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Tales by Dots and Lines

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Page 103: Consider any 2 numbers. Find their average/arithmetic mean. Repeat this by taking other pairs. What do you observe?
Page 103: Calculate and mark the mean of each collection of data below.
Page 104: Mark the mean for the collections below. Can you explain how the mean is the centre of each collection?
Page 104: Can you explain how the mean is the centre of each collection? Verify that this holds for all the collections of…
Page 105: Can there be more than one such 'centre'? In other words, is there any other value such that the sum of the…
Page 105: Will including a new value in the data increase or decrease the mean? Similarly, if a value smaller than the mean is…
Page 105: What happens to the mean when an existing value is removed? When will the mean increase, decrease, or stay the same?…
Page 106: Explore if it is possible to include or remove 2 values such that the mean is unchanged. You may use the following…
Page 106: Can we include 2 values less than the mean and 1 value greater than the mean, so that the mean remains the same? Try…
Page 106: Consider the data: 8, 3, 10, 13, 4, 6, 7, 7, 8, 8, 5. Calculate its mean. Now, consider this data with every value…
Page 107: That is, the new average is 3 more than the previous average. Try to explain, using algebra, what the average is…
Page 107: What happens to the average if every value in the collection is doubled? You may have guessed that the average also…
Page 108: Will including a new value to the data increase or decrease the median? Let us consider the following data. The…
Page 109: Average weight of the players = (Sum of weight of all players) ÷ (Number of players). Let the unknown weight be w kg.
Page 109: The average harvest per tree = (Total number of coconuts harvested) ÷ (Number of trees). The data of harvest per…
Page 110: What is the average family size of this class?
Page 110: What is the median family size of this class? We know that there are 36 values in the data. The median would be the…
Page 111: Cells are named and referred to using the column headers labelled A, B, C, ..., and row headers labelled 1, 2, 3,…
Page 112: What formula would you type to find out the class average marks in Science? Find out if the class average marks in…
Page 113: Find the mean of the following data and share your observations: (i) The first 50 natural numbers. (ii) The first 50…
Page 113: The dot plot below shows a collection of data and its average; but one dot is missing. Mark the missing value so…
Page 114: (i) Should the teacher get all the heights measured again without the shoes to find the correct average height? Or…
Page 114: The three dot plots below show the lengths, in minutes, of songs of different albums. Which of these has a mean of…
Page 114: Find the median of 8, 10, 19, 23, 26, 34, 40, 41, 41, 48, 51, 55, 70, 84, 91, 92. (i) If we include one value to the…
Page 115: Examine the statements below and justify if the statement is always true, sometimes true, or never true. (i)…
Page 115: The mean of the numbers 8, 13, 10, 4, 5, 20, y, 10 is 10.375. Find the value of y.
Page 115: The mean of a set of data with 15 values is 134. Find the sum of the data.
Page 115: Consider the data: 12, 47, 8, 73, 18, 35, 39, 8, 29, 25, p. Which of the following number(s) could be p if the…
Page 115: (i) Find the average number of times students rode their cycles. (ii) Find the median number of times students rode…
Page 116: Describe the data using its minimum, maximum, mean and median.
Page 116: Now, observe the following graph, drawn as a line graph using the same data. Do both these graphs represent the same…
Page 117: We call such a graph made up of lines a line graph. Line graphs are generally used to visualise data across time.…
Page 118: Step 1: Identify what is given. Notice how the graph is organised, what scale is used, and what patterns the data…
Page 118: Why are the trends so distinct in these two states? What factors determine a region's temperature? You might be…
Page 119: What could be the possible method used to derive this data? Discuss. Identify two consecutive years where the…
Page 120: Which of the following statements are valid inferences? From 2012 till 2024, the worldwide count of space object…
Page 120: The following graphs show monthly average rainfall data of a few cities.
Page 121: What could be the possible method to compile this data? Mark these cities on a map of India. What is common to how…
Page 122: The average number of customers visiting a shop and the average number of customers actually purchasing items over…
Page 122: (i) What could be the possible method to compile this data? (ii) Mark the data for Mangaluru, Port Blair, and…
Page 123: (i) What are your observations? (ii) What was the approximate number of births in July 2017? (iii) What time period…
Page 124: Share your observations. Based on this infographic, answer the following: (i) The value of Karnataka is hidden. Can…
Page 125: Look at the three coloured strips carefully. (i) What activity does each colour stand for? (ii) The three strips…
Page 126: What would your strip for a weekday look like? How similar or different is it to Manoj's? What would a strip of your…
Page 126: Share your observations on this graph. What do you find interesting?
Page 127: Mean Grids: (i) Fill the grid with 9 distinct numbers such that the average along each row, column, and diagonal is…
Page 127: Give two examples of data that satisfy each of the following conditions: (i) 3 numbers whose mean is 8. (ii) 4…
Page 127: Fill in the blanks such that the median of the collection is 13: 5, 21, 14, ____, ____, ____. How many possibilities…
Page 127: Fill in the blanks such that the mean of the collection is 6.5: 3, 11, ____, ____, 15, 6. How many possibilities…
Page 128: There were 2 new admissions to Sudhakar's class just a couple of days after the class average height was found to be…
Page 128: Is 17 the average of the data shown in the dot plot below? Share the method you used to answer this question.
Page 128: The weights of people in a group were measured every month. The average weight for the previous month was 65.3 kg…
Page 129: (i) Choose data from any 3 states you find interesting and present it through a line graph using an appropriate…
Page 130: In 1983, the majority in rural areas used kerosene as a primary lighting source while the majority in urban areas…
Page 130: Answer the following questions based on the line graph. (i) How long do children aged 10 in urban areas spend each…
Page 131: Individual project: Make your own activity strip for different days of the week. (i) Do you eat and sleep at regular…
Page 131: Small group project: Make a group of 3-4 members. Do at least one of the following: (i) Track daily sleep time of…
Page 131: (i) At which place does the sun rise the earliest in January? What is the approximate day length at this place in…
Page 132: (i) Find out on what dates amavasya (new moon) and purnima (full moon) were in this month. (ii) What do you notice?…

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