CHAPTER – 15 STATISTICS ONE MARK QUESTIONS 1. Define Range. 2. Find the range of given data 108, 107, 105, 106, 107, 104, 103, 101, 104 3. Find the range of 16,18,18,16,18,20,17,19,16,24 4. Find the range of 90,50,72,69,85,100,73,85,93 5. Find the range of 25, 37, 11, 20, 14, 18, 16, 30, 35, 17 6. Find the range of 17,10,12,8,12,16,19 7. Compute the range of the following frequency distribution Marks scored out of 10 0 1 2 3 4 5 6 7 8 9 10 No. of 2 7 10 11 22 28 10 5 3 2 0 students 8) Find the value of range of frequency distribution Age in years 14 15 16 17 18 19 20 No. of 1 2 2 2 6 4 0 students 9) Find the range of the following distribution Class Interval 10-20 20-30 30-40 40-50 50-60 Frequency 8 10 15 18 19 10) Find the range of the following data Profit 0-10 10-20 20-30 30-40 40-50 No. of firms 0 6 0 7 15 11) Calculate the range for the distribution given below Height in cms 150 151 152 154 159 160 165 166 No. of 2 2 9 15 18 10 4 1 Boys 12) Find the mean of the following data -3, -2,-1,0,1,2,3,4, 13) Find the mean of 4,6,5,9,12,3,1 14) Write the mean of given data 6,7,10,12,13,4,8,12 15) Write the mean of 6,8,10,12,14,16,18,20,22,24 16) Find the mean of the first n natural numbers. 17) Find the median for the following data 4,6,9,4,2,8,10 18) Find the median for the following data 4,6,5,9,12,3,1,10,13 19) Find the median for the series 25,20,23,32,40,27,30,25,20,10,55,41 20) Find the median for the series 5,9,10,12,6,4,2,15 21) Write the formula for mean deviation of the grouped data about mean 22) Two series A and B with equal means have standard deviations 9 and 10 respectively, which series is more consistent. 23) If the coefficient of variation and standard deviation are 60,21 respectively, What is the arithmetic mean of the distribution. 24) If variance = 4Sq.ft. Find S.D ANSWERS ONE MARK QUESTIONS 1) Range is the difference between the maximum and the minimum observation of the distribution. 2) Range = 108 – 101 = 7 3) Range = 24 – 16 = 8 4) Range = 100 – 50 = 50 5) Range = 37 - 11 = 26 6) Range = 19 – 8 = 11 7) Range = 10 – 0 = 10 8) Range = 19 – 4 = 5 9) Range = 60 – 10 = 50 10) Range = 50 – 10 = 40 11) Range = 166 – 150 = 16 12) Mean = 13) Mean = 14 ) 15) 16) 17) Arrange the values in ascending order 2, 4, 4, 6, 8, 9, 10 Median = 6 18) 1, 3, 4, 5, 6, 9, 10, 12, 13 Median = 6 19) Arrange the values in ascending order 10, 20, 20, 23, 25, 25, 27, 30, 32, 40, 41, 55 Median = 20) 2,4,5, 6,9 ,10,12, 15 21) M.D( ) = 22) B Series 23) C.V = 24) Variance = 4 5 MARKS QUESTIONS 1) Find the mean deviation about the mean for the following data. Marks Obtained 10-20 20-30 30-40 40-50 50-60 60-70 70-80 No. of Students 2 3 8 14 8 3 2 2) Find the mean deviation about the mean for the following frequency distribution Class 0-4 4-8 8-12 12-16 16-20 Interval Frequency 4 6 8 5 2 3) Find the mean deviation about the mean for the data Income 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 per day No. of 4 8 9 10 7 5 4 3 persons 4) Find the mean deviation about the mean for the data Height in cms 95-105 105-115 115-125 125-135 135-145 145-155 No. of Boys 9 13 26 30 12 10 5) Find the mean deviation about the mean for the data Wages (in Rs.) 50 100 150 175 200 225 300 No. of Workers 5 10 15 20 10 5 5 6) Find the mean deviation about the mean for the data Salesmen 4-8 8-12 12-16 16-20 20-24 24-28 28-32 32-36 36-40 Reports 11 13 16 14 10 9 17 6 4 7) Find the mean deviation about the mean for the data Marks 0-10 10-20 20-30 30-40 40-50 Scored No. of 3 8 12 10 7 Students 