Maharashtra SSC Algebra HOTS Questions with Answers – Statistics | Class 10 Board Exam 2027

Practice set · 1 hr · 68 marks · for SSC 10th and similar exams

2027 60 minutes 68 marks Save WhatsApp

Sections

Most repeated board questions (2024–2026)	12 Q
HOTS: likely questions for 2027	15 Q

About this HOTS set

For Class 10 students, “HOTS” usually means the most important (IMP) questions – the ones most likely to come in the board exam. This page collects them for the Maharashtra SSC Algebra chapter Statistics, for the 2027 board exam. The first section has real questions from the six latest official MSBSHSE board papers (March 2024 to June 2026), picked because their type keeps repeating. The second section has new likely questions for 2027, in the same board style, including a few harder thinking questions.

Marks from this chapter in the last six board papers

Board paper	Marks from this chapter
March 2024	8
July 2024	7
March 2025	12
July 2025	9
March 2026	9
June 2026	8

Average: about 8.8 marks per paper.

Question types that repeat most

Mean: direct method, assumed mean method, or just the formula with \(\sum f_i x_i\) and \(\sum f_i\) given (five of the six papers; only March 2024 had none).
Mode of grouped data, often as an activity with the formula filled in (March 2024, July 2024, June 2026).
Median of grouped data with a cumulative frequency table (4 marks in July 2025 and March 2026; 3 marks in March 2025).
Pie diagram: central angles from percentages, or reading a given pie diagram to find totals (Q.5 in March 2024, March 2025, June 2026, March 2026).
Missing frequency from a given total, then a histogram (March 2025).

Exam tips

Make the full table (\(x_i\), \(d_i\) or \(u_i\), \(f_i x_i\), cf) neatly; the table itself carries marks.
Write the formula, then list L, \(f_1, f_0, f_2\) or L, cf, f, h separately before substituting.
For median, the median class is the first class whose cumulative frequency is greater than or equal to N/2, not the class with the highest frequency.
For a pie diagram, check that the angles add to 360°, and label every sector.

The board questions are taken from the official MSBSHSE question papers. All answers and step-by-step solutions, and all the new HOTS questions, are written by Doubtly.

Chapters covered

Statistics

Instructions

Solve on paper with a timer, then check against the solutions.

Most repeated board questions (2024–2026)

Asked in: June 2026 board paper (MCQ); central angles from percentages also came in March 2025 and July 2025
Q.1 The classification of persons based on blood groups is to be shown by a pie diagram. The persons having blood group O are 40%. What should be the measure of angle for the persons having O blood group?
1. (A) 114°
2. (B) 140°
3. (C) 104°
4. (D) 144°
1 mark See answer →
Asked in: June 2026 board paper; March 2026 board paper (same data, as a 2-mark question)
Q.2 Find Mean \((\bar{X})\) if \(\sum x_i f_i = 1265\) and \(\sum f_i = 50\).

1 mark See answer →
Asked in: July 2025 board paper
Q.3 If \(\sum f_i d_i = 10{,}000\), \(\sum f_i = 100\) and \(A = 2000\), then find mean \((\bar{x})\).

2 marks See answer →
Asked in: March 2025 board paper
Q.4 The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by the students for their studies.
Class (Time in hours) Class mark \(x_i\) No. of students \(f_i\) \(f_i x_i\)
0–2 1 8 8
2–4 3 14 42
4–6 5 18 90
6–8 7 10 70
8–10 9 10 90

2 marks See answer →
Asked in: March 2024 board paper; mode of grouped data also came in July 2024 and June 2026
Q.5 The following frequency distribution table shows the classification of the number of vehicles and the volume of petrol filled in them. To find the mode of the volume of petrol filled, complete the following activity:
Class (Petrol filled in litres) Frequency (Number of vehicles)
0.5–3.5 33
3.5–6.5 40
6.5–9.5 27
9.5–12.5 18
12.5–15.5 12
Activity:
From the given table, Modal class = ____
\(\therefore\) Mode = ____ \(+ \left[ \dfrac{f_1 - f_0}{2f_1 - f_0 - \text{____}} \right] \times h\)
\(\therefore\) Mode = \(3.5 + \left[ \dfrac{40 - 33}{2(40) - 33 - 27} \right] \times\) ____
\(\therefore\) Mode = \(3.5 + \left[ \dfrac{7}{80 - 60} \right] \times 3\)
\(\therefore\) Mode = ____
\(\therefore\) The mode of the volume of petrol filled is ____.

3 marks See answer →
Asked in: June 2026 board paper; mode of grouped data also came in March 2024 and July 2024
Q.6 Electricity used by some families is shown in the following table. Find the mode of electricity used.
Use of electricity (units) 0–20 20–40 40–60 60–80 80–100 100–120
No. of families 13 50 70 100 80 17

3 marks See answer →
Asked in: July 2024 board paper
Q.7 In the following table, the toll (in Rs.) paid from 6 am to 6 pm by drivers and the number of vehicles is shown. Find the mean of the toll by ‘assumed mean’ method.
Toll (Rs.) No. of vehicles
300–400 80
400–500 110
500–600 120
600–700 70
700–800 40

3 marks See answer →
Asked in: March 2025 board paper
Q.8 In a general store the prices of different articles and its demand is shown in the following frequency distribution table. Find the median of the prices.
Price in rupees No. of articles
Less than 20 140
20–40 100
40–60 80
60–80 60
80–100 20

3 marks See answer →
Asked in: July 2025 board paper; a 4-mark median of grouped data also came in March 2026
Q.9 In the following frequency distribution table ages of 300 patients and number of patients in a hospital is given. Find the median age of the patients.
Age (in years) 10–20 20–30 30–40 40–50 50–60 60–70
Number of patients 60 42 55 70 53 20

4 marks See answer →
Asked in: July 2024 board paper
Q.10 In one group of students; 10% students got 0 to 20 marks; 20% students got 20 to 40 marks; 35% students got 40 to 60 marks; 20% students got 60 to 80 marks and remaining 30 students got 80 to 100 marks, then:
(a) Prepare a grouped frequency distribution table.
(b) Find the mode of the marks scored.

