Question

The marks obtained by 40 students of Class X in an examination are given below:

9, 7, 19, 7, 8, 14, 17, 21, 20, 3, 3, 22, 12, 6, 17, 10, 14, 9, 5, 19, 14, 0, 24, 4, 4, 8, 13, 15, 20, 19, 8, 23, 5, 23, 8, 24, 10, 17, 11, 17

Prepare a frequency distribution table with equal class intervals starting from 0-5 (where 5 is not included) and answer the following questions.

a. What is the lower limit of the first class interval?

b. What is the upper limit of the last class interval?

c. What is the class size of each class?

d. Which class interval has the highest frequency?

e. What is the class mark of the third class interval?​

Answer 1

QUESTION

The marks obtained by 40 students of Class X in an examination are given below:

9, 7, 19, 7, 8, 14, 17, 21, 20, 3, 3, 22, 12, 6, 17, 10, 14, 9, 5, 19, 14, 0, 24, 4, 4, 8, 13, 15, 20, 19, 8, 23, 5, 23, 8, 24, 10, 17, 11, 17

Prepare a frequency distribution table with equal class intervals starting from 0-5 (where 5 is not included)

ANSWER

Maximum marks = 24

Minimum marks = 0

Range = 24 - 0 = 24

Class Size = Upper class limit - Lower class limit

Class Size = 5 - 0 = 5

Since $\sf \dfrac{24}{5} = 4.8$ , so we should have five classes , each of size 5 . the classes of equal size covering the given data are 0 - 5 , 5 - 10 , 10 - 15 , 15 - 20 and 20 - 35

Thus , we obtain the adjacent frequency distribution table

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{cccc}\sf marks &\sf Tally \: marks&\sf frequency \\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 0 - 5&\sf \cancel{llll} &\sf 5 \\\\\sf 5 - 10 &\sf \cancel{llll} \:\cancel{llll} \: {l} &\sf 11 \\\\\sf 10 - 15&\sf \cancel{llll} \:lll&\sf 8 \\\\\sf 15 - 20&\sf \cancel{llll}\:lll&\sf 8\\\\\sf 20 - 25&\sf \cancel{llll} \: lll &\sf 8 \\\\\sf Total &\sf &\sf 40\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{\bf{}}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\end{array}}\end{gathered}\end{gathered}\end{gathered}$

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a. What is the lower limit of the first class interval?

→ Lower limit of the first class interval (0-5) is 0.

b. What is the upper limit of the last class interval?

→ Upper limit of the last class interval (20-25) is 25.

c. What is the class size of each class?

→ Class size of each class is 5.

d. Which class interval has the highest frequency?

→ Class interval 5-10 has the highest frequency.

e. What is the class mark of the third class interval?

→ Class mark of the third class interval (10-15) is $\sf \dfrac{10 + 15}{2} = \dfrac{25}{2} = 12.5$

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⭐ ADDITIONAL INFORMATION ⭐

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♪ frequency distribution table - A tabular arrangement of given numerical data showing the frequency of each observation is called a frequency distribution and the table itself is called a frequency distribution table .

♪ Class interval - Each group into which the raw data is condensed is known as class interval.

♪ Class limits - The end numbers of a class interval are called class limits. The smaller number is the lower class limit and the larger number is the upper class limit.

♪ Class size (or width) - The difference between the upper limit and the lower limit of a class is known as its class size.

♪ Class mark - The class mark is the mid - point of the class interval

★ Upper limit + lower limit / 2

Answer 2

frequency distribution table

marks⠀⠀⠀⠀Frequency

0 - 05 ⠀⠀⠀⠀⠀⠀ 5

5 -10⠀⠀⠀⠀⠀⠀⠀11

10-15⠀⠀⠀⠀⠀⠀⠀8

15 - 20⠀⠀⠀⠀⠀⠀ 8

20 - 25⠀⠀⠀⠀⠀ ⠀8

a. What is the lower limit of the first class interval?

• Lower limit of the first class interval (0-5) is 0.

b. What is the upper limit of the last class interval?

• Upper limit of the last class interval (20-25) is 25.

c. What is the class size of each class?

• Class size of each class is 5.

d. Which class interval has the highest frequency?

• Class interval 5-10 has the highest frequency.

e. What is the class mark of the third class interval?

→ Class mark of the third class interval (10-15) is

$\sf \dfrac{10 + 15}{2} = \dfrac{25}{2} = 12.5$