Each of our Ganita Prakash Class 8 Worksheet and NCERT Class 8 Maths Chapter 5 Tales by Dots and Lines Worksheet with Answers focuses on conceptual clarity.
Tales by Dots and Lines Worksheet Class 8
Class 8 Maths Tales by Dots and Lines Worksheet
Tales by Dots and Lines Class 8 Ganita Prakash Worksheet
The Balancing Act
Rohan has recorded the number of minutes he studied the story book each day for five days. He wants to represent this data using a single number but Is unsure whether the mean or the median would be more appropriate. While discussing with his friend Ruhl, he explores how changes In data values, can affect these measures of central tendency.
Question 1.
The study times In minutes are 30, 40, 50, 70, and 90. Answer the following questions,
Question 1.
Arrange the data in ascending order and then find the mean and median.
Answer:
Mean; 56 minutes, Median : 50 minutes
Question 2.
Draw a dot plot for the given data and clearly indicate the mean.
Answer:
Question 3.
Is the mean equal to the midpoint of the smallest and largest values? Justify your answer using calculations.
Answer:
No
Question 4.
Find the distance of each data value from the mean. Show that the sum of the distances of the values less than the mean is equal to the sum of the distances of values greater than the mean.
Answer:
Question 5.
A new data value of 110 minutes is added.
(i) Predict whether the mean will increase or decrease, giving a reason.
(ii) Calculate the new mean to verify your prediction.
Answer:
(i) Yes
(ii) New mean = 65
Question 6.
If a value equal to the original mean is added to the data, what happens to the mean? Explain.
Answer:
Mean remains the same
Question 7.
Can there be more than one value that acts as the centre of this data? Explain your reasoning.
Answer:
No
Question 2.
Construct a set of five distinct numbers such that the mean lies outside the two middle numbers. Explain how this is possible.
Answer:
Question 3.
If the mean of 6 numbers is 14, answer the following questions.
(a) A new number 20 is added. Will the mean increase or decrease? Find the new mean.
(b) Instead, if the number added is 8, what happens to the mean?
Answer:
(a) Mean increases
(b) Mean decreases
Question 4.
If the mean of a data set is 25, answer the following questions.
(a) If a value equal to the mean is removed, does the mean change? Justify.
(b) If two values, one 5 more and one 5 less than the mean, are added, what happens to the mean?
Answer:
(a) Mean does not change
(b) Mean remains unchanged
Question 5.
(a) Fill the grid so that the average of the numbers in every row column and diagonal is 15.
(b) Is it possible to change only one number in your grid and still keep the average 15 for all rows and columns? Explain briefly.
Answer:
(a)
| 14 | 19 | 12 |
| 13 | 15 | 17 |
| 18 | 11 | 16 |
(b) No
Question 6.
Is it possible to remove two numbers from the data 3, 6, 9, 12, 15 so that the mean does not change? Explain your answer.
Answer:
Yes.
Question 7.
The number of times students attended an after-school programme in a month is shown in the dot plot below. One student attended the programme twice during that month. Answer the following questions.
(a) Find the average number of times students attended the programme.
(b) Find the median number of times students attended the programme.
Answer:
(a) 5.80
(b) 55
Question 8.
The mean of 5 observations is 6, answer the following questions.
(a) Find the new mean if each observation is multiplied by 3.
(b) Find the new mean if each observation is divided by 2.
Answer:
(a) 18
(2) 3
Question 9.
For the data set: 4, 9, 11, 15, 20, 24, answer the following questions.
(a) Find the median
(b) Insert one value so that the median increases.
(c) Insert one value so that the median remains unchanged.
Answer:
(a) 13
(b) 15 (Answer may vary)
(c) 13
Question 10.
A data set has an odd number of observations.
(a) What happens to the median if a very large value is added?
(b) What happens to the median if a very small value is added?
Answer:
(a) Median increases.
(b) Median decreases.
Question 11.
