Amarchand SinghviInternational School

Subject : Mathematics

Class : IX

Chapter : 14 – Statistics

Topic : Frequency distribution table, Bar graph and

Histogram with uniform base length

Teacher : Ms. Laveena Longwani

E-Learning Programme

Chapter – 14 StatisticsDeleted syllabus

Topic: Histogram with varying base length, mean, median and mode of ungrouped dataExercise: 14.3(Q6 to Q9), 14.4

What is data?

• Collection of facts, such as numbers, words, measurements, observations or just descriptions of things.

For example: information collected for a survey, record of

attendance of students, etc.

What is statistics?

• Extraction of meaningful information from data is called statistics.

• In simple words it is representation of data using graphs.

• Range: The difference of highest and lowest values of a data is called range

• Frequency: The number of times an event occurs or the number of times any observation is repeated is its frequency.

Ungrouped Frequency Distribution Table

Question: Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows:

0 1 2 2 1 2 3 1 3 0

1 3 1 1 2 2 0 1 2 1

3 0 0 1 1 2 3 2 2 0

Prepare a frequency distribution table for the data given below.

Number of heads occurring

Tally marks Frequency

0 |||| | 6

1 |||| |||| 10

2 |||| |||| 9

3 |||| 5

Total 30

Solution:

Here as you can see frequency of 0 is 6, this means that 0 is repeated in the data 6 times.Similarly, 1 is repeated 10 times, 2 is repeated 9 times and 3 is repeated 5 times.Also, Highest value in data = 3Lowest value in data = 0Thus, range = 3 – 0 = 3

Grouped Frequency Distribution Table• When the data is represented in groups or intervals

such as 0 – 5, 5 – 10, 10 – 15,…then this representation is called grouped frequency distribution table.

• These groupings are called ‘classes’ or ‘class-intervals’ and their size is called ‘class width’.

• In each interval the least number is called the lower class limit and the greatest number is called upper class limit. For example in the interval 5 – 10, 5 is the lower limit and 10 is the upper limit.

Question: A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:

2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5

3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7

2.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8

3.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4

4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6

Construct a grouped frequency distribution table for this data, using intervals of size 0.5 starting from the interval 2 – 2.5.

Solution:

Life of batteries (in years)

Tally Marks Frequency

2.0 – 2.5 || 2

2.5 – 3.0 |||| | 6

3.0 – 3.5 |||| |||| |||| 14

3.5 – 4.0 |||| |||| | 11

4.0 – 4.5 |||| 4

4.5 – 5.0 ||| 3

Total 40

How to make class intervals continuous? • Consider the following frequency distribution table which gives the height of

20 students in a class.

• Now suppose 2 new students are admitted to the class with height 155.5 cm and 140.5 cm.

• But in the above table there is no such class interval in which they can be added because the intervals are not continuous.

Height in cm Number of students

135 – 140 4

141 – 145 3

146 – 150 2

151 – 155 6

156 – 160 5

Total 20

• So the method to make it continuous is:

1. Consider any two consecutive intervals.

2. Lets consider intervals 141 – 145 and 146 – 150.

3. Upper limit of 141 – 145 = 145, Lower limit of 146 – 150 = 146

4. Find out the difference: 146 – 145 = 1

5. Half the difference = 1

2= 0.5

6. Now subtract this difference from lower limit of each interval and add this difference to upper limit of each interval.

So the new intervals are:

(135 – 0.5)-(140 + 0.5) = 134.5-140.5

(141 – 0.5)-(145 + 0.5) = 140.5-145.5

(146 – 0.5)-(150 + 0.5) = 145.5-150.5

(151 – 0.5)-(155 + 0.5) = 150.5-155.5

(156 – 0.5)-(160 + 0.5) = 155.5-16.0.5

Continuous intervals

• So now the heights of two new students can be included in the table which is as follows:

Height in cm Number of students

134.5-140.5 4

140.5-145.5 4

145.5-150.5 2

150.5-155.5 6

155.5-16.0.5 6

Total 22

Graphical Representation of Data

1. Bar Graphs

2. Histograms of uniform width and of varying width

3. Frequency Polygon

Bar Graph

• Bar graph is a pictorial representation of data in which bars of uniform width are drawn with equal spacing on one axis(usually X- axis) and values are shown on another axis(usually Y-axis).

Histogram

• It is similar to bar graph but Histogram is used for continuous class intervals.

• There is no gap between the bars in Histogram.

Question: The length of 40 leaves of a plant are measured correct to one millimeter,

and the obtained data is represented in the following table. Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]

Length (in mm) Number of leaves

118 – 126 3

127 – 135 5

136 – 144 9

145 – 153 12

154 – 162 5

163 – 171 4

172 – 180 2

Solution:(i) The data given in the question is represented in discontinuous class interval. So, we have to make it in continuous class interval. The difference is 1, so taking half of 1, we subtract ½ = 0.5 from lower limit and add 0.5 to the upper limit. Then the table becomes:

Length (in mm) Number of leaves

117.5 – 126.5 3

126.5 – 135.5 5

135.5 – 144.5 9

144.5 – 153.5 12

153.5 – 162.5 5

162.5 – 171.5 4

171.5 – 180.5 2

Because the class intervals does not start from zero,a break in the X-axis is shown, known as Kink

>

Note: This presentation is a part of the E-Learning Program of Amarchand

Singhvi International School and is created only for educational purpose.

Compilation & presentation : Ms. Laveena Longwani

Web support & management : Mr. Deepak Chellani

Technical support : Mr. Shivam Gundecha

E-learning Program Co-ordination:

Mr. Prashant Chaturvedi

Produced by

Mr. Mridul Varma (Principal)

Amarchand Singhvi International School

Parekh Parisar, Ward 7A, Gandhidham – Kutch

Gujarat 370201 India