Let's go through and solve questions 66-70 as requested from your uploaded file.

Question 66:

Assertion (A): In the above histogram, 32 is the frequency of TV watched for 4-5 hours.
Reason (R): Class size is the difference between the upper limit and the lower limit of a class interval.

• Solution:

  • The assertion is about the frequency of 32 for TV watched for 4-5 hours.
  • The reason states the class size is the difference between the upper and lower limits of a class interval, which is correct.

  Based on these, both the assertion and reason are true, but the reason is not explaining the assertion. Therefore, the correct answer is:

  Answer: (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

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Question 67:

Assertion (A): The following data can be represented as a histogram.
Reason (R): A histogram is a graphical representation of discrete or continuous data. The y-axis is plotted by frequency, and the x-axis is plotted with the range of values divided into intervals.

• Solution:

  • A histogram is indeed used for representing continuous data with frequencies on the y-axis and intervals on the x-axis. The statement in the reason is correct.
  • Given that the assertion says the data can be represented as a histogram, and the reason correctly explains the principles of a histogram, both statements are true, and the reason explains the assertion.

  Answer: (a) Both assertion (A) and reason (R) are true, and the reason is the correct explanation of assertion (A).

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Question 68:

Observe the Pie chart, if the total number of students is 600, then how many students like mathematics?

• Solution: The answer choices are:

  • (a) 100
  • (b) 150
  • (c) 200
  • (d) 300

  Without the specific pie chart available, let's assume an appropriate angle for the mathematics section. If we estimate based on the choices, the fraction of students can be derived. The correct fraction that would fit 600 students must be selected based on the actual pie chart angles.

  Without the chart, it is difficult to pinpoint, but using logical estimation based on normal pie chart divisions for common values, let's assume:

  Answer: (b) 150 students is a plausible answer.

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Question 69:

Observer the above Pie chart and answer the following questions
(Since the specific question for this number wasn't fully available in the document, we can’t provide an exact answer. However, it likely asks about interpreting the given data based on student preferences.)

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Question 70:

There is no clear specific question associated with 70 in the document. The questions appear to conclude at question 69.

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Would you like more detailed explanations for any of these solutions or any related questions? Here are five related questions you might want to explore:

1. What are the key differences between histograms and bar charts?
2. How do you calculate class intervals in frequency distributions?
3. What is the central angle in a pie chart, and how is it calculated?
4. Can a pie chart ever represent continuous data, and why or why not?
5. How can you estimate the mode from a histogram?

Tip: For histogram interpretation, always check if the class intervals are equal; this affects the accuracy of comparing frequencies visually.