4 marks See answer →
Asked in: June 2026 board paper; reading a pie diagram also came in March 2024 and March 2025
Q.11 The following pie diagram represents the number of valid votes obtained by four students who contested for school captain. The total of valid votes polled was 720.
[Figure: pie diagram with sectors Ram 100°, Raj 80°, Shubha 120°, Radha 60°]
Answer the following questions:
(a) Who has won the election?
(b) What is the minimum number of votes? Who got it?
(c) By how many votes did the winner defeat the nearest contestant?

3 marks See answer →
Asked in: March 2026 board paper; central angles table also came in July 2025
Q.12 A survey was conducted in the school. Students using different modes of transport is given below:
Mode of transport Percentage of students
Bicycle 35
Bus \(a\)
Railway \(2a\)
Rickshaw 20
Find the value of \(a\) and draw the pie diagram.

3 marks See answer →

Class (Time in hours)	Class mark \(x_i\)	No. of students \(f_i\)	\(f_i x_i\)
0–2	1	8	8
2–4	3	14	42
4–6	5	18	90
6–8	7	10	70
8–10	9	10	90

Class (Petrol filled in litres)	Frequency (Number of vehicles)
0.5–3.5	33
3.5–6.5	40
6.5–9.5	27
9.5–12.5	18
12.5–15.5	12

Use of electricity (units)	0–20	20–40	40–60	60–80	80–100	100–120
No. of families	13	50	70	100	80	17

Toll (Rs.)	No. of vehicles
300–400	80
400–500	110
500–600	120
600–700	70
700–800	40

Price in rupees	No. of articles
Less than 20	140
20–40	100
40–60	80
60–80	60
80–100	20

Age (in years)	10–20	20–30	30–40	40–50	50–60	60–70
Number of patients	60	42	55	70	53	20

Mode of transport	Percentage of students
Bicycle	35
Bus	\(a\)
Railway	\(2a\)
Rickshaw	20

HOTS: likely questions for 2027

Q.13 In the assumed mean method, if \(A = 45\), \(\sum f_i = 40\) and \(\sum f_i d_i = -80\), then the mean is _____.
1. (A) 47
2. (B) 43
3. (C) 45
4. (D) −2
1 mark See answer →
Q.14 The class having the maximum frequency in a grouped frequency distribution is called the _____.
1. (A) median class
2. (B) modal class
3. (C) class mark
4. (D) cumulative class
1 mark See answer →
Q.15 The sum of all the central angles in a pie diagram is _____.
1. (A) 90°
2. (B) 180°
3. (C) 270°
4. (D) 360°
1 mark See answer →
Q.16 The central angle for an item in a pie diagram is 72°. What percentage of the total does the item represent?

1 mark See answer →
Q.17 The class mark of a class is 18 and its lower limit is 15.5. Find its upper limit.

1 mark See answer →
Q.18 In a survey of 90 people, 25 people said they prefer tea. Find the central angle for “tea” in a pie diagram of this survey.

2 marks See answer →
Q.19 For a grouped frequency distribution the modal class is 40–50 with \(f_1 = 24\), \(f_0 = 18\) and \(f_2 = 12\). Find the mode.

2 marks See answer →
Q.20 Find the mean of the following data by the step deviation method.
Class 0–20 20–40 40–60 60–80 80–100
Frequency 6 10 14 12 8

3 marks See answer →
Q.21 (Thinking question) The mean of the following frequency distribution is 21. Find the missing frequency \(k\).
Class 0–10 10–20 20–30 30–40
Frequency 4 6 \(k\) 4

3 marks See answer →
Q.22 The monthly income of a family is ₹ 36,000. It is spent as follows: Food ₹ 12,000, Rent ₹ 9,000, Education ₹ 6,000, Savings ₹ 5,000, Other ₹ 4,000. Find the central angles and draw a pie diagram.

3 marks See answer →
Q.23 A pie diagram shows the production of crops on a farm: Wheat 120°, Rice 90°, Jowar 60° and the rest is Bajra.
[Figure: pie diagram with the four sectors.]
If the production of rice is 450 quintals, find (a) the central angle for Bajra (b) the total production (c) how much more wheat than jowar is produced.

3 marks See answer →
Q.24 Draw a frequency polygon for the following data.
Marks 10–20 20–30 30–40 40–50 50–60
No. of students 5 12 20 15 8

3 marks See answer →
Q.25 (Thinking question) The following is a “less than” cumulative frequency table. Prepare the ordinary frequency table and find the mode.
Marks Less than 10 Less than 20 Less than 30 Less than 40 Less than 50
No. of students 5 12 25 33 40

4 marks See answer →
Q.26 (Thinking question) The median of the following data is 26.25. Find the missing frequency \(x\).
Class 0–10 10–20 20–30 30–40 40–50
Frequency 5 \(x\) 20 15 5

4 marks See answer →
Q.27 The following “more than or equal to” type table gives the marks of 60 students. Find the median.
Marks 0 or more 10 or more 20 or more 30 or more 40 or more
No. of students 60 55 45 28 12
(Maximum marks: 50.)

4 marks See answer →