Question

Q6 )If the mode of the data
10,11,12,10,15,14,15,13,12,x,9,7 is 15 , then the value of x is :

Answer 1

Answer :

The value of x - 15.

Step-by-step explanation:

Given :

Mode of the data  - $\sf 10,11,12,10,15,14,15,13,12,x,9,7\;is\; 15$

To Find :

The value of 'x'.

Solution :

The first step is :

Change the given mode into Ascending order.

So,

Given mode - $\sf 10,11,12,10,15,14,15,13,12,x,9,7\;is\; 15$

Ascending Order :

$\sf 7,9,10,10,11,12,12,13,14,15,15\;and\;x$

{ Here, We consider 'x' as the least/smallest value becasue, We don't know the exact value of 'x' }

Since, Mode is the most repeated value,

x = 15.

⇒ 10 & 13 already repeated twice then 15 should be repeated thrice to become the mode.

∴ The value of x - 15.

$\rule{300}{1.5}$

$\bigstar\;\heartsuit\; \textbf{\underline{\underline{Extra Information:}}}}\;\heartsuit$

★ Mode :

The mode is the numbers of a set of data values is the value that appears most often.

★ Example :

{6, 3, 9, 6, 6, 5, 9, 3}

{ Here, the Mode is 6 (it occurs most often) }

★ Ascending Order :

The numbers that are arranged from smallest to largest.

In simple words it is Increasing.

★ Example :

2, 5, 12, 91 are in ascending order.

★ Descending Order :

The numbers that are arranged from largest to smallest.

In simple words it is Decreasing.

★ Example :

10, 9, 8, 7, 2 are in descending order.

Answer 2

AnswEr :

⠀

$\huge\red {\boxed{ \bold{x = 15}}}$

⠀

Explanation :

☑ Given :

• If the mode of the data

10,11,12,10,15,14,15,13,12,x,9,7 is 15 , then the value of x is :

☑ To Find :

• Find the Value of x.

☑ Solution :

• Given Data-

10, 11, 12, 10, 15, 14, 15, 13, 12, x, 9, 7

• Arrange the Given Data in Ascending Order-

7, 9, 10, 10, 11, 12, 12, 13, 14, 15, 15 and, x

━━━━━━━━━━━━━━━━━━━━━━━━

$\purple{\boxed{ \star \frak{ \: Definition \: of \: Mode : }}}$

Mode is that Value of the Observation which Occurs Maximum Numbers of time.

━━━━━━━━━━━━━━━━━━━━━━━━

✯ Here 10, 12 and 15 Occurs 2 times(Maximum times) each.

▣ Since 15 is the Mode [Given]

$\large\therefore$ 15 must Occur at least One More time than 10 and 12.

So Possible Value of $\large{\boxed{ \bold {x=15 }}}$

⠀

⠀

$\huge{\red{\ddot{\smile}}}$