Statistics Test

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Statistics Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

Calculate the mode for $$17, 12, 19, 11, 20, 11, 20, 19, 10, 25,19$$.

A
$$12$$

B
$$17$$

C
$$19$$

D
$$25$$

Solution

Mode is the value which occurs most often in the data set of values.
Given data set is $$17,12,19,11,20,11,20,19,10,25,19$$
In the above data set, value $$19$$ has occurred many times i.e., 3 times.
Therefore the mode of the given data set is $$19$$
Question 2
1 / -0

Mean of the first six even numbers is

A
$$7$$

B
$$5$$

C
$$3$$

D
$$1$$

Solution

Formula used:
$$Arithmetic\ mean= \dfrac{Sum\ of\ given\ numbers}{Total\ numbers}$$

Apply the above formula, we get
Mean$$=\displaystyle \frac{2+4+6+8+10+12}{6}$$
= $$\displaystyle \frac{42}{6}=7$$
Question 3
1 / -0

Median of the observatios $$5$$, $$7$$, $$14$$, $$12$$, $$15$$, $$17$$, $$17$$, $$5$$, $$14$$, $$7$$, $$5$$ is

A
$$14$$

B
$$12$$

C
$$11.8$$

D
$$7$$

Solution

By arranging the given no's in increasing order, we get:
$$ 5,5,5,7,7,12,14,14,15,17,17 $$
Total terms $$= 11$$
since, the middle most term is $$ 6^{th} $$.
$$\therefore $$ value of median is $$12$$
$$\therefore $$ Option $$B$$ is correct.
Question 4
1 / -0

Find the mode of $$14$$, $$25$$, $$14$$, $$28$$, $$18$$, $$17$$, $$18$$, $$14$$, $$23$$, $$22$$, $$14$$, $$18$$.

A
$$14$$

B
$$25$$

C
$$28$$

D
$$18$$

Solution

Here, we arrange the data in the ascending order :- $$14,14,14,14,17,18,18,18,22,23,25,28$$
The value $$14$$ has maximum frequency.
Therefore, the mode of the data is $$14$$.
Question 5
1 / -0

Find the mean of first ten odd natural numbers.

A
$$10$$

B
$$11$$

C
$$12$$

D
None of these

Solution

$${\textbf{Step -1: Listing first 10 odd natural numbers .}}$$

$${\text{First 10 odd natural numbers = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19}}$$

$${\textbf{Step -2: Calculating mean}}$$

$${\text{We know that, mean of n numbers = }}\dfrac{{{\text{Sum of n numbers}}}}{{\text{n}}}$$

$$\therefore {\text{ Mean of first 10 odd natural numbers,}}$$
$${\text{M = }}\dfrac{{{\text{1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19}}}}{{{\text{10}}}}$$

$$ \Rightarrow {\text{ M = }}\dfrac{{{\text{100}}}}{{{\text{10}}}}{\text{ = 10}}$$

$${\textbf{Thus, the mean of first 10 odd natural numbers is 10 .}}$$
Question 6
1 / -0

The mean of first six multiples of $$4$$ is

A
$$13.5$$

B
$$14.5$$

C
$$14$$

D
$$16$$

Solution

$$\textbf{Step 1: Write all 6 multiples of 4}$$

$$\text{First six multiples of 4 are: }4, 8, 12, 16, 20, 24$$

$$\textbf{Step 2: Find Mean of all 6 observations}$$

$$\text{Mean }= \cfrac{4 + 8 + 12 + 16 + 20+ 24}{6}$$ $$\left[\because \boldsymbol{\textbf{Mean }= \cfrac{\textbf{Sum of observations}}{\textbf{Total observations}}}\right]$$

$$\text{Mean }= \cfrac{112}{6}$$

$$\text{Mean }= 14$$

$$\textbf{Hence, Option C is correct.}$$
Question 7
1 / -0

If the median of $$\displaystyle \frac{x}{5}$$ $$\displaystyle x$$ $$\displaystyle \frac{x}{4}$$ $$\displaystyle \frac{x}{2}$$ and $$\displaystyle \frac{x}{3}$$ $$\displaystyle \left ( where\, x> 0 \right )$$ is $$8$$ then the value of $$x$$ would be

A
$$24$$

B
$$32$$

C
$$8$$

D
$$16$$

Solution

Arranging in ascending order the values are
$$\displaystyle \frac{x}{5},\frac{x}{4},\frac{x}{3},\frac{x}{2},x $$
Middle value $$=\displaystyle \frac{x}{3}\Rightarrow \frac{x}{3}=8\Rightarrow x=24 $$
Question 8
1 / -0

Mode of a set of observations is the value which

A
occurs most frequently

B
divides the observations into two equal parts

C
is the mean of the middle two observations

D
is the sum of the observations

Solution

The value which occurs most number of times i.e. most frequently is called the mode of the series.
Question 9
1 / -0

A cricket player scored the following runs in $$11$$ one-day international matches:
$$65$$, $$30$$, $$7$$, $$60$$, $$65$$, $$65$$, $$30$$, $$28$$, $$30$$, $$15$$, $$30$$ Find the modal runs.

A
$$20$$ runs

B
$$25$$ runs

C
$$30$$ runs

D
$$35$$ runs

Solution

From the given observations:
$$65$$, $$30$$, $$7$$, $$60$$, $$65$$, $$65$$, $$30$$, $$28$$, $$30$$, $$15$$, $$30$$
Here, $$30$$ is the most frequent observation. hence, $$30$$ is the mode of the given data.
Question 10
1 / -0

The arithmetic mean of first five natural numbers is

A
$$3$$

B
$$4$$

C
$$5$$

D
$$6$$

Solution

Formula used:
$$Arithmetic\ mean= \dfrac{Sum\ of\ given\ numbers}{Total\ numbers}$$

Apply the above formula, we get
$$\displaystyle AM=\frac{1+2+3+4+5}{5}=3$$

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Re-Attempt Weekly Quiz Competition

Statistics Test - 13

Result

Statistics Test - 13

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Question 1

$$12$$

$$17$$

$$19$$

$$25$$

Solution

Question 2

$$7$$

$$5$$

$$3$$

$$1$$

Solution

Question 3

$$14$$

$$12$$

$$11.8$$

$$7$$

Solution

Question 4

$$14$$

$$25$$

$$28$$

$$18$$

Solution

Question 5

$$10$$

$$11$$

$$12$$

None of these

Solution

Question 6

$$13.5$$

$$14.5$$

$$14$$

$$16$$

Solution

Question 7

$$24$$

$$32$$

$$8$$

$$16$$

Solution

Question 8

occurs most frequently

divides the observations into two equal parts

is the mean of the middle two observations

is the sum of the observations

Solution

Question 9

$$20$$ runs

$$25$$ runs

$$30$$ runs

$$35$$ runs

Solution

Question 10

$$3$$

$$4$$

$$5$$

$$6$$

Solution

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