Statistics - ICSE STD 10 Mathematics Questions

Find out the mode from the following data:

Wages (in ₹)	No. of persons
125	3
175	8
225	21
275	6
325	4
375	2

View full solution →

Q 2[2 Mark Question Answer]2 Marks

If the mean of n observation $ax_1, ax_2, ax_3,....,ax_n$ is a$\overline{ X }$, show that $\left(a x_1-a \overline{ X }\right)+\left(a x_2-a \overline{ X }\right)+\ldots\left(a x_{ n }-a \overline{ X }\right) = 0$

View full solution →

Q 3[2 Mark Question Answer]2 Marks

The following table give the marks scored by students in an examination:

Marks	0 - 5	5 - 10	10 - 15	15 - 20	20 - 25	25 - 30	30 - 35	35 - 40
No. of students	3	7	15	24	16	8	5	2

(i) Find the modal group
(ii) Which group has the least frequency?

View full solution →

Q 4[2 Mark Question Answer]2 Marks

The median of the following observation 11, 12, 14, 18, (x + 4), 30, 32, 35, 41 arranged in ascending order is 24. Find x.

View full solution →

Q 5[2 Mark Question Answer]2 Marks

Find the mean of first five natural numbers.

View full solution →

Q 6[2 Mark Question Answer]2 Marks

Find the mean of $4, 7, 12, 8, 11, 9, 13, 15, 2, 7.$

View full solution →

Q 7[3 marks sum]3 Marks

The Mean of n observation $x_1, x_2,..., x_n$ is $\overline{ X }$. $f (a - b)$ is added to each of the observation, show that the mean of the new set of observation is $\overline{ X } + (a - b).$

View full solution →

Q 8[3 marks sum]3 Marks

Following table present educational level (middle stage) of females in Arunachal pradesh according to 1981 census:

Age group	Number of females (to the nearest ten)
10 - 14	300
15 - 19	980
20 - 24	800
25 - 29	380
30 - 34	290

Draw a histogram to represent the above data.

View full solution →

Q 9[3 marks sum]3 Marks

Draw a histogram to represent the following data:

Pocket money in ₹	No. of Students
150 - 200	10
200 - 250	5
250 - 300	7
300 - 350	4
350 - 400	3

View full solution →

Q 10[3 marks sum]3 Marks

Draw the histogram for the following frequency distribution and hence estimate the mode for the distribution.

Class	Frequency
0 - 5	2
5 - 10	7
10 - 15	18
15 - 20	10
20 - 25	8
25 - 30	5
Total	24

View full solution →

Q 11[3 marks sum]3 Marks

Draw a histogram and frequency polygon to represent the following data (on the same scale) which shows the monthly cost of living index of a city in a period of 2 years:

Cost of living Index	Number of months
440 - 460	2
460 - 480	4
480 - 500	3
500 - 520	5
520 - 540	3
540 - 560	2
560 - 580	1
580 - 600	4
Total	24

View full solution →

Q 12[5 marks sum]5 Marks

Use graph paper for this question.
The table given below shows the monthly wages of some factory workers.
(i) Using the table, calculate the cumulative frequency of workers.
(ii) Draw the cumulative frequency curve.
Use 2 cm = ₹500, starting the origin at ₹6,500 on X-axis, and 2 cm = 100 worker at they Y-axis.
(iii) Use your graph to write down the median wages in ₹.

Wages in ₹ (CLass)	No. of workers (frequency)	Cumulative frequency f(x)
6500 - 7000	10	-
7000 - 7500	18	-
7500 - 8000	22	-
8000 - 8500	25	-
8500 - 9000	17	-
9000 - 9500	10	-
9500 - 10000	8	-

View full solution →

Q 13[5 marks sum]5 Marks

The mark of 200 students in a test were recorded as follows:

Marks %	No. of students
10 - 19	7
20 - 29	11
30 - 39	20
40 - 49	46
50 - 59	57
60 - 69	37
70 - 79	15
80 - 89	7

Draw the cumulative frequency table.
Draw an ogive and use it to find:
(i) The median
(ii) The number of students who scored more than 35% marks.

View full solution →

Q 14[5 marks sum]5 Marks

Attempt this question on graph paper. Marks obtained by $200$ students in examination are given below:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No. of students	$5$	$10$	$14$	$21$	$25$	$34$	$36$	$27$	$16$	$12$

Draw an ogive for the given distribution taking $2$ cm $= 10$ makrs on one axis and $2\ cm = 20$ students on the other axis.
From the graph find:
(i) the median
(ii) the upper quartile
(iii) number of student scoring above $65$ marks.
(iv) If to students qualify for merit scholarship, find the minimum marks required to qualify.

View full solution →

Q 15[5 marks sum]5 Marks

The marks obtained by $200$ students in an examination are given below :

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
No.of students	$5$	$10$	$11$	$20$	$27$	$38$	$40$	$29$	$14$	$6$

Using a graph paper, draw an Ogive for the above distribution. Use your Ogive to estimate:
(i) the median;
(ii) the lower quartile;
(iii) the number of students who obtained more than $80\%$ marks in the examination and
(iv) the number of students who did not pass, if the pass percentage was $35.$
Use the scale as $2 cm = 10$ marks on one axis and $2 cm = 20$ students on the other axis.

View full solution →

Q 16[5 marks sum]5 Marks

The marks obtained by $100$ students in a Mathematics test are given below:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No. of Students	$3$	$7$	$12$	$17$	$23$	$14$	$9$	$6$	$5$	$4$

Draw an ogive for the given distribution on a graph sheet.
(Use a scale of $2 cm = 10$ units on both axis).
use the ogive to estimate the :
(i) median.
(ii) lower quartile.
(iii) number of students who obtained more than 85% marks in the test.
(iv) number of students who did not pass in the test if the pass percentage was $35.$

View full solution →

Q 17[4 marks sum]4 Marks

The monthly income of a group of 320 employees in a company is given below:

Monthly Income	No. of Employees
6000-7000	20
7000-8000	45
8000-9000	65
9000-10000	95
10000-11000	60
11000-12000	30
12000-13000	5

Draw an ogive the given distribution on a graph sheet taking 2 cm = Rs. 1000 on one axis and 2 cm = 50 employees on the other axis. From the graph determine:
(1) the median wage
(2) the number of employees whose income is below Rs. 8500.
(3) if the salary of a senior employee is above Rs. 11,500, find the number of senior employees in the company.
(4) the upper quartile.

View full solution →

Q 18[4 marks sum]4 Marks

(Use a graph paper for this question.) The daily pocket expenses of 200 students in a school are given below:

Pocket expenses (in ₹)	Number of students (frequency)
0 - 5	10
5 - 10	14
10 - 15	28
15 - 20	42
20 - 25	50
25 - 30	30
30 - 35	14
35 - 40	12

Draw a histogram representing the above distribution and estimate the mode from the graph.

View full solution →

Q 19[4 marks sum]4 Marks

The marks obtained by $120$ students in a test are given below:

Marks	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80	80 - 90	90 - 100
No. of Students	5	9	16	22	26	18	11	6	4	3

Draw an ogive for the given distribution on a graph sheet.
Use suitable scale for ogive to estimate the following :
(i) the median.
(ii) The number of students who obtained more than 75% marks in the test.

View full solution →

Q 20[4 marks sum]4 Marks

Draw a histogram from the following frequency distribution and find the mode from the graph: