Rs Aggarwal (2015) Solutions for Class 10 Math Chapter 9 Mean, Median, Mode Of Grouped Data, Cumulative Frequency Graph And Ogive are provided here with simple step-by-step explanations. These solutions for Mean, Median, Mode Of Grouped Data, Cumulative Frequency Graph And Ogive are extremely popular among Class 10 students for Math Mean, Median, Mode Of Grouped Data, Cumulative Frequency Graph And Ogive Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal (2015) Book of Class 10 Math Chapter 9 are provided here for you for free. You will also love the ad-free experience on Meritnationâ€™s Rs Aggarwal (2015) Solutions. All Rs Aggarwal (2015) Solutions for class Class 10 Math are prepared by experts and are 100% accurate.

#### Question 1:

Find the mean, using direct method:

 Class 0-10 10-20 20-30 30-40 40-50 Frequency 3 5 9 5 3

 Class Frequency $\left({f}_{i}\right)$ Mid Values $\left({x}_{i}\right)$ $\left({f}_{i}×{x}_{i}\right)$ 0-10 3 5 15 10-20 5 15 75 20-30 9 25 225 30-40 5 35 175 40-50 3 45 135 ${\sum }_{{f}_{i}}=25$ $\sum \left({f}_{i}×{x}_{i}\right)=625$

#### Question 2:

Find the mean, using direct method:

 Class 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 7 5 6 12 8 2

 Class Frequency $\left({f}_{i}\right)$ Mid Values $\left({x}_{i}\right)$ $\left({f}_{i}×{x}_{i}\right)$ 0-10 7 5 35 10-20 5 15 75 20-30 6 25 150 30-40 12 35 420 40-50 8 45 360 50-60 2 55 110 ${\sum }_{{f}_{i}}=40$ $\sum \left({f}_{i}×{x}_{i}\right)=1150$

#### Question 3:

Find the mean, using direct method:

 Class 10-20 20-30 30-40 40-50 50-60 60-70 Frequency 11 15 20 30 14 10

 Class Frequency $\left({f}_{i}\right)$ Mid Values $\left({x}_{i}\right)$ $\left({f}_{i}×{x}_{i}\right)$ 10-20 11 15 165 20-30 15 25 375 30-40 20 35 700 40-50 30 45 1350 50-60 14 55 770 60-70 10 65 650 $\sum {f}_{i}=100$ $\sum \left({f}_{i}×{x}_{i}\right)=4010$

#### Question 4:

Find the mean, using direct method:

 Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Number of students 6 8 13 7 3 2 1

 Class Frequency $\left({f}_{i}\right)$ Mid Values $\left({x}_{i}\right)$ $\left({f}_{i}×{x}_{i}\right)$ 10-20 6 15 90 20-30 8 25 200 30-40 13 35 455 40-50 7 45 315 50-60 3 55 165 60-70 2 65 130 70-80 1 75 75 $\sum {f}_{i}=40$ $\sum \left({f}_{i}×{x}_{i}\right)=1430$

#### Question 5:

Find the mean, using direct method:

 Class 25-35 35-45 45-55 55-65 65-75 Frequency 6 10 8 12 4

 Class Frequency $\left({f}_{i}\right)$ Mid values $\left({x}_{i}\right)$ $\left({f}_{i}×{x}_{i}\right)$ 25-35 6 30 180 35-45 10 40 400 45-55 8 50 400 55-65 12 60 720 65-75 4 70 280 $\sum {f}_{i}=40$ $\sum \left({f}_{i}×{x}_{i}\right)=1980$

#### Question 6:

Find the mean, using direct method:

 Class 0-100 100-200 200-300 300-400 400-500 Frequency 6 9 15 12 8

 Class Frequency $\left({f}_{i}\right)$ Mid values $\left({x}_{i}\right)$ $\left({f}_{i}×{x}_{i}\right)$ 0-100 6 50 300 100-200 9 150 1350 200-300 15 250 3750 300-400 12 350 4200 400-500 8 450 3600 $\sum {f}_{i}=50$ $\sum \left({f}_{i}×{x}_{i}\right)=13200$

#### Question 7:

The mean of the following frequency distribution is 24. Find the value of p.

