Grade 9 : Mathematics - 14. Statistics (Set 3)

Question 1

If the mean of six observations $10, 12, 16, 20, x,$ and 24 is 17, what is the value of $x$?

Accepted Answer

B) 20

Answer

A) 18

Answer

C) 22

Answer

D) 24

Question 2

What is the class mark of the class interval $35 - 55$?

Accepted Answer

B) 45

Answer

A) 40

Answer

C) 50

Answer

D) 55

Question 3

In a histogram representing continuous data, the area of each rectangle is directly proportional to which quantity?

Accepted Answer

C) Frequency of the corresponding class

Answer

A) Class mark

Answer

B) Class width only

Answer

D) Cumulative frequency

Question 4

Find the mean of the first 9 natural numbers.

Accepted Answer

B) 5

Answer

A) 4.5

Answer

C) 5.5

Answer

D) 6

Question 5

Marks ($x_i$)	Frequency ($f_i$)
5	3
10	5
15	8
20	3
25	1

Calculate the mean mark for the distribution shown in the table.

Accepted Answer

C) 13.5

Answer

A) 12.5

Answer

B) 13.0

Answer

D) 14.0

Question 6

For discontinuous class intervals $10-19, 20-29, 30-39$, what are the true class boundaries for the interval $20-29$?

Accepted Answer

A) 19.5 - 29.5

Answer

B) 20 - 29

Answer

C) 19.5 - 28.5

Answer

D) 20.5 - 29.5

Question 7

In constructing a histogram with unequal class widths, a class interval $20-30$ has frequency 15. If the minimum class size in the distribution is 5, what is the adjusted length of the rectangle for this class?

Accepted Answer

A) 7.5

Answer

B) 10

Answer

C) 15

Answer

D) 30

Question 8

Find the median of the dataset: $14, 21, 11, 9, 27, 18, 25$.

Accepted Answer

B) 18

Answer

A) 14

Answer

C) 21

Answer

D) 25

Question 9

Find the median of the eight observations: $23, 17, 31, 12, 28, 19, 35, 26$.

Accepted Answer

B) 24.5

Answer

A) 23

Answer

C) 25

Answer

D) 26

Question 10

The marks obtained by 10 students in a test are: $7, 8, 4, 7, 9, 7, 5, 8, 6, 7$. What is the mode of this data?

Accepted Answer

B) 7

Answer

A) 6

Answer

C) 8

Answer

D) 9

Question 11

If the mean of 15 observations is 24, and 6 is added to each observation, what is the new mean?

Accepted Answer

C) 30

Answer

A) 24

Answer

B) 28

Answer

D) 36

Question 12

If the mean of 10 observations is 18, and every observation is multiplied by 3, what is the new mean?

Accepted Answer

C) 54

Answer

A) 18

Answer

B) 21

Answer

D) 162

Question 13

The mean weight of 20 boys is 45 kg, and the mean weight of 30 girls is 40 kg. What is the combined mean weight of all 50 students?

Accepted Answer

B) 42 kg

Answer

A) 41 kg

Answer

C) 42.5 kg

Answer

D) 43 kg

Question 14

Marks ($x_i$)	Frequency ($f_i$)
5	3
10	5
15	8
20	3
25	1

What is the cumulative frequency corresponding to the class interval $20 - 30$?

Accepted Answer

C) 21

Answer

A) 10

Answer

B) 11

Answer

D) 27

Question 15

Which of the following scenarios describes primary data collection?

Accepted Answer

B) Conducting personal face-to-face interviews to gather first-hand information

Answer

A) Using census data published in an official government portal

Answer

C) Extracting stock market trends from a financial journal

Answer

D) Downloading historical weather logs from a meteorological website

Question 16

The observations $11, 13, 15, x, x+2, 22, 25, 29$ are arranged in ascending order. If the median of the data is 18, find the value of $x$.

Accepted Answer

C) 17

Answer

A) 15

Answer

B) 16

Answer

D) 18

Question 17

Determine the range of the dataset: $42, 18, 75, 31, 9, 64, 53, 88$.

Accepted Answer

B) 79

Answer

A) 70

Answer

C) 88

Answer

D) 97

Question 18

A bar graph displays books read by a club across 4 terms: Term 1: 40 books, Term 2: 60 books, Term 3: 75 books, Term 4: 50 books.

What is the percentage increase in the number of books read from Term 1 to Term 3?

Accepted Answer

C) 87.5%

Answer

A) 35%

Answer

B) 75%

Answer

D) 187.5%

Question 19

The mean of 20 observations was calculated as 35. Later, it was found that an observation 45 was wrongly copied as 25. What is the correct mean?

Accepted Answer

C) 36

Answer

A) 34

Answer

B) 35.5

Answer

D) 37

Question 20

To construct a frequency polygon directly without drawing a histogram, class frequencies are plotted against which of the following?

Accepted Answer

C) Class marks

Answer

A) Lower class limits

Answer

B) Upper class limits

Answer

D) Class widths

Grade 9 : Mathematics - 14. Statistics (Set 3)