Tales by Dots and Lines Class 8 Solutions

For each collection, add all plotted values and divide by the number of dots. Mark that result on the number line. The mean is the balance point: the total horizontal distance of dots to its left equals the total distance of dots to its right.

The mean is the unique balance point because the total deviations on its two sides are equal. It need not be the midpoint of the least and greatest values; repeated values affect the balance. Moving the proposed centre in either direction increases one side's total distance and decreases the other, so there cannot be a second centre.

Adding a value above the current mean raises the mean; adding one below lowers it; adding one equal to it preserves it. Removing a value above the mean lowers the mean, removing one below raises it, and removing one equal to it preserves it. This follows from the fair-share interpretation.

Yes. The added or removed values must themselves have the old mean. For mean (m), two values (m-d,m+d) work. Three values such as (m-a,m-b,m+a+b) also work, including two values below (m) and one above it; reversing the signs gives two above and one below.

The sum is 79, so the mean is (79/11\approx7.18). Adding 10 to every value gives mean (17.18); subtracting 1 gives (6.18); multiplying every value by 2 gives (14.36). In general, adding (c) changes mean (a) to (a+c), and multiplying by (k) changes it to (ka).

The old median is 8. After including 11, the two middle values are 8 and 11, so the new median is ((8+11)/2=9.5). More generally, inserting a value above the median cannot lower it, while inserting one below cannot raise it.

Let the missing weight be (w). Then ((349+w)/10=39.2), so (349+w=392) and (w=43). The missing weight is 43 kg.

The recorded total was (25.6\times15=384). The correct total is (384-3=381), so the correct average is (381/15=25.4) coconuts per tree.

There are 36 students and the weighted total is (3(3)+4(11)+5(9)+6(7)+7(3)+8+9+10=188). Thus the mean is (188/36\approx5.22). Positions 18 and 19 both lie among the nine 5s (positions 15 through 23), so the median is 5.

Farooq's Mathematics mark is in E5. Cell B7 contains 27, Gowri's Odia mark. Ashwin scored above 30 in Telugu (31), English (33), and Mathematics (34); Social Science is exactly 30, so it is excluded.

Science average: =AVERAGE(G2:G23), which is about 33.14. Odia averages about 31.23 while Telugu averages about 33.59, so Odia is not greater. Enter =AVERAGE(B2:B23) through =AVERAGE(G2:G23) for all subjects. Enter =SUM(B2:G2) for Ratna and fill down; the totals are 200, 250, 185, 266, 194, 183, 112, 248, 225, 102, 273, 147, 188, 148, 213, 242, 232, 197, 103, 177, 246, 183.

For an arithmetic sequence, the mean is the average of its first and last terms. Hence the answers are ((1+50)/2=25.5), ((1+99)/2=50), and ((4+200)/2=102).

The 10 visible dots total (83). With one missing dot, the required total is (11\times9=99). Therefore the missing value is (99-83=16); place the dot at 16.

There is no need to measure everyone again. Every recorded height is 1 cm too large, so the mean is also 1 cm too large. The correct mean is 150.2 - 1 = 149.2 cm, choice (d).

Plot A. Its seven values are (5,5,5.25,5.5,5.75,6,6.5), whose sum is 39. Thus its mean is (39/7\approx5.57) minutes.

The middle values are 41 and 41, so the median is 41. One value: add 41. Two values: add 40 and 48 (many pairs preserving the two middle 41s work). One removal: remove an extreme such as 8; the middle value of the remaining 15 values is still 41.

(i) Sometimes true: removing a below-median value may lower the median or leave it unchanged. (ii) Always true when the inserted value is strictly below the old mean. (iii) Sometimes true: four suitably placed values can preserve the median, but arbitrary ones need not. (iv) Never true: adding four values below the median cannot increase it.

The required total is (8\times10.375=83). The known values total 70, so (y=83-70=13).

Sum = number of values × mean, so the sum is (15\times134=2010).

After sorting the ten fixed values, 29 is in the sixth position unless p is below 29. Thus p can be 40, 100, 29, 47, or 30: choices (iii), (iv), (v), (vi), and (vii).

