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Mode of Grouped Data PYQs

Class 10 Statistics Board Questions (2014 – 2026)

Topic Overview

Mode is the value with the highest frequency. Identify the Modal Class first. Use the formula $L + \left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)h$. Don't forget the Empirical Relationship: $\text{Mode} = 3\text{Median} - 2\text{Mean}$.

Q1 2026
00:00
If the mean and median of a frequency distribution are 43 and 43.4 respectively, then the mode of the distribution is:
(a)(A) 44.2
(b)(B) 43.2
(c)(C) 42.4
(d)(D) 44.8
Mode $= 3(43.4) - 2(43) = 44.2$.
Ans: (A) 44.2
Q2 2024
00:00
The relationship between mean, median and mode is:
(a)(A) 3 Median = Mode + 2 Mean
(b)(B) 3 Mean = Mode + 2 Median
(c)(C) Mode = 3 Mean - 2 Median
(d)(D) Median = 3 Mode - 2 Mean
Standard empirical formula is $3 \text{Median} = \text{Mode} + 2 \text{Mean}$.
Ans: (A)
Q3 2023
00:00
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetimes. | Lifetimes (hrs) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 | |-----------------|------|-------|-------|-------|--------|---------| | Frequency | 10 | 35 | 52 | 61 | 38 | 29 |
Modal class: 60-80. Mode $= 60 + [(61-52)/(122-52-38)] \times 20 = 65.625$.
Ans: 65.625 hours
Q4 2026
00:00
Determine the modal marks of the students from the following data: | Marks | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | |-------|-------|-------|-------|-------|--------| | Freq | 5 | 18 | 30 | 22 | 15 |
Modal class: 40-60. $L=40, f_1=30, f_0=18, f_2=22, h=20$.
Mode $= 40 + [(30-18)/(60-18-22)] \times 20 = 40 + [12/20] \times 20 = 52$.
Ans: 52
Q5 2026
00:00
PASSAGE: School Health Monitoring. To monitor the fitness levels of students, a school conducted a health check-up for 100 students of Class X. The following distribution gives the heart rates (beats per minute) of these students. | Heart Rate (bpm) | 65-70 | 70-75 | 75-80 | 80-85 | 85-90 | |------------------|-------|-------|-------|-------|-------| | No. of students | 12 | 30 | 25 | 18 | 15 |
(i) Find the modal heart rate of the students.
(ii) Find the median heart rate of the students.
(iii) Calculate the mean heart rate of the students.
(i) Mode: Modal class is 70-75. Mode $= 70 + [(30-12)/(60-12-25)] \times 5 = 73.91$ bpm.
(ii) Median: $N/2=50$, median class 75-80. Median $= 75 + [(50-42)/25] \times 5 = 76.6$ bpm.
(iii) Mean: $\sum fx / 100 = 77.25$ bpm.
00:00
If the mean and median of a frequency distribution are 43 and 43.4 respectively, then the mode of the distribution is:
(a)(A) 44.2
(b)(B) 43.2
(c)(C) 42.4
(d)(D) 44.8
Mode $= 3(43.4) - 2(43) = 44.2$.
Ans: (A) 44.2
Q2 2024
00:00
The relationship between mean, median and mode is:
(a)(A) 3 Median = Mode + 2 Mean
(b)(B) 3 Mean = Mode + 2 Median
(c)(C) Mode = 3 Mean - 2 Median
(d)(D) Median = 3 Mode - 2 Mean
Standard empirical formula is $3 \text{Median} = \text{Mode} + 2 \text{Mean}$.
Ans: (A)
Q3 2023
00:00
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetimes. | Lifetimes (hrs) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 | |-----------------|------|-------|-------|-------|--------|---------| | Frequency | 10 | 35 | 52 | 61 | 38 | 29 |
Modal class: 60-80. Mode $= 60 + [(61-52)/(122-52-38)] \times 20 = 65.625$.
Ans: 65.625 hours
Q4 2026
00:00
Determine the modal marks of the students from the following data: | Marks | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | |-------|-------|-------|-------|-------|--------| | Freq | 5 | 18 | 30 | 22 | 15 |
Modal class: 40-60. $L=40, f_1=30, f_0=18, f_2=22, h=20$.
Mode $= 40 + [(30-18)/(60-18-22)] \times 20 = 40 + [12/20] \times 20 = 52$.
Ans: 52
Q5 2026
00:00
PASSAGE: School Health Monitoring. To monitor the fitness levels of students, a school conducted a health check-up for 100 students of Class X. The following distribution gives the heart rates (beats per minute) of these students. | Heart Rate (bpm) | 65-70 | 70-75 | 75-80 | 80-85 | 85-90 | |------------------|-------|-------|-------|-------|-------| | No. of students | 12 | 30 | 25 | 18 | 15 |
(i) Find the modal heart rate of the students.
(ii) Find the median heart rate of the students.
(iii) Calculate the mean heart rate of the students.
(i) Mode: Modal class is 70-75. Mode $= 70 + [(30-12)/(60-12-25)] \times 5 = 73.91$ bpm.
(ii) Median: $N/2=50$, median class 75-80. Median $= 75 + [(50-42)/25] \times 5 = 76.6$ bpm.
(iii) Mean: $\sum fx / 100 = 77.25$ bpm.