Grade 9 : Mathematics - 14. Statistics (Set 4)

Question 1

Marks ($x_i$)	10	20	30	40	50
Number of Students ($f_i$)	8	12	15	10	5

The table above gives the marks obtained by 50 students in a mathematics test. What is the mean mark of the students?

Accepted Answer

B) 28.4

Answer

A) 27.2

Answer

C) 29.6

Answer

D) 30.0

Question 2

Marks ($x_i$)	10	20	30	40	50
Number of Students ($f_i$)	8	12	15	10	5

Find the value of $k$ if the mean of the frequency distribution in the table is 13.

Accepted Answer

B) 4

Answer

A) 3

Answer

C) 5

Answer

D) 6

Question 3

For a grouped frequency distribution, the class marks are given as $15, 25, 35, 45, 55$.

What is the class interval corresponding to the class mark 35?

Accepted Answer

B) 30 – 40

Answer

A) 25 – 35

Answer

C) 35 – 45

Answer

D) 28 – 42

Question 4

Marks ($x_i$)	10	20	30	40	50
Number of Students ($f_i$)	8	12	15	10	5

Based on the cumulative frequency table above, what is the frequency of the class interval $20 - 30$?

Accepted Answer

B) 12

Answer

A) 9

Answer

C) 14

Answer

D) 26

Question 5

In constructing a histogram for a frequency distribution with unequal class intervals, the heights of the rectangles are adjusted.

Which formula is correct for finding the adjusted frequency of a class?

Accepted Answer

B) $	ext{Adjusted Frequency} = \frac{	ext{Minimum Class Width}}{	ext{Class Width}} 	imes 	ext{Frequency}$

Answer

A) $	ext{Adjusted Frequency} = \frac{	ext{Class Width}}{	ext{Minimum Class Width}} 	imes 	ext{Frequency}$

Answer

C) $	ext{Adjusted Frequency} = \frac{	ext{Frequency}}{	ext{Total Frequency}} 	imes 	ext{Class Width}$

Answer

D) $	ext{Adjusted Frequency} = 	ext{Frequency} 	imes 	ext{Class Mark}$

Question 6

The mean of 10 observations is 18.

If each observation is multiplied by 3 and then 5 is added to each result, what is the new mean of the observations?

Accepted Answer

B) 59

Answer

A) 54

Answer

C) 63

Answer

D) 49

Question 7

In a statistical study, the maximum value in a data set is 94 and the minimum value is 22.

If the data is to be grouped into 8 classes of equal width, what is the class size for each interval?

Accepted Answer

B) 9

Answer

A) 8

Answer

C) 10

Answer

D) 12

Question 8

Marks ($x_i$)	10	20	30	40	50
Number of Students ($f_i$)	8	12	15	10	5

What percentage of students receive ₹300 or more as monthly pocket money?

Accepted Answer

C) 50%

Answer

A) 33.3%

Answer

B) 40%

Answer

D) 60%

Question 9

Consider the raw data set: $14, 22, 9, 31, 18, 27, 12, 35, 20$.

What is the median of this data set?

Accepted Answer

B) 20

Answer

A) 18

Answer

C) 22

Answer

D) 19

Question 10

The following 10 observations are arranged in ascending order: $8, 11, 13, 15, x+1, x+3, 24, 28, 30, 32$.

If the median of the data is 19, find the value of $x$.

Accepted Answer

C) 17

Answer

A) 15

Answer

B) 16

Answer

D) 18

Question 11

The monthly expenditures (in thousands of rupees) of 12 households are: $15, 18, 22, 18, 25, 18, 30, 22, 18, 25, 20, 18$.

What is the mode of this data set?

Accepted Answer

A) 18

Answer

B) 20

Answer

C) 22

Answer

D) 25

Question 12

In a frequency polygon, the mid-points (class marks) of consecutive class intervals are $12, 22, 32, 42, 52$.

What are the lower and upper limits of the first class interval?

Accepted Answer

B) 7 and 17

Answer

A) 5 and 15

Answer

C) 10 and 20

Answer

D) 2 and 22

Question 13

The mean weight of 6 members of a fitness club is 65 kg. When a new member joins, the mean weight becomes 67 kg.

What is the weight of the new member?

Accepted Answer

C) 79 kg

Answer

A) 72 kg

Answer

B) 75 kg

Answer

D) 82 kg

Question 14

Marks ($x_i$)	10	20	30	40	50
Number of Students ($f_i$)	8	12	15	10	5

What is the upper limit of the modal class in the distribution above?

Accepted Answer

B) 30

Answer

A) 20

Answer

C) 40

Answer

D) 50

Question 15

A grouped frequency distribution for workers' ages is given in discontinuous class intervals: $20–29, 30–39, 40–49, 50–59$.

What is the true upper limit of the class interval $30–39$?

Accepted Answer

B) 39.5

Answer

A) 39.0

Answer

C) 40.0

Answer

D) 30.5

Question 16

In a histogram with unequal class widths, the class interval $20–35$ has a frequency of 21. The minimum class width in the whole distribution is 5.

What is the adjusted frequency for the class $20–35$?

Accepted Answer

A) 7

Answer

B) 14

Answer

C) 21

Answer

D) 35

Question 17

The mean of 50 numbers was calculated to be 38. Later, it was found that the number 48 was incorrectly recorded as 84 during the calculation.

What is the correct mean of the numbers?

Accepted Answer

B) 37.28

Answer

A) 36.88

Answer

C) 38.72

Answer

D) 39.12

Question 18

Marks ($x_i$)	10	20	30	40	50
Number of Students ($f_i$)	8	12	15	10	5

How many students scored marks in the range $20–30$ (including 20 but less than 30)?

Accepted Answer

B) 14

Answer

A) 12

Answer

C) 18

Answer

D) 27

Question 19

Consider the data set: $18, 42, 75, 29, 88, 12, 63, 95, 34$.

What is the range of this data set?

Accepted Answer

B) 83

Answer

A) 77

Answer

C) 88

Answer

D) 95

Question 20

Section A of Grade 9 has 30 students with a mean score of 70 in a statistics test. Section B has 20 students with a mean score of 80.

What is the combined mean score of all 50 students?

Accepted Answer

B) 74

Answer

A) 73

Answer

C) 75

Answer

D) 76

Grade 9 : Mathematics - 14. Statistics (Set 4)