 Marks 0-10 10-20 20-30 30-40 40-50 Number of students 15 20 35 p 10

 Class Frequency $\left({f}_{i}\right)$ Mid Values $\left({x}_{i}\right)$ $\left({f}_{i}×{x}_{i}\right)$ 0-10 15 5 75 10-20 20 15 300 20-30 35 25 875 30-40 p 35 35 p 40-50 10 45 450 $\sum {f}_{i}=80+p$ $\sum \left({f}_{i}×{x}_{i}\right)=1700+35p$

#### Question 8:

Find the missing frequencies f1 and f2 in the table in given below, it is being given that the mean of the given frequency distribution is 50.

 Class 0-20 20-40 40-60 60-80 80-100 Total Frequency 17 f1 32 f2 19 120

 Class Frequency $\left({f}_{i}\right)$ Mid values $\left({x}_{i}\right)$ $\left({f}_{i}×{x}_{i}\right)$ 0-20 17 10 170 20-40 f1 30 30 f1 40-60 32 50 1600 60-80 52- f1 70 3640-70 f1 80-100 19 90 1710 $\sum {f}_{i}=120$ $\sum \left({f}_{i}×{x}_{i}\right)=7120-40{f}_{1}$

#### Question 9:

The mean of the following frequency distribution is 57.6 and the sum of the observations is 50

 Class 0-20 20-40 40-60 60-80 80-100 100-120 Frequency 7 f1 12 f2 8 5

 Class Frequency $\left({f}_{i}\right)$ Mid values $\left({x}_{i}\right)$ $\left({f}_{i}×{x}_{i}\right)$ 0-20 7 10 70 20-40 f1 30 30 f1 40-60 12 50 600 60-80 18- f1 70 1260-70 f1 80-100 8 90 720 100-120 5 110 550 $\sum {f}_{i}=50$ $\sum \left({f}_{i}×{x}_{i}\right)=3200-40{f}_{1}$

#### Question 10:

Find the mean, using assumed-mean method:

 Marks 0-10 10-20 20-30 30-40 40-50 50-60 Number of students 12 18 27 20 17 6

 Class Frequency $\left({f}_{i}\right)$ Mid values$\left({x}_{i}\right)$ Deviation $\left({d}_{i}\right)$ ${d}_{i}=\left({x}_{i}-25\right)$ $\left({f}_{i}×{d}_{i}\right)$ 0-10 12 5 -20 -240 10-20 18 15 -10 -180 20-30 27 25=A 0 0 30-40 20 35 10 200 40-50 17 45 20 340 50-60 6 55 30 180 $\sum {f}_{i}=100$ $\sum \left({f}_{i}×{d}_{i}\right)=300$

#### Question 11:

Find the mean, using assumed-mean method:

 Class 0-40 40-80 80-120 120-160 160-200 Frequency 12 20 35 30 23

 Class Frequency $\left({f}_{i}\right)$ Mid values$\left({x}_{i}\right)$ Deviation $\left({d}_{i}\right)$ $\left({d}_{i}\right)=\left({x}_{i}-100\right)$ $\left({f}_{i}×{d}_{i}\right)$ 0-40 12 20 -80 -960 40-80 20 60 -40 -800 80-120 35 100=A 0 0 120-160 30 140 40 1200 160-200 23 180 80 1840 $\sum {f}_{i}=120$ $\sum \left({f}_{i}×{d}_{i}\right)=1280$

#### Question 12:

Find the mean, using assumed-mean method:

 Class 100-120 120-140 140-160 160-180 180-200 Frequency 10 20 30 15 5

 Class Frequency $\left({f}_{i}\right)$ Mid values$\left({x}_{i}\right)$ Deviation $\left({d}_{i}\right)$ ${d}_{i}=\left({x}_{i}-150\right)$ $\left({f}_{i}×{d}_{i}\right)$ 100-120 10 110 -40 -400 120-140 20 130 -20 -400 140-160 30 150=A 0 0 160-180 15 170 20 300 180-200 5 190 40 200 $\sum {f}_{i}=80$ $\sum \left({f}_{i}×{d}_{i}\right)=-\text{3}00$

#### Question 13:

Find the mean, using assumed-mean method:

