700 exceed the number of male candidates, and 100 to 250 ignores the forced minimum.

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38.

For any frequency distribution, 50th percentile and ............................ are same.

A.Mean
B.Median
C.Quartile Deviation
D.Standard Deviation

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: B

The 50th percentile is the same as the median.

The pth percentile is the value below which p per cent of the observations lie. The median is the middle value of the ordered distribution, with half the observations below it and half above, so it is by definition the 50th percentile. It is also the second quartile, Q2.

The mean equals the median only in a symmetrical distribution, so it is not the same for any frequency distribution. Quartile deviation and standard deviation are measures of dispersion, not positions in the distribution, so they cannot equal a percentile.

Discuss in Forum

39.

The following is the information about area of states and population :

State	A	B	C	D
Area (in square km.)	80,000	50,000	10,000	5,000
Population (in lakh)	16	10	4	3

Which is the most thickly populated state ?

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: D

The most thickly populated state is D.

Population density is population divided by area. One lakh is 100,000:

\[ \begin{aligned} A &: 1{,}600{,}000 / 80{,}000 = 20 \\ B &: 1{,}000{,}000 / 50{,}000 = 20 \\ C &: 400{,}000 / 10{,}000 = 40 \\ D &: 300{,}000 / 5{,}000 = 60 \end{aligned} \]

D has 60 persons per square km, the highest. A has the largest population but also by far the largest area, so it is as thinly populated as B at 20 per square km, and C is in the middle at 40.

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40.

If a frequency distribution has some extreme scores then appropriate measure of central tendency will be ......................... .

A.Mean
B.Median
C.Mode
D.Range

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: B

The appropriate measure is the median.

The mean uses the value of every score, so a few extreme scores pull it towards them. The median is the middle value of the ordered data and depends only on position, so it is unaffected by how extreme the end values are. For skewed data such as incomes it is the preferred average.

The mode is the most frequent value and can be unstable or multiple, and the range is a measure of dispersion, not of central tendency.

Interpretation of Data Questions and Answers

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