Question

Please find mode. Help me urgent

Answer 1

a. 3:1

b. see below

c. 70

d. 0-20

Explanation:

Part a:

The third quartile divides the given data into two parts: the lower half and the upper half.

Upper half:
`\sf (3N)/(4) = (3* 40 )/(4) = 30`

Lower half: 40 - 30 = 10

The lower half contains 30 students, and the upper half contains 10 students. Therefore, the third quartile divides the given data into a ratio is 30:10 = 3:1 .

Part b.

Cumulative frequency table:

The cumulative frequency of a value is the number of observations that are less than or equal to that value.

It's table is:

`\boxed{ \begin{aligned} \textsf{Marks Obtained} &| \textsf{cumulative frequency} \\ 0 - 20 &| 12 \\ 20 - 40 &| 15 - 12 = 3 \\ 40 - 60 &| 26 - 15 = 11 \\ 60 - 80 &| 34 - 26 = 8 \\ 80 - 100 &| 40 - 36 = 6 \\ &| n = 40 \end{aligned}}`

Part c.

Third quartile (Q3):

The third quartile is the middle value of the upper half of a distribution.

we can find a third quartile by using this formula:

`\sf \begin{aligned} \sf Q_3 & = \left((3N)/(4)\right)th \: term \\\\ & = \left( ( 3\cdot 40)/(4) \right) th term \\\\ &= 30 th \: term \end{aligned}`

Since 30th term lies in the range of 60 - 80,

We can find the third quartile by using following:

`\sf Q_3 = L + (i)/(f) \left((3N)/(4) - cf\right)`

Where:

• L = Lower boundary of the interval containing the third quartile
• N = Total number of data points
• CF = Cumulative frequency of the interval before Q3
• i = Width of the interval containing Q3
• f = frequency

In this case:

• L = 60
• f = 8
• i = 80 - 60 = 20
• cf = 26

Substituting value in above formula, we get

`\begin{aligned} Q_3 & = 60 + (20)/(8) \left((3* 40)/(4) - 26 \right) \\\\ &= 60 + (20)/(8) \left(30 - 26 \right) \\\\ &= 60 + (20)/(8) * 4 = \\\\ &= 60+10 \\\\ &= 70 \end{aligned}`

Part d.

Part d.Mode:

The mode of a distribution is the value that appears most often.

`\sf \textsf{Mode} = \textsf{The mark that appears most often} = \textsf{0-20}`

Therefore, mode is 0-20.