Question 24
The following graphs show the sunrise and sunset times across the year at 4 locations in India. Observe how the graphs are organised. Are you able to identify which lines indicate the sunrise and which indicate the sunset?
Answer the following questions based on the graphs:
(i) At which place does the sun rise the earliest in January? What is the approximate day length at this place in January?
(ii) Which place has the longest day length over the year?
(iii) Share your observations—what do you find interesting? What are you curious to find out?
These graphs show how the times of sunrise and sunset change throughout the year for different places.
Step 1 — Identifying Sunrise and Sunset Lines Let us look at the y-axis, which shows time. The top graphs show times from about 16:00 to 20:00. These are evening times. So, the lines in the top graphs indicate sunset times. The bottom graphs show times from about 04:00 to 08:00. These are morning times. So, the lines in the bottom graphs indicate sunrise times.
Step 2 — Earliest Sunrise and Day Length in January We need to find the place where the sun rises earliest in January. We look at the bottom graphs (sunrise times) for the month of January. For Kibithu (blue line, left graph), the sunrise time in January is approximately 05:30. For Ghuar Moti (yellow line, left graph), the sunrise time in January is approximately 07:45. For Srinagar (cyan line, right graph), the sunrise time in January is approximately 07:30. For Kanyakumari (orange line, right graph), the sunrise time in January is approximately 06:30. The earliest sunrise in January is at Kibithu.
Now, let us find the approximate day length at Kibithu in January. Sunrise time for Kibithu in January is approximately 05:30. Sunset time for Kibithu in January (from the top left graph) is approximately 17:30. The day length is the difference between the sunset time and the sunrise time.
Step 3 — Place with the Longest Day Length We need to find the place that has the longest day length over the year. Day length is the time from sunrise to sunset. We look for the largest vertical gap between the sunset curve (top) and the sunrise curve (bottom) for each location. This usually happens around June or July.
Let us calculate the maximum day length for each place: For Kibithu (blue line): Maximum sunset time (around June/July) is approximately 18:45. Minimum sunrise time (around June/July) is approximately 04:00. Day length for Kibithu = 18:45 - 04:00 = 14 hours 45 minutes.
For Ghuar Moti (yellow line): Maximum sunset time (around June/July) is approximately 19:45. Minimum sunrise time (around June/July) is approximately 05:45. Day length for Ghuar Moti = 19:45 - 05:45 = 14 hours 00 minutes.
For Srinagar (cyan line): Maximum sunset time (around June/July) is approximately 19:45. Minimum sunrise time (around June/July) is approximately 05:15. Day length for Srinagar = 19:45 - 05:15 = 14 hours 30 minutes.
For Kanyakumari (orange line): Maximum sunset time (around June/July) is approximately 18:45. Minimum sunrise time (around June/July) is approximately 06:00. Day length for Kanyakumari = 18:45 - 06:00 = 12 hours 45 minutes.
Comparing these, Kibithu has the longest day length over the year.
Step 4 — Observations and Curiosities Let us share our observations and what we are curious about.
Observations: The top graphs show sunset times, and the bottom graphs show sunrise times. Sunrise and sunset times change throughout the year in a wave-like pattern. Places further north, like Srinagar, Kibithu, and Ghuar Moti, have a much larger change in day length over the year. Kanyakumari, which is closer to the equator, has a day length that stays almost constant, around 12 hours. Kibithu (in the east) has much earlier sunrises and sunsets compared to Ghuar Moti (in the west). This is because of their different longitudes (east-west positions).
Curiosities: We are curious about how the exact latitude (north-south position) of a place affects the variation in its day length. We want to know why places with similar latitudes but different longitudes have similar day length patterns but different clock times for sunrise and sunset. We wonder how these graphs would look for places very close to the North Pole or in the Southern Hemisphere.
Answer
(i) The sun rises earliest in January at Kibithu. The approximate day length at Kibithu in January is 12 hours. (ii) Kibithu has the longest day length over the year. (iii) Observations: The top graphs show sunset times, and the bottom graphs show sunrise times. Sunrise and sunset times change throughout the year, following a wave-like pattern. Places further north (like Srinagar, Kibithu, Ghuar Moti) have a much larger change in day length over the year compared to Kanyakumari, which is closer to the equator and has a day length that stays almost constant around 12 hours. Kibithu (in the east) has much earlier sunrises and sunsets compared to Ghuar Moti (in the west), even though their day length patterns are similar. This is due to their different longitudes. Curiosities: We are curious about how the exact latitude of a place affects the variation in its day length. We want to know why places with similar latitudes but different longitudes have similar day length patterns but different clock times for sunrise and sunset. We wonder how these graphs would look for places very close to the North Pole or in the Southern Hemisphere.
More questions in FIO
Find the mean of the following data and share your observations:
(i) The first 50 natural numbers. (ii) The first 50 odd numbers. (iii) The first 50 multiples of 4.
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Sudhakar, the class teacher, asks Shreyas to measure the heights of all 24 students in his class and calculate the average height. Shreyas informs the teacher that the average height is 150.2 cm. Sudhakar discovers that the students were wearing uniform shoes when the measurements were taken and the shoes add 1 cm to the height.
(i) Should the teacher get all the heights measured again without the shoes to find the correct average height? Or is there a simpler way?
(ii) What is the correct average height of the class?
(a) 174.2 cm
(b) 126.2 cm
(c) 150.2 cm
(d) 149.2 cm
(e) 151.2 cm
(f) None of the above
(g) Insufficient information
The three dot plots below show the lengths, in minutes, of songs of different albums. Which of these has a mean of 5.57 minutes? Explain how you arrived at the answer.