The mean of a numbers LS 32. Etght numbers are 28, 35, 30, 40, 31, 2d1, 36, and 34. Find the missing number.
Answer:
25
Question 12.
The average score of a class of 25 students is 64. One student’s score was recorded as 74 instead of 47.
(a) Find the correct total score.
(b) Find the corrected average score.
Answer:
(a) 1573
(b) 62.92
Question 13.
The table shows the number of books read by students in a month:
| Books Read | Frequency |
| 0 | 4 |
| 1 | 9 |
| 2 | 12 |
| 3 | 6 |
| 4 | 3 |
(a) Find the mean number of books read.
Answer:
1. 85
(b) Find the median.
Answer:
2
(c) Which measure better represents the data? Give a reason.
Answer:
The median better represents the data.
Visualising and Interpreting data
Question 14.
The following line graph shows the estimated number of patients visiting state-run government hospitals each month over a certain period of time. Observe the graph and answer the following questions.
(a) What general pattern do you observe in the number of patients visiting government hospitals over the given time period?
Answer:
The number of patients visiting government hospitals shows a repeating rise and fall pattern over time.
(b) Estimate the number of patients (in lakhs) who visited the hospitals in April 2021.
Answer:
3 lakhs
(c) What time period does the graph represent?
Answer:
Jan 2020 to Dec 2022
(d) Compare the number of patients visiting state-run government hospitals in the month of October for the years 2020, 2021, and 2022. Which year shows the highest number?
Answer:
October 2021 and October 2022
(e) Using the graph, estimate the total number of patients (in lakhs) who visited state-run government hospitals during the year 2021.
Answer:
43 Lakhs
Question 15.
The following line graph shows the number of hours Muskan slept each night during a week. Observe the graph and answer the following questions.
(a) On which day did Muskan get the maximum sleep?
Answer:
Saturday
(b) On which day did she get the minimum sleep?
Answer:
Wednesday
(c) Find the difference between the maximum and minimum hours of sleep during the week.
Answer:
3 hours 12 minutes
(d) What is the average number of hours Muskan slept per night during the week?
Answer:
7 hours and 34 minutes (approx.)
Question 16.
The table shows the number of customers at an Ice cream parlour during each lunchtime.
(a) Draw a line graph for the following data.
| Day | Customers |
| Monday | 42 |
| Tuesday | 47 |
| Wednesday | 3 |
| Thursday | 36 |
| Friday | 40 |
| Saturday | 31 |
Answer:
(b) On which day did the ice cream parlour have the most customers?
Answer:
Tuesday
(c) How many customers visited the ice cream parlour in total during the week.
Answer:
Question 17.
The monthly electricity consumption (in units) of a household is recorded over a year. Answer the following questions.
(a) Why is a line graph suitable to represent this data?
Answer:
A line graph is suitable because the electricity consumption is recorded over time.
(b) What information does the steepness of the line convey?
Answer:
The steepness of the line shows the rate of change in electricity consumption.
Question 18.
Observe the given line graph and choose the correct statements from the following. For the incorrect statements, give a reason to justify your answer.
Average Monthly Temperatures in City A and City B
(a) City A is better suited to raising seasonal crops than City B.
(b) Global warming has affected City B much more than it has affected City A.
(c) The climate of city B is consistently warmer than that of City A.
(d) The temperature in City A fluctuates more over the course of the year than the temperature in City B does.
Answer:
(a) incorrect
(b) incorrect
(c) incorrect
(d) correct
Question 20.
Collect data on your daily screen time (the total time spent using a mobile phone, computer, tablet, or television) for seven days.
(a) Represent it using a line graph.
(b) Draw an infographic for the same data, and find the mean and median screen time.
(c) What pattern do you observe?
