Data Handling Class 7 Notes Maths Chapter 3

Students can go through AP 7th Class Maths Notes Chapter 3 Data Handling to understand and remember the concepts easily.

Class 7 Maths Chapter 3 Notes Data Handling

→ The information collected is called DATA.

→ Before collecting a data we Should know that what we would use it for.

1. Performance of your class in mathematics.
2. Performance of India in world cup cricket.
3. Female literacy rate in year area.
4. Number of infants in a village.

→ Tally marks are used to represent data.

→ Tally, marks represents 1, 2, 3, 4, 5 respectively.

→ 7 can be denoted by Tally marks as

→ 21 can be denoted by tally marks as

→ Arithmetic mean (or) mean: (AM) or
Mean = \(\frac{\text { Sum of all observations }}{\text { Number of observations }}\)
Ex: 1) Find the mean of 1, 2, 3, 10
Solution:
Mean = \(\frac{1+2+3+10}{4}\) = \(\frac{16}{4}\) = 4

Ex: 2)A batsman scored the following number of runs in 5 innings 30, 29, 16, 10, 50. Calculate the mean runs scored.
Mean = \(\frac{30+29+16+10+50}{4}\) = \(\frac{135}{5}\) = 27

→ In some data AM will be greater than few values and also less than few values of the data.

→ Range : The difference between the maximum and minimum of a data is called its Range.
Range = Max. value – Min. value
Ex: 1) Find the range of first 10 natural num-bers ?
Answer:
Range = 10 – 1 = 9

Ex: 2)Find the range of first 100 whole number.
Answer:
Range = 99 – 0 = 99

→ Mode; In a data, an observation which occurs most frequently is called mode and is denoted by Z.
Ex: 1) Find the mode of 9, 9, 9, 8, 7, 5, 9, 1, 9, 0.
Answer:
Mode = 9

→ Bimodal data : A data having two modes is called Bimodal data.
Ex: Find the mode of 7, 3, 5, 6, 7, 7, 3, 3, 1.
Answer:
Mode = 3 and 7.

→ Trimodal data : Data having 3 modes is called Trimodal data.
Ex: Find the mode of 7, 3, 1, 2, 3, 4, 1, 2, 7, 1.
Answer:
Mode = 1, 2, 3

→ Some times a data may not have any mode.
Ex: Find the mode of 7, 8, 9, 3, 5, 6, 1.
Answer:
No mode.

→ Data having n-modes is called n-modal data.

→ Median : In a given data, arranged in ascending or descending order, the median is the middle observation.
Ex: Find the median of 7, 8, 0, 1, 5.
Answer:
Ascending order (A.O.) is 0, 1, 5, 7, 8
Median = 5. ‘

→ If the data is having ‘n’ observations then (\(\frac{n+1}{2}\)) th observation is the median of the data after arranging either in AO. (Or) D.O.
Ex: Find the median of 7, 4, 3, – 1, – 2.
Solution:
Number of observations = 5
A.O = – 2, – 1, (3), 4, 7
Median = 3.
(\(\frac{5+1}{2}\))th = (\(\frac{6}{2}\))th = 3rd observation is the median of above data.

→ In a data if the number of observations are even then take the average of two middle observations after arranging in AO. (or) D.O.
Ex: Find the median of 60, 70, 30, 10, 100, 120.
Solution:
AO. 10, 30,60, 70,100,120
Middle observation 60 & 70
Median = \(\frac{60+70}{2}\) = \(\frac{130}{2}\) = 65

→ If there are n observations in data and ‘n’ is even then the average of \(\frac{n}{2}\) th and (\(\frac{n}{2}\) + 1) th observation is taken as the median.
Ex: Find the median of 12, 8, 10, 2, 16, 14
Solution:
A.O. 2, 8, 10, 12, 14, 16
Middle most, values 10 & 12.
Median = \(\frac{10+12}{2}\) = \(\frac{22}{2}\) = 11.

→ \(\frac{n}{2}\) = \(\frac{6}{2}\) = 3^rd observation.
\(\frac{n}{2}\) + 1 = 3 + 1 = 4^th observation.
Average of 3^rd, 4^th observation is the median \(\frac{10+12}{2}\) = \(\frac{22}{2}\) = 11.

→ Bar graphs: While representing a data we use bars (or) rectangles is called Bar graph we should use proper scale to represent the data through Bar graph.
Ex:

→ Double bar graph help to compare two collections of a data at a glance.
Ex:

→ In bar graphs the length of all bars is not same.

→ In bar graphs the width of all bars is same.

→ A bar graph is a representation of numbers using bars of uniform width.

→ Double bar graphs help to compare two collections of data at a glance.