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 data (in the given list) without affecting the median, what could that value be?
(ii) If we include two values to the data without affecting the median what could the two values be?
(iii) If we remove one value from the data without affecting the median what could the value be?
Examine the statements below and justify if the statement is always true, sometimes true, or never true.
(i) Removing a value less than the median will decrease the median.
(ii) Including a value less than the mean will decrease the mean.
(iii) Including any 4 values will not affect the median.
(iv) Including 4 values less than the median will increase the median.
The mean of the numbers 8, 13, 10, 4, 5, 20, y, 10 is 10.375. Find the value of y.
The mean of a set of data with 15 values is 134. Find the sum of the data.
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 median of this data is 29?
(i) 10 (ii) 25 (iii) 40 (iv) 100 (v) 29 (vi) 47 (vii) 30
The number of times students rode their cycles in a week is shown in the dot plot below. Four students rode their cycles twice in that week.
(i) Find the average number of times students rode their cycles. (ii) Find the median number of times students rode their cycles. (iii) Which of the following statements are valid? Why? (a) Everyone used their cycle at least once. (b) Almost everyone used their cycle a few times. (c) There are some students who cycled more than once on some days. (d) Exactly 5 students have used their cycles more than once on some days. (e) The following week, if all of them cycled 1 more time than they did the previous week, what would be the average and median of the next week's data?
A dart-throwing competition was organised in a school. The number of throws participants took to hit the bull's eye (the centre circle) is given in the table below. Describe the data using its minimum, maximum, mean and median.
The average number of customers visiting a shop and the average number of customers actually purchasing items over different days of the week is shown in the table below. Visualise this data on a line graph.
The average number of days of rainfall in each month for a few cities is shown in the table below:
(i) What could be the possible method to compile this data?
(ii) Mark the data for Mangaluru, Port Blair, and Rameswaram in the line graph shown below. You can round off the values to the nearest integer.
(iii) Based on the line for New Delhi in the graph fill the data in the table.
(iv) Which city among these receives the most number of days of rainfall per year? Which city gets the least number of days of rainfall per year?
(v) Looking at the table, when is the rainy season in New Delhi and Rameswaram?
The following line graph shows the number of births in every month in India over a time period:
(i) What are your observations?
(ii) What was the approximate number of births in July 2017?
(iii) What time period does the graph capture?
(iv) Compare the number of births in the month of January in the years 2018, 2019, and 2020.
(v) Estimate the number of births in the year 2019.
Mean Grids:
(i) Fill the grid with 9 distinct numbers such that the average along each row, column, and diagonal is 10.
(ii) Can we fill the grid by changing a few numbers and still get 10 as the average in all directions?
Give two examples of data that satisfy each of the following conditions:
(i) 3 numbers whose mean is 8.
(ii) 4 numbers whose median is 15.5.
(iii) 5 numbers whose mean is 13.6.
(iv) 6 numbers whose mean = median.
(v) 6 numbers whose mean > median.
Fill in the blanks such that the median of the collection is : . How many possibilities exist if only counting numbers are allowed?
Fill in the blanks such that the mean of the collection is : , , , , , . How many possibilities exist if only counting numbers are allowed?
Check whether each of the statements below is true. Justify your reasoning. Use algebra, if necessary, to justify.
(i) The average of two even numbers is even.
(ii) The average of any two multiples of 5 will be a multiple of 5.
(iii) The average of any 5 multiples of 5 will also be a multiple of 5.
There were 2 new admissions to Sudhakar’s class just a couple of days after the class average height was found to be 150.2 cm.
(i) Which of the following statements are correct? Why? (a) The average height of the class will increase as there are 2 new values. (b) The average height of the class will remain the same. (c) The heights of the new students have to be measured to find out the new average height. (d) The heights of everyone in the class has to be measured again to calculate the new average height.
(ii) The heights of the two new joinees are 149 cm and 152 cm. Which of the following statements about the class’ average height are correct? Why? (a) The average will remain the same. (b) The average will increase. (c) The average will decrease. (d) The information is not sufficient to make a claim about the average.
(iii) Which of the following statements about the new class average height are correct? Why? (a) The median will remain the same. (b) The median will increase. (c) The median will decrease. (d) The information is not sufficient to make a claim about median.
Is 17 the average of the data shown in the dot plot below? Share the method you used to answer this question.
The weights of people in a group were measured every month. The average weight for the previous month was 65.3 kg and the median weight was 67 kg. The data for this month showed that one person has lost 2 kg and two have gained 1 kg. What can we say about the change in mean weight and median weight this month?
The following table shows the retail price (in ₹) of iodised salt in the month of January in a few states over 10 years. For your calculations and plotting you may round off values to the nearest counting number.
(i) Choose data from any 3 states you find interesting and present it through a line graph using an appropriate scale.
(ii) What do you find interesting in this data? Share your observations.
(iii) Compare the price variation in Gujarat and Uttar Pradesh.
(iv) In which state has the price increased the most from 2016 to 2025?
(v) What are you curious to explore further?
The following graphs show the sunrise and sunset times across the year at 4 locations in India. Observe how the graphs are organised. Are you able to identify which lines indicate the sunrise and which indicate the sunset?
Answer the following questions based on the graphs:
(i) At which place does the sun rise the earliest in January? What is the approximate day length at this place in January?
(ii) Which place has the longest day length over the year?
(iii) Share your observations—what do you find interesting? What are you curious to find out?