Answer:
Worksheet On Tales by Dots and Lines Class 8
A. Choose the correct option.
1. Which of the following best represents the mean on a dot plot?
(a) The point with the maximum number of dots
(b) The midpoint of the smallest and largest values
(c) The point where the dot plot looks symmetric
(d) The balancing point of all data values
Answer:
The point with the maximum number of dots
2. For the data: 4, 6, 10, 16, 18, 22. Which statement is always true?
(a) Mean = Median = 13
(b) Mean is greater than the median.
(c) Mean lies between the smallest and largest values.
(d) Mean must be one of the data values.
Answer:
(c) Mean lies between the smallest and largest values.
3. The mean of five numbers is 20. If one number equal to 20 is removed, the new mean will
(a) increase
(b) decrease
(c) remain the same
(d) become zero
Answer:
(c) remain the same
4. Which situation will definitely decrease the mean of a data set?
(a) Adding a value equal to the mean
(b) Removing a value equal to the mean
(c) Adding a value smaller than the mean
(d) Removing a value smaller than the mean
Answer:
(c) Adding a value smaller than the mean
5. Why is the mean called a “balance point”?
(a) It is the middle number
(b) It minimises the total distance of data values
(c) Distances on both sides are equal
(d) It appears most often
Answer:
(c) Distances on both sides are equal
6. Which of the following changes will definitely change the median?
(a) Adding a value equal to the median
(b) Adding a value much larger than the median
(c) Adding two values symmetrically around the median
(d) None of these
Answer:
(b) Adding a value much larger than the median
7. A line graph is most suitable when the data shows
(a) parts of a whole.
(b) comparison between categories.
(c) change over time.
(d) frequency of values.
Answer:
(c) change over time.
8. If two lines on a graph cross each other, it means:
(a) Both quantities are equal at that point
(b) Both quantities stop changing
(c) The scale is incorrect
(d) The data is wrong
Answer:
(a) Both quantities are equal at that point
Directions. (For Q.9 – 10): In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
9. Assertion (A): The mean is always one of the given data values.
Reason (R): The mean is the average value of the data.
Answer:
(d) Assertion (A) is false but Reason (R) is true.
10. Assertion (A): A line graph helps in identifying trends such as increase or decrease in data.
Reason (R): The data points in a line graph are connected in square.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B. Fill in the blanks.
1. The mean of a data set is found by dividing the ______ of all observations by the ______ of observations.
Answer:
sum,number
2. The mean is a measure of ______ tendency.
Answer:
central
3. Extreme values doesn’t affect the ______ of the data.
Answer:
median
4. A line graph is mainly used to show change over ______.
Answer:
time
C. State whether the following statements are true (T) or false (F).
1. Adding a value greater than the mean will decrease the mean.
Answer:
false
2. Extreme values do not affect the mean.
Answer:
True
3. In a dot plot, each dot represents exactly one observation.
Answer:
True
4. Dot plots are useful only when the number of data values is very large.
Answer:
false
5. In a line graph, the vertical axis usually represents time.
Answer:
false
D. Solve the following.
Question 1.
Find the mean of the following sets:
(a) The first 20 natural numbers.
(b) The first 20 odd numbers.
(c) The first 20 multiples of 3.
Answer:
(a) 10.5
(b) 20
(c) 31.5
Question 2.
Consider a class with 15 studeats. Their average score is 72. Oae student’s score was 87, but was mistakenly recorded as 78. Find the corrected average.
Answer:
72.6
Question 3.
Find the median of these numbers: 8, 12, 15, 18, 20, 25, 30.
(a) If you add 17 to this set, what is the new median?
(b) If you remove 8 from the set, what is the new median?
Answer:
(a) 17.5
(b) 19
Question 4.
The monthly maximum temperatures (°C) of two cities are:
City A: 25, 26, 28, 30, 32, 34, 35, 34, 32, 30, 28, 26
City B: 15, 18, 22, 26, 30, 35,’ 38, 36, 32, 28, 22, 18
(a) Draw a line graph for both cities on the same plot.
Answer:
(b) Which city has more temperature variation?
Answer:
City B