The frequencies give 43 students and a total of 197 rides, so the mean is (197/43\approx4.58). The 22nd value is 4, so the median is 4. Statement (a) is false because three students rode zero times. (b) is a reasonable summary. Statements (c) and (d) cannot be inferred: weekly totals do not reveal which days had multiple rides.

If everyone rides once more next week, both mean and median rise by 1, to about 5.58 and 5.

There are 62 students. The minimum is 1 trial and maximum is 10 trials. The weighted sum is 473, so the mean is (473/62\approx7.63). Positions 31 and 32 are both 8, so the median is 8.

Yes; they encode the same monthly maximum temperatures. Punjab varies greatly, from about 19°C in January to 38°C in June, then falls. Kerala stays roughly 29-33°C, peaking around April. A monthly-minimum graph would use the same months and method but plot each month's minimum readings.

A suitable method is to combine official launch records from national agencies and operators, count every qualifying object placed into Earth orbit or beyond by launch year and country, remove duplicate records, and then aggregate country and worldwide totals using one consistent definition.

The first is invalid because worldwide launches fall in some years, including 2024. The USA three-fourths statement is a valid approximation for 2022-24. The Nepal statement is invalid because an unshown country cannot be treated as zero. China plus Russia in 2024 is about 400, so the fourth is valid.

From the plotted points, 2016 to 2017 rises from roughly 200 to about 500, more than doubling. No other adjacent pair shown clearly reaches twice the previous year's value.

Average each calendar month's rainfall across several years at each weather station. Kovalam, Udupi, and Mumbai form the west-coast group; Rameswaram, Chennai, and Puri form the east-coast group. West-coast peaks occur mainly June-August; Rameswaram peaks October-December, Chennai around November, and Puri July-September.

January-March are generally dry.

Put Monday-Sunday on the horizontal axis and customer count on the vertical axis. Plot visiting as (16, 19, 10, 14, 20, 22, 35) and purchasing as (10, 8, 7, 11, 12, 16, 26), then join each series separately. Both peak on Sunday; purchasing remains below visiting every day.

Plot the three table rows after rounding. Reading New Delhi's line gives about 1, 1, 1, 1, 1, 4, 10, 10, 4, 1, 0, 1 days from January to December. Annual totals are about 112.1 for Mangaluru, 125.8 for Port Blair, 42.3 for Rameswaram, and 35 for New Delhi. Port Blair is highest and New Delhi lowest.

New Delhi's rain season is July-August (broader monsoon June-September); Rameswaram's is October-December.

Births show a repeating seasonal cycle: peaks near 1.9 million around September-November and lows near 1.4-1.5 million around spring. July 2017 is about 1.7 million. The graph runs approximately April 2017 to March 2020. January is about 1.7M in 2018, 1.65M in 2019, and 1.75M in 2020. Summing the twelve approximate 2019 readings gives about 20 million births; graph readings are estimates.

Karnataka's dark-purple shade suggests roughly +80 to +90, similar to Tamil Nadu (+85) and Andhra (+92). The five strongest displayed rice preferences are Manipur (+100), Nagaland (+99), Mizoram (+97), Tripura (+96), and Meghalaya (+95). The strongest wheat preferences are Rajasthan (-93), Haryana (-81), Punjab (-78), Madhya Pradesh (-60), and Delhi (-45).

More balanced examples include Bihar (+3), Maharashtra (-15), Uttarakhand (-18), Himachal Pradesh (-19), and Uttar Pradesh (-30).

Light blue is sleep; yellow is recreation/friends/media; orange is classes or study; green is eating; purple is washing/dressing/exercise; grey is travel. The strips are Sunday, Saturday, Friday from left to right: the left has no school, the middle has a shorter study block, and the right has the full school day.

The long movie is Sunday about 9:00-13:00. School lunch is about 13:00. The strips also reveal sleep times, commute, meal duration, and how weekday and weekend routines differ.

Average sleep is about 9.5 hours at age 6, falls through childhood and the teenage years, stays near 8 hours through much of adulthood, then rises toward about 8.5 hours in older age. The many closely spaced observations make a smooth line more readable than dozens of columns.

Each line must total 30. One solution is 13, 6, 11/8, 10, 12/9, 14, 7. It comes from adding 5 to every entry of the Lo Shu magic square. Rotating or reflecting this grid gives further solutions while keeping nine distinct values.