 Class 0-20 20-40 40-60 60-80 80-100 100-120 Frequency 20 35 52 44 38 31

 Class Frequency $\left({f}_{i}\right)$ Mid Values$\left({x}_{i}\right)$ Deviation $\left({d}_{i}\right)$ ${d}_{i}=\left({x}_{i}-50\right)$ $\left({f}_{i}×{d}_{i}\right)$ 0-20 20 10 -40 -800 20-40 35 30 -20 -700 40-60 52 50=A 0 0 60-80 44 70 20 880 80-100 38 90 40 1520 100-120 31 110 60 1860 $\sum {f}_{i}=220$ $\sum \left({f}_{i}×{d}_{i}\right)=2760$

#### Question 14:

Find the arithmetic mean of each of the following frequency distributions using step-deviation method:

 Marks 0-10 10-20 20-30 30-40 40-50 50-60 Number of students 12 18 27 20 17 6

 Class Frequency$\left({f}_{i}\right)$ Mid Values$\left({x}_{i}\right)$ ${u}_{i}=\frac{\left({x}_{i}-A\right)}{h}$ $\text{=}\frac{\left({x}_{i}-25\right)}{10}$ $\left({f}_{i}×{u}_{i}\right)$ 0-10 12 5 −2 −24 10-20 18 15 −1 −18 20-30 27 25=A 0 0 30-40 20 35 1 20 40-50 17 45 2 34 50-60 6 55 3 18 $\sum {f}_{i}=100$ $\sum \left({f}_{i}×{u}_{i}\right)=30$

#### Question 15:

Find the arithmetic mean of each of the following frequency distributions using step-deviation method:

 Class Number of students 4-8 2 8-12 12 12-16 15 16-20 25 20-24 18 24-28 12 28-32 13 32-36 3

 Class Frequency $\left({f}_{i}\right)$ Mid values$\left({x}_{i}\right)$ ${u}_{i}=\frac{\left({x}_{i}-A\right)}{h}$ $\text{=}\frac{\left({x}_{i}-18\right)}{4}$ $\left({f}_{i}×{u}_{i}\right)$ 4-8 2 6 -3 -6 8-12 12 10 -2 -24 12-16 15 14 -1 -15 16-20 25 18=A 0 0 20-24 18 22 1 18 24-28 12 26 2 24 28-32 13 30 3 39 32-36 3 34 4 12 $\sum {f}_{i}=100$ $\sum \left({f}_{i}×{u}_{i}\right)=48$

#### Question 16:

Find the arithmetic mean of each of the following frequency distributions using step-deviation method:

 Class 0-30 30-60 60-90 90-120 120-150 150-180 Frequency 12 21 34 52 20 11

 Class Frequency $\left({f}_{i}\right)$ Mid values$\left({x}_{i}\right)$ ${u}_{i}=\frac{\left({x}_{i}-A\right)}{h}$ $\text{=}\frac{\left({x}_{i}-75\right)}{30}$ $\left({f}_{i}×{u}_{i}\right)$ 0-30 12 15 −2 −24 30-60 21 45 −1 −21 60-90 34 75 = A 0 0 90-120 52 105 1 52 120-150 20 135 2 40 150-180 11 165 3 33 $\sum {f}_{i}=150$ $\sum \left({f}_{i}×{u}_{i}\right)=80$

#### Question 17:

Find the arithmetic mean of each of the following frequency distributions using step-deviation method:

 Class 0-20 20-40 40-60 60-80 80-100 100-120 120-140 Frequency 12 18 15 25 26 15 9

 Class Frequency $\left({f}_{i}\right)$ Mid values$\left({x}_{i}\right)$ ${u}_{i}=\frac{\left({x}_{i}-A\right)}{h}\phantom{\rule{0ex}{0ex}}\text{=}\frac{\left({x}_{i}-70\right)}{20}$ $\left({f}_{i}×{u}_{i}\right)$ 0-20 12 10 −3 −36 20-40 18 30 −2 −36 40-60 15 50 −1 −15 60-80 25 70 = A 0 0 80-100 26 90 1 26 100-120 15 110 2 30 120-140 9 130 3 27 $\sum {f}_{i}=120$ $\sum \left({f}_{i}×{u}_{i}\right)=-4$

