Information Investigation and Analysis (Class- 6, Experience- 11)

[Exercise- page 233]

E.11.1. Marks obtained by 40 students in a class test in Mathematics are as follows: 

8, 7, 9, 4, 6, 8, 9, 10, 5, 4, 9, 8, 7, 6, 8, 7, 9, 10, 6, 4, 5, 8, 9, 7, 10, 6, 10, 8, 9, 8, 6, 5, 8, 9, 10, 7, 4, 10, 8, 6.

a) Arrange the data in decreasing order. 

b) Prepare a table using tally marks.

Solution:

a) Arranging the data in decreasing order:

10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 5, 5, 5, 4, 4, 4, 4

b) Table using tally marks:

E.11.2. Aumiya is a student of class six. The number of students in her school from class one to class six are: 

Draw a bar chart taking the number of students along the vertical line. [Hint: Mark the numbers of students along the vertical line in such a way that all the numbers are in the bar chart.]

Solution:

Answer will be posted soon. Please wait...

E.11.3. In a one-day cricket match between Bangladesh and Australia, a bowler of Bangladesh team bowled ten overs. Runs conceded by him in different overs are shown in the bar chart below: Answer the following questions from the diagram: 

a. In which over the maximum runs were conceded? 

b. What is the total run conceded in ten overs? 

c. What is the average/mean runs per over?

Solution:

 

a. In the diagram 4th bar is longest and it reached to 12. So, maximum runs were 12.

b. Total run conceded in ten over= 5 + 7 + 3 + 12 + 4 + 7 + 2 + 6 + 4 + 5 = 55 runs

c. Average runs per over=     Total runsNumber of over = 5510 = 5.5

E.11.4. Write down the prime numbers less than 50. Find the average/mean and the median of the numbers.

Solution:

Here are the prime numbers less than 50: 

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 

To find the average/mean: 

Average = 2+3+5+7+11+13+17+19+23+29+31+37+41+43+47                                    15

Average = 328 15

Average = 21.87

To find the median, we arrange the numbers in ascending order: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47 

Since there are 15 numbers, the median will be the middle number. In this case, the median is the 8th number, which is 19. 

So, the average/mean of the prime numbers less than 50 is approximately 21.87, and the median is 19.

E.11.5. 

Heights (in meter) of the bars are given. Find the median of the data.

Solution:

 

To find the median of the given data set, you first need to arrange the heights in ascending order: 

7, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 21, 23, 24, 25, 25 

There are 18 data points in total. Since there's an even number of data points, the median will be the average of the two middle values. 

The two middle values are 16 and 18. 

So, the median = 16 + 18     2 = 34 2 = 17

Therefore, the median height of the bars is 17 meters.

E.11.6. Find the average/mean, median and the mode of the data:

Solution:

Average/Mean: To find the average, you sum up all the values and divide by the total number of values.

Sum of all values = 12+7+23+11+9+14+25+5+18+13+21+17+3+10+16+24+19+15+8+27+17+15+12+26+23+22+28+12+29+17 

Sum = 498 

Total number of values = 30 

Average =                 SumTotal Number of Values = 498 30 = 16.6

Median: To find the median, you need to arrange the data in ascending order and then find the middle value. Since there are 30 data points, the median will be the average of the 15th and 16th values. 

After sorting the data: 3,5,7,8,9,10,11,12,12,12,13,14,15,15,16,17,17,17,18,19,21,22,23,23,24,25,26,27,28,29 

Median = 15^th value + 16^th value                 2
            = 16 + 17     2 = 16.5

Mode: The mode is the value that appears most frequently in the data set. The modes in this dataset are 12, 17 each appearing 3 times.

So, the results are: 

Average/Mean ≈ 16.6  

Median = 16.5 

Mode = 12, 17

E.11.7 Talk to 20/25 students of your class/ your previous class/ your following class. Collect the following data (their ages, daily study times, daily games times, daily sleeping times etc.) and prepare a list or a table according to the sample below. 

Using the List or table, find the answers to the following questions. 

a) Using the different types of information of the students mentioned in the list, find the mean/average, median and mode of any three. In this case, which one is more effective according to you – comment with justification. 

b) Draw a line graph using the daily study time of the students. 

c) “Those who have more study time, they have less sleep

time”—verify the validity of the proverb from the list prepared by information obtained by you. 

d) Is there a relationship between more study time of students with their games time and TV watching time? Find out. 

e) Is there any relationship between students having more games time, with their study time, sleeping time and TV watching time? Find out. 

f) Write a summary of your own opinion about the differences/ similarities of the study time and games time of the students of the classes of which you collected and analyzed the data.

Solution:

Sample Data-

Now, let's proceed to answer the questions:

a) Mean/Average, Median, and Mode:

Mean/Average: We can find the mean of any three variables such as age, study time, game time, or sleep time.

Median: We can find the median of any three variables as well.

Mode: We can find the mode of any three variables.

To determine which measure is more effective, it depends on the context and distribution of the data. For example, the mean might be more sensitive to extreme values, while the median is more robust to outliers. The mode indicates the most common value, which can be useful for categorical data. In this case, we would need to analyze the distribution of the data and the specific question being addressed to determine the most effective measure.

b) Line Graph: We can create a line graph using the daily study time of the students.

c) Verification of the Proverb: We can analyze the relationship between study time and sleep time to verify the proverb.

d) Relationship Between Study Time and Games/TV Time: We can calculate correlations or perform regression analysis to determine if there's a relationship between study time and games/TV time.

e) Relationship Between Games Time and Study/Sleep/TV Time: Similar to the previous question, we can analyze correlations or perform regression analysis to find any relationships.

f) Summary of Differences/Similarities: We can summarize the differences and similarities in study time and game time among the students, possibly discussing factors that influence these behaviors and any observed patterns in the data.

Let me know which specific calculations or analyses you would like to proceed with.