Questions: Tales by Dots and Lines
Tales by Dots and Lines24 min readLesson 7 of 7
Q1 Find the mean of 12, 15, 18, 21 and 24.
Answer (English): The sum is 12 + 15 + 18 + 21 + 24 = 90 and there are 5 values, so the mean is 90 ÷ 5 = 18. All five values are evenly spaced, so the mean is also the middle value, 18.
Hinglish: Sum = 90 aur count = 5, isliye mean 90 ÷ 5 = 18. Values evenly spaced hain, isliye mean bhi middle value 18 hai.
Q2 Find the median of 5, 9, 14, 14, 18, 22 and 30.
Answer (English): The values are already in order and there are 7 values, so the median is the 4th value, which is 14. The repeated 14 does not change the position of the middle.
Hinglish: Values already sorted hain aur 7 values hain, isliye median 4th value 14 hai. 14 do baar aane se middle ki position nahi badalti.
Q3 A data set has mean 20 and 6 values. A new value 35 is added. What is the new mean?
Answer (English): The old total is 20 × 6 = 120. Adding 35 gives a total of 155 over 7 values, so the new mean is 155 ÷ 7 ≈ 22.14. Because the new value is larger than the old mean, the mean rises.
Hinglish: Purana total 20 × 6 = 120. 35 jodne par total 155 aur count 7, isliye naya mean 155 ÷ 7 ≈ 22.14. Naya value purane mean se bada hai, isliye mean badhta hai.
Q4 How does doubling each value affect the mean? Support the answer with an example.
Answer (English): Doubling every value doubles the total, so the mean is also doubled. For 2, 4 and 6 the mean is 4; doubling gives 4, 8 and 12 with mean 8. Algebraically, if the mean of x₁, …, xₙ is a, the mean of 2x₁, …, 2xₙ is 2a.
Hinglish: Har value double karne se total double hota hai, isliye mean bhi double hota hai. 2, 4, 6 ka mean 4 hai; double karne par 4, 8, 12 ka mean 8. Algebraically, mean of 2x values = 2 × mean of x values.
Q5 A frequency table shows the value 3 with frequency 4, the value 4 with frequency 6 and the value 5 with frequency 2. Find the mean.
Answer (English): The total of value × frequency is 3 × 4 + 4 × 6 + 5 × 2 = 12 + 24 + 10 = 46. The total frequency is 4 + 6 + 2 = 12, so the mean is 46 ÷ 12 = 3.83. The mean is closer to 4 because most values are 4.
Hinglish: Value × frequency ka total 12 + 24 + 10 = 46 hai. Total frequency 12 hai, isliye mean 46 ÷ 12 = 3.83. Zyadatar values 4 hain, isliye mean 4 ke kareeb hai.
Q6 A student's marks are 18, 22, 25 and 35. Which measure, mean or median, better describes the typical mark, and why?
Answer (English): The mean is (18 + 22 + 25 + 35) ÷ 4 = 100 ÷ 4 = 25. The median is the average of 22 and 25, which is 23.5. The mark 35 is much larger than the others and pulls the mean up, so the median 23.5 gives a better picture of the typical score. This is why the median is preferred when data has extreme values.
Hinglish: Mean = 100 ÷ 4 = 25 aur median = (22 + 25) ÷ 2 = 23.5. 35 baaki marks se kaafi bada hai, isliye mean upar khinch jata hai; typical score ke liye median 23.5 behtar hai. Extreme values ke saath median zyada useful hota hai.
Q7 Explain how the median changes when a very large value is added to an odd-sized data set.
Answer (English): With an odd number of values the median is one middle value. Adding a very large value makes the new count even, and the median becomes the average of the two middle values of the enlarged set. For example, 1, 2, 3, 4, 5 has median 3; adding 100 gives two middle values 3 and 4, so the median is 3.5, which rises slightly. Adding a very small value would lower it slightly.
Hinglish: Odd values mein median ek middle value hoti hai. Bahut bada value add karne se count even ho jata hai aur median do middle values ka average ban jati hai. 1, 2, 3, 4, 5 ka median 3 tha; 100 add karne par middle 3 aur 4, isliye median 3.5 ho gayi. Chhota value add karne par median thoda ghatti hai.
Q8 A dot plot shows 2 dots at 4, 3 dots at 6 and 1 dot at 10. Find the mean and median.
Answer (English): There are 6 values with total 2 × 4 + 3 × 6 + 1 × 10 = 8 + 18 + 10 = 36, so the mean is 36 ÷ 6 = 6. The ordered values are 4, 4, 6, 6, 6, 10; the two middle values are 6 and 6, so the median is 6. The single 10 pulls the mean up a little but does not move the median.
Hinglish: 6 values hain aur total 8 + 18 + 10 = 36, isliye mean 36 ÷ 6 = 6. Ordered values 4, 4, 6, 6, 6, 10 hain; do middle values 6 aur 6, isliye median 6 hai. Ek 10 mean ko thoda upar kheenchta hai, median ko nahi.
Q9 How would you read a line graph of monthly rainfall to compare two cities?
Answer (English): First read the axes: months on the horizontal axis and rainfall on the vertical axis, along with the scale. Then find the peak and the driest months for each city, compare the shapes of the two lines, and check how far apart the lines are in the same month. Support every statement with a point from the graph, such as "the rainfall peaked in July at about 28 units" rather than a vague claim that it rained a lot.
Hinglish: Pehle axes padho: months horizontal aur rainfall vertical, aur scale dekho. Phir har city ke peak aur dry months dhoondho, dono lines ki shape compare karo, aur same month mein lines ka gap dekho. Har statement ko graph ke point se support karo, jaise "rainfall July mein lagbhag 28 units par peak tha", na ki sirf "bahut baarish hui".
Q10 A line graph shows a class's average marks rising from 60 in test 1 to 70 in test 2 and staying at 70 in test 3. What does the graph tell us, and what does it not tell us?
Answer (English): It tells us that the class average improved by 10 marks between test 1 and test 2 and then remained the same in test 3. It does not tell us which students improved, whether the same students were present in all three tests, or how the marks were spread. An average describes the class as a whole, and individual student data is needed for those questions.
Hinglish: Graph batata hai ki class average test 1 se test 2 tak 10 marks badha aur test 3 mein same raha. Lekin yeh nahi batata ki kaun se students improve hue, teeno tests mein same students the ya nahi, aur marks ka spread kya tha. Average poore class ko describe karta hai, individual data ke liye alag jankari chahiye.
Quiz pointer
The five-question quiz for this chapter is separate from these answers. Take it without looking back, then redo any missed question by writing the data in order first. For graph questions, read the axes and scale before reading any value, and quote a point from the graph whenever you make a claim.