question_answer 1)

Total number of students of a school in different years is shown in the following table.

Years	Number of animals
1996	400
1998	535
2000	472
2002	600
2004	623

A Prepare a pictograph of students using one symbol 9 to represent 100 students and answer the following questions. (a) How many symbols represent total number of students in the year 2002? (b) How many symbols represent total number of students in the year 1998? B. Prepare another pictograph of students using any other symbol each representing 50 students. Which pictograph do you find more informative?

Answer:

(A) According to the question, 100 students can be represented by = 1 symbol \[\overset{\text{O}}{\mathop{\updownarrow }}\,\] \[\therefore \]1 student can be represented by\[\frac{1}{100}\] symbols Now, for year 1996, 400 students can be represented by \[\frac{400\times 1}{100}=5\] symbols For year 1998, 535 students can be represented by \[\frac{535\times 1}{100}=5\] symbols + 35 students = 5 complete symbols and 1 incomplete symbol For year 2000, 472 students can be represented by \[\frac{472\times 1}{100}\] = 4 complete symbols + 72 students = 4 complete symbols and 1 incomplete symbol For year 2002, 600 students can be represented by \[\frac{600\times 1}{100}\] = 6 complete symbols For year 2004, 623 students can be represented by \[\frac{623\times 1}{600}\] 6 complete symbol +23 students = 6 complete symbols and 1 incomplete symbol Hence, the required pictograph of given data is shown below (a) 6 symbols represent total number of students in the year 2002. (b) 5 complete symbols and 1 incomplete symbol represent total number of students for the year 1998. (B) According to the question, 50 students can be represented by 1 symbol \[\therefore \]1 student can be represented by \[\frac{1}{50}\]symbols Now, for year 1996, 400 students can be represented by\[\frac{400\times 1}{50}\] symbols \[=\frac{400}{50}=8\] complete symbols For year 1998, 535 students can be represented by \[\frac{535\times 1}{50}=\frac{535}{50}\] symbols = 10 complete symbols + 1 incomplete symbol For year 2000, 472 students can be represented by \[\frac{472\times 1}{50}\] symbols \[=\frac{472}{50}=9\]complete symbols + 1 incomplete symbol For year 2002, 600 students can be represented by \[\frac{600\times 1}{50}\] symbols \[=\frac{600}{50}=12\]complete symbols For year 2004, 623 students can be represented by \[\frac{623\times 1}{50}\] symbols \[=\frac{623}{50}=12\]complete symbols + 1 incomplete symbol Hence, the required pictograph of given data is shown below Therefore, we observe that pictograph B is more informative because it gives better approximation.