8) Find the mean deviation about median for the data Wages (in Rs.) 0-25 25-50 50-75 75-100 100-125 125-150 No. of Persons 10 30 40 25 20 15 9) Find the mean deviation about median for the data Marks 0-10 10-20 20-30 30-40 40-50 50-60 No. of Girls 6 8 14 16 4 2 10) Find the mean deviation about median for the data Heights 10-12 12-14 14-16 16-18 18-20 (in feet) No. of 2 6 8 3 1 Trees 11) Find the mean deviation about median for the Age distribution of 100 persons given below Age 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 Number 5 6 12 14 26 12 16 9 12) Find the variance for the following data 6 10 14 18 24 28 30 2 4 7 12 8 4 3 13) Find the variance for the following data 4 8 11 17 20 24 32 3 5 9 5 4 3 1 14) Find the mean deviation about median for the following frequency distribution Marks 0-10 10-20 20-30 30-40 40-50 No. of 5 8 15 16 6 Students 15) Find the standard deviation ( ) & Coefficient of variance for the following series 4,6,10,12,18 16) Find the mean and variance for the following data 2,4,5,6,8,17 17) Find the mean, variance and standard deviation for the following data. 5,8,12,15,7,9,13,11 18) Find the variance and standard deviation for the following data x 5 10 15 20 25 f 3 2 5 8 2 19) Find the mean, variance and standard deviation of first 10 multiples of 2 SOLUTIONS 5 MARK QUESTIONS Solution 1) Marks No. of Mid points Obtained students 10 -20 2 15 30 30 60 20 -30 3 25 75 20 60 30 -40 8 35 280 10 80 40 -50 14 45 630 0 0 50 -60 8 55 440 10 80 60 -70 3 65 195 20 60 70 -80 2 75 150 30 60 N= 40 1800 400 Getting Mean = = 1m Writing first two columns --- 1m Next two columns --- 1m Last two columns --- 1m M.D ( ) = --- 1m Solution 2) Class Frequency Mid Interval points 0-4 4 2 8 7.2 28.8 4-8 6 6 36 3.2 19.2 8-12 8 10 80 0.8 6.4 12 -16 5 14 70 4.8 24.0 16 -20 2 18 36 8.8 17.6 N= 25 230 96.0 Getting Mean = Mean Deviatio n: M.D ( ) = --- 1m Writing first two columns --- 1m Next two columns --- 1m Last two columns --- 1m Solution 3) Income No. of Mid per day persons points 0-100 4 50 200 308 1232 100 -200 8 150 1200 208 1664 200 -300 9 250 2250 108 972 300 -400 10 350 3500 8 80 400 -500 7 450 3150 92 644 500 -600 5 550 2750 192 960 600 -700 4 650 2600 292 1168 700 -800 3 750 2250 392 1176 N=50 17900 7896 Mean = Writing first two columns --- 1m Next two columns --- 1m Last two columns --- 1m Mean = --- 1m Mean Deviation: M.D --- 1m Solution 4 Height in No. of Mid cms boys points 95 -105 9 100 900 25.3 227.7 105 -115 13 110 1430 15.3 198.9 11 5-225 26 120 3120 5.3 137.9 125 -135 30 130 3900 4.7 141.0 135 -145 12 140 1680 14.7 176.4 145 -155 10 150 1500 24.7 247.0 N=100 12530 1128.8 Getting Mean = Writing first two columns --- 1m Next two columns --- 1m Last two columns --- 1m Mean Deviation: M.D --- 1m Solution 5 Wages in No. of Rs. boys 50 5 250 116 580 100 10 1000 66 660 150 15 2250 16 240 175 20 3500 9 180 200 10 2000 34 340 225 5 1125 59 295 300 5 1500 134 670 N=70 11625 2965 Getting Mean = Writing first two columns --- 1m Next two columns --- 1m Last two columns --- 1m Mean Deviation: M.D --- 1m Solution 6) Salesmen Reports Mid points 4-8 11 6 66 13.92 153.12 8-12 13 10 130 9.92 128.96 12 -16 16 14 224 5.92 94.72 16 -20 14 18 252 1.92 26.88 20 -24 10 22 220 2.08 20.8 24 -28 9 26 234 6.08 54.72 28 -32 17 30 510 10.08 171.36 32 -36 6 34 204 14.08 84.48 36 -40 4 38 152 18.08 72.32 N=100 1992 807.36 Getting Mean = 19.92 --- 1m Writing first two columns --- 1m Next two columns --- 1m Last two columns --- 1m Mean Deviation: M.D --- 1m Solution 7) Marks No.