(i) 6,8,10 and 4,8,12. (ii) 10,15,16,20 and 1,15,16,30. (iii) 10,12,14,15,17 and 8,11,13,16,20. (iv) 1,2,3,3,4,5 and 2,4,6,6,8,10. (v) 1,1,2,2,3,15 and 0,1,1,2,2,18.

For example, use 12, 12, 30. Sorted, the data are 5,12,12,14,21,30, whose median is (12+14)/2 = 13. There are infinitely many possibilities because the last value can be any counting number at least 21 while the two middle positions are preserved.

The required total is (6\times6.5=39); known values total 35, so the blanks must sum to 4. With positive counting numbers, the ordered pairs are (1,3), (2,2), and (3,1): three placements, or two if order is ignored.

None is always true. Two even numbers can average to an odd number, for example (2+4)/2=3. Two multiples of 5 can average to 7.5, using 5 and 10. Five multiples of 5 can average to a non-multiple of 5, for example 0,5,10,15,25 have mean 11.

Initially only (c) is necessarily correct: measure the two newcomers and combine their total with the known old total (24\times150.2); no remeasurement is needed. Their mean is ((149+152)/2=150.5), above 150.2, so the class mean increases slightly (choice b). The old data values are not given, so the new median cannot be determined (choice d).

No. Counting the dots gives 25 values with total 443, so the mean is (443/25=17.72), not 17. Equivalently, the total rightward deviation from 17 exceeds the total leftward deviation by 18 units.

The total change is -2 + 1 + 1 = 0 kg, so the mean remains 65.3 kg. The median cannot be determined from this information because it depends on which people changed and their positions in the sorted list.

Choose any three state rows, put 2016-2025 on the x-axis, and use a common rupee scale. Most series rise overall but fluctuate. Gujarat is fairly flat around ₹13-17 until its 2025 rise to ₹19.20; Uttar Pradesh rises more strongly from ₹16.15 to ₹24.81. West Bengal has the largest 2016-2025 increase: ₹23.99 - ₹9.47 = ₹14.52.

Useful follow-up questions include inflation adjustment and transport or policy effects.

(i) Valid: in 1983 the rural majority used kerosene while the urban majority used electricity. (ii) Valid: kerosene's share falls over time in both. (iii) Invalid: the graph shows roughly 90%, not 10%, of urban households using electricity in 2000. (iv) Invalid: household primary-source shares do not provide any information about power cuts.

At age 10, urban children spend about 2.1 hours daily. Rural children's average reaches about 1.5 hours at age 14, choice (d). The age-15 average is not twice the age-10 average, so statement (a) is false. Statement (b) is also unsupported: an average above 1 hour does not mean every rural child spends at least 1 hour.

Use 48 half-hour cells per day and one consistent colour per activity. Total each activity's cells across the observed days, multiply by 0.5 hour, and divide by the number of days. Draw the resulting average-day strip, then repeat for one adult and compare sleep, meals, outdoor time, work/study, travel, and recreation.

Use one row per person or school and fixed columns for date, category, start, end, breaks, and total duration. For sleep, include naps and compute separate child, adult, and elderly means and medians. For schools, compare total school span, class time, and break time. Keep units and definitions consistent, show the distributions with strips or line graphs, and report sample size before conclusions.

Kibithu has the earliest January sunrise, about 6:00, and sunset around 16:30, giving roughly 10.5 hours of daylight. Srinagar has the longest summer day, about 14.5 hours. Kanyakumari shows the least seasonal change, while the northern locations show a larger summer-winter swing; eastern Kibithu's clock times are earlier than Ghuar Moti's.

The full moon is around day 6: moonrise is near sunset and moonset near sunrise. The new moon is around day 21: moonrise and moonset are close to sunrise and sunset respectively, shown by the 24-hour wrap in the plotted lines. Both times move later by roughly 45-60 minutes per day, with the apparent breaks caused by wrapping past midnight.

Two players alternately claim empty hexagons. Each tries to make one continuous chain joining their assigned opposite sides; pieces never move and the first completed connection wins. A useful strategy is to create two separated routes that cannot both be blocked with one move, while watching for the opponent's analogous bridge connections.