Students often refer to Class 8 Maths Notes and Part 2 Chapter 5 Tales by Dots and Lines Class 8 Notes during last-minute revisions.
Class 8 Maths Chapter 5 Tales by Dots and Lines Notes
Class 8 Tales by Dots and Lines Notes
→ Last year, we looked at the mean as a fair share. Here, we learnt how the sum of the distances of the values to their left and right is the same.
→ We saw that when values greater than the mean are inserted, the mean increases. When values less than the mean are inserted, the mean decreases. Similar phenomena can be observed with the median.
→ Line graphs can be used to visualise change over time.
→ We saw that examining data can lead to new questions and directions to probe further.
The Balancing Act
Mean: The mean is a measure of central tendency. It represents the average value of a data set.
It can be calculated by using a formula
Mean = \(\frac{\text { Sum of all observations }}{\text { Number of observations }}\)
Effect of adding or removing a value on the mean:
Adding a number greater than the mean increases the mean.
Adding a number less than the mean decreases the mean.
Removing a number greater than the mean decreases the mean.
The mean remains unchanged if the mean of the added values equals the original mean.
The median is the middle value of the observations arranged in ascending order. When a new value greater than the earlier median is added, the median increases; when a value less than the earlier median is added, the median decreases.
Effect of increasing or multiplying each observation by the same number:
If each observation is increased by a number (k), then the mean increases by the same number (k).
New mean = old mean + k
If each observation is multiplied by a number (y), then the mean is also multiplied by that number.
New mean = y × original mean
Sometimes an observation is missing or wrongly recorded. The mean can be used to find the correct or missing value. Frequency shows how many times the same observation occurs in the collected data. It makes calculations easier and helps us read the observations clearly.
When frequencies are given, the mean is found by multiplying each value (x) by its frequency (f) and then dividing by the total number of observations.
Mean = \(\frac{\text { Sum of all observations }(f \times x)}{\text { Number of observations }(f)}\)
When frequencies are given median is found by using the cumulative frequency.
The total number of observations obtained by adding the frequencies one by one as we move from the smallest value to the largest value is known as the cumulative frequency.
Median:
When total observations are even
Median = Average of \(\frac{n^{\text {th }}}{2}\) and \(\left(\frac{n}{2}+1\right)^{t h}\) observations
When total observations are Odd
Median = Value of \(\left(\frac{n+1}{2}\right)^{t h}\) observation
Spreadsheet: A spreadsheet is used to collect data digitally. It consists of small boxes called cells, and each cell has a unique address such as A3 or B2.
Here, A and B represent columns, while 3 and 2 represent row numbers. This helps us distinguish each cell easily.
In a spreadsheet, we can calculate the sum and average by using the formula =SUM(initial cell name: last cell name) and =AVERAGE (initial cell name: last cell name), respectively.
Visualising and Interpreting Data
Line Graph: A line graph is used to show how one quantity changes with respect to another over a period of time.
A line graph helps us
- Compare values easily.
- Understand patterns and trends
- Make simple predictions based on past data.
To identify and interpret the information, follow a two-step process.
- Step 1: Identify what is given.
- Step 2: Infer and interpret from what is given.
Infographics
Infographics can help present complex data and concepts in a visually engaging way, making it easier to understand and analyse information.
Example: The following table shows the production of wheat (in lakh tonnes) in five states of India during a particular year.
Show in an Infographic Chart.
(i) Which state has the highest wheat production?
(ii) Which state has more wheat production than Haryana?
(iii) Which state has wheat production less than 100 lakh tonnes?
(iv) Find the mean wheat production of the given states.
Solution:
(i) Uttar Pradesh
(ii) Punjab, Uttar Pradesh, and Madhya Pradesh
(iii) Rajasthan
(iv) Mean wheat production = \(\frac{120+100+150+130+90}{5}\)
= \(\frac {590}{5}\)
= 118 lakh tonnes
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