#### Question 18:

Find the arithmetic mean of each of the following frequency distributions using step-deviation method:

 Marks 0-14 14-28 28-42 42-56 56-70 Number of students 7 21 35 11 16

 Class Frequency $\left({f}_{i}\right)$ Mid values$\left({x}_{i}\right)$ ${u}_{i}=\frac{\left({x}_{i}-A\right)}{h}\phantom{\rule{0ex}{0ex}}\text{=}\frac{\left({x}_{i}-35\right)}{14}$ $\left({f}_{i}×{u}_{i}\right)$ 0-14 7 7 −2 −14 14-28 21 21 −1 −21 28-42 35 35 = A 0 0 42-56 11 49 1 11 56-70 16 63 2 32 $\sum {f}_{i}=90$ $\sum \left({f}_{i}×{u}_{i}\right)=8$

#### Question 19:

Find the arithmetic mean of each of the following frequency distributions using step-deviation method:

 Class 10-15 15-20 20-25 25-30 30-35 35-40 Frequency 5 6 8 12 6 3

 Class Frequency $\left({f}_{i}\right)$ Mid values$\left({x}_{i}\right)$ ${u}_{i}=\frac{\left({x}_{i}-A\right)}{h}\phantom{\rule{0ex}{0ex}}\text{=}\frac{\left({x}_{i}-22.5\right)}{5}$ $\left({f}_{i}×{u}_{i}\right)$ 10-15 5 12.5 −2 −10 15-20 6 17.5 −1 −6 20-25 8 22.5 = A 0 0 25-30 12 27.5 1 12 30-35 6 32.5 2 12 35-40 3 37.5 3 9 $\sum {f}_{i}=40$ $\sum \left({f}_{i}×{u}_{i}\right)=17$

#### Question 20:

Find the arithmetic mean of each of the following frequency distributions using step-deviation method:

 Age (in years) 18-24 24-30 30-36 36-42 42-48 48-54 Number of workers 6 8 12 8 4 2

 Class Frequency $\left({f}_{i}\right)$ Mid values$\left({x}_{i}\right)$ ${u}_{i}=\frac{\left({x}_{i}-A\right)}{h}\phantom{\rule{0ex}{0ex}}\text{=}\frac{\left({x}_{i}-33\right)}{6}$ $\left({f}_{i}×{u}_{i}\right)$ 18-24 6 21 −2 −12 24-30 8 27 −1 −8 30-36 12 33 = A 0 0 36-42 8 39 1 8 42-48 4 45 2 8 48-54 2 51 3 6 $\sum {f}_{i}=40$ $\sum \left({f}_{i}×{u}_{i}\right)=2$

#### Question 21:

Find the arithmetic mean of each of the following frequency distributions using step-deviation method:

 Class 84-90 90-96 96-102 102-108 108-114 114-120 Frequency 15 22 20 18 20 25

 Class Frequency$\left({f}_{i}\right)$ Mid values$\left({x}_{i}\right)$ ${u}_{i}=\frac{\left({x}_{i}-A\right)}{h}\phantom{\rule{0ex}{0ex}}\text{=}\frac{\left({x}_{i}-99\right)}{6}$ $\left({f}_{i}×{u}_{i}\right)$ 84-90 15 87 −2 −30 90-96 22 93 −1 −22 96-102 20 99 = A 0 0 102-108 18 105 1 18 108-114 20 111 2 40 114-120 25 117 3 75 $\sum {f}_{i}=120$ $\sum \left({f}_{i}×{u}_{i}\right)=81$

#### Question 22:

Find the arithmetic mean of each of the following frequency distributions using step-deviation method:

 Class 500-520 520-540 540-560 560-580 580-600 600-620 Frequency 14 9 5 4 3 5

 Class Frequency$\left({f}_{i}\right)$ Mid values$\left({x}_{i}\right)$ ${u}_{i}=\frac{\left({x}_{i}-A\right)}{h}\phantom{\rule{0ex}{0ex}}\text{=}\frac{\left({x}_{i}-550\right)}{20}$ $\left({f}_{i}×{u}_{i}\right)$ 500-520 14 510 −2 −28 520-540 9 530 −1 −9 540-560 5 550 = A 0 0 560-580 4 570 1