Statistics Test

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Statistics Test - 33

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Weekly Quiz Competition

Question 1
1 / -0

The arithmetic mean of 5 numbers is 27. lf one of the number is excluded the mean of the remaining number is 25. Find the excluded number.

A
27

B
25

C
30

D
35

Solution

Sum of 5 numbers =27 $$\times $$ 5 =135
When one of the numbers is excluded.
Sum of remaining 4 numbers = 4 $$\times $$ 25 = 100
Excluded number = 135 -100 = 35.
Question 2
1 / -0

The bar graph shows the number of cakes sold at a shop in four days. What is the difference in number of cakes between the highest and the lowest daily sale?

A
$$20$$

B
$$35$$

C
$$30$$

D
$$40$$

Solution

From the above bar graph, the highest number of cakes sold is $$45$$ (i.e., on Sunday).
and the lowest number of cakes sold is $$25$$ (i.e., on Monday).

Therefore, the difference between the highest and lowest number of cakes $$=45-25=20$$.

Hence, option $$A$$ is correct.
Question 3
1 / -0

Given above is a bar graph showing the heights of six mountain peaks. Read the above diagram and answer the following:
Write the ratio of the heights of highest peak and the lowest peak.

A
$$22 : 15$$

B
$$15 : 22$$

C
$$20 : 13$$

D
$$13 : 22$$

Solution

From the above bar graph,
Height of highest peak $$= 8800\ m$$
Height of lowest peak $$= 6000\ m$$

Hence the required ratio will be,
Ratio $$=8800 : 6000$$
$$ = 22 :15$$

Hence, option $$A$$ is correct.
Question 4
1 / -0

The mean of $$20$$ observations is $$15$$. One observation $$20$$ is deleted and two more observations are included to the data. If the mean of new set of observations is $$15$$, then find the sum of the two new observations included.

A
$$30$$

B
$$35$$

C
$$33$$

D
$$32$$

Solution

Mean $$ = \dfrac { \text{Sum of observations}}{\text{Total number of observations}} $$
Given, mean of $$ 20 $$ observations $$ = 15 $$.
Thus, sum of $$ 20 $$ observations $$ = 15 \times 20 = 300 $$
When $$ 20 $$ is deleted and two more observations are included in the data, sum of observation $$ = 300 - 20 + X + Y = 280 + X + Y $$.
And number of observations is $$ 20 - 1 + 2 = 21 $$
Given, Mean of wages of new set of observations $$ = 15 $$
$$ = \dfrac {280 + X + Y }{21} = 15 $$
$$ \Rightarrow 280 + X + Y= 15 \times 21 = 315 $$
$$ \Rightarrow X + Y = 315 - 280 = 35 $$
Question 5
1 / -0

If $$1 - 5, 6 - 10, 11 - 15, 16 - 20, ...$$ are the classes of a frequency distribution then the lower boundary of the class $$11 - 15$$ is _____

A
$$11$$

B
$$11.5$$

C
$$10.5$$

D
$$10$$

Solution

In order to make class intervals even we need to add $$0.5$$ and reduce $$0.5$$ from class boundaries
$$1-5$$ = $$0.5 - 5.5$$
$$6-10$$ = $$5.5 - 10.5$$
$$11 - 15$$ = $$10.5 - 15.5$$
so , lower boundary of class $$11-15$$ = $$10.5$$
Question 6
1 / -0

An orderly distribution of the raw data into certain specified categories is known as

A
Frequency distribution

B
Frequency

C
Cumulative frequency

D
Primary data

Solution

When we arrange the given set of data in a table by writing independent data values and the number of times it appears in the data list is called frequency distribution table.
Question 7
1 / -0

If $$1 - 5, 6 - 10, 11 - 15, ...$$ are the classes of a frequency distribution then the size of the class is _____

A
$$4$$

B
$$5$$

C
$$3$$

D
$$2.5$$

Solution

As the classes are of inclusive form,
Size of the class is $$=(Upper\ limit - Lower\ limit + 1 )$$
So, size of the class $$=( 5 - 1 + 1) = 5 $$
Question 8
1 / -0

The range of $$8, 17, 28, 16, 30, 28, 15, 5, 19$$ and $$35$$ is _____

A
$$20$$

B
$$18$$

C
$$30$$

D
$$16$$

Solution

The difference between the maximum and minimum data entries is called the range
So, Range = maximum number - minimum number
Range = $$35 -5$$
Range =$$30$$
Question 9
1 / -0

The class mark of a class is $$25$$ and if the upper limit of that class is $$40$$ then its lower limit is _____

A
$$30$$

B
$$20$$

C
$$15$$

D
$$10$$

Solution

$$\text{Class mark} = \cfrac { \text{Lower limit} + \text{Upper limit} }{2} $$
$$ \Rightarrow 25 = \cfrac {\text{Lower limit} + 40}{2} $$
$$\Rightarrow \text{Lower limit} = 50 - 40 = 10 $$
Question 10
1 / -0

The lower limit and upper limit of an exclusive class interval are $$15$$ and $$25$$ respectively. Then the class mark is _____

A
$$26.5$$

B
$$20$$

C
$$28$$

D
$$27$$

Solution

Let $$M$$ be the class mark
$$ M= \dfrac { \text{Lower limit} + \text{Upper limit}}{2} \\= \dfrac {15 + 25}{2} \\= 20 $$

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Re-Attempt Weekly Quiz Competition

Statistics Test - 33

Result

Statistics Test - 33

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SHARING IS CARING

Question 1

27

25

30

35

Solution

Question 2

$$20$$

$$35$$

$$30$$

$$40$$

Solution

Question 3

$$22 : 15$$

$$15 : 22$$

$$20 : 13$$

$$13 : 22$$

Solution

Question 4

$$30$$

$$35$$

$$33$$

$$32$$

Solution

Question 5

$$11$$

$$11.5$$

$$10.5$$

$$10$$

Solution

Question 6

Frequency distribution

Frequency

Cumulative frequency

Primary data

Solution

Question 7

$$4$$

$$5$$

$$3$$

$$2.5$$

Solution

Question 8

$$20$$

$$18$$

$$30$$

$$16$$

Solution

Question 9

$$30$$

$$20$$

$$15$$

$$10$$

Solution

Question 10

$$26.5$$

$$20$$

$$28$$

$$27$$

Solution

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