Statistics PDF - Mean Calculation

Join Telegram- Maths by Aditya Ranjan Statistics Statistics / lakf[;dh [CLASSROOM SHEET] MEAN@ekè;...

Join Telegram- Maths by Aditya Ranjan Statistics Statistics / lakf[;dh [CLASSROOM SHEET] MEAN@ekè; 2. The arithmetic mean of the following data is _________. The arithmetic mean of a given data is the sum 23, 17,20,19,21 of all observations divided by the number of observations. For example, a cricketer's scores fuEufyf r la[;kvksa dk vadxf.krh;@lekarj ekè; ____ gksxkA in five ODI matches are as follows: 12, 34, 45, 23, 17,20,19,21 50, 24. To find his average score we calculate SSC CGL TIER - II 02/03/2023 the arithmetic mean of data using the mean (a) 20 (b) 19 r formula: (c) 23 (d) 21 fdlh fn, x, MsVk dk ekè; çs{k.kksa ds ;ksxiQYk dks izs{k.kksa dh mean of six observations 5, 7, 9, , 11 3. If the si la[;k ls foHkkftr djus ij izkIr gksrk gS mnkgj.k ds fy,] ikap and 12 is 9 then the value of  is : ,dfnolh; eSpksa esa ,d fØdsVj ds Ldksj 12] 34] 45] 50] 24 ;fn Ng izs{k.kksa5, 7, 9, , 11 vkSj12 dk ekè; 9 gS] rks an by gSaA mldk vkSlr Ldksj Kkr djus ds fy, ge ekè; lw=k dh  dk eku gS% n lgk;rk ls MsVk dk lekUrj ekè; Kkr djrs gSaA (a) 10 (b) 15 Mean/ekè; (c) 22 (d) 25 ja R s 4. If the mean of the data 28, 26, 22, 11, 13, x Sum of all observations / lHkh i{sz k.kkas dk ÕkksxiQYkis 20, then find the value of 'x'. = Number of observations / isz{k.kksa dh la[Õkk ;fn 28] 26] 22] 11] 13] x vkadM+ksa dk ekè; 20 gS] rks a th Mean/ekè; = (12 + 34 + 45 + 50 + 24)/5 'x' dk eku Kkr dhft, A Mean/ekè; = 165/5 = 33 (a) 20 (b) 30 Mean is denoted by x (pronounced as x bar). (c) 25 (d) 28 ty a ekè; dks x }kjk iznf'kZr djrs gSaA FOR DISCRETE FREQUENCY DISTRIBUTION di M MEAN OF GROUPED DATA If X takes values x 1 , x 2 , x 3.........x n with (oxhZÑr vk¡dM+ksa dk lekUrj ekè;) corresponding frequencies f1, f2, f3,........., fn If x1, x2, x3,................, xn are n values of a respectively, then arithmetic mean of these variable X, then the arithmetic mean or simply values is given by: mean of these values is denoted by X and is defined as: ;fn X dk eku x1, x2, x3.........xn rFkk laxr vko`fÙk;ka Øe'k%f1, f2, f3,........., fn gks] rks bu ekuksa dk lekarj n ekè; gksxk% x1  x 2  x 3 .............x n x i X or X  i 1 f1x1  f2 x 2  f3 x 3 .............fn x n n n X f1  f2  f3 ....... fn A 1. The arithmetic mean of the following data is n _________. f x i i n or X  i 1 where N = 1 f i = f + f + f +.....f 2 3 n 12, 34, 45, 50, 24 N i 1 fuEufyf r la[;kvksa dk vadxf.krh;@lekarj ekè; ____ 5. Find the mean of the following distribution: gksxkA fuEufyf r forj.k dk ekè; Kkr dhft,% 12, 34, 45, 50, 24 (x) 4 6 9 10 15 (f) 5 10 10 7 8 (a) 30 (b) 36 (a) 9 (b) 10 (c) 33 (d) 25 (c) 12 (d) 8 Aditya Aditya Ranjan Ranjan (Excise (Excise Inspector) Inspector) Selected gSSelection fnyk,axs 11 Join Telegram- Maths by Aditya Ranjan Statistics 6. The following table shows the number of 11. Arithmetic Mean (AM) of the following data is- commercial clerks at 100 stations in a electric fuEufyf[kr MkVk dk lekarj (AM) ekè; gS& department: Class- fuEufyf r rkfydk esa ,d fo|qr foHkkx ds 100 LVs'kuksa interval 6-10 10-14 14-18 18-22 22-26 ds def'kZ;y Dydks± dh la[;k crkbZ xbZ gS% Frequency 5 12 7 5 1 Number of (a) 10 (b) 12 Commercial (x) 3 1 2 0 4 5 (c) 14 (d) 18 Clerks Number of 12. The mean of the following distribution is 26, (f) 12 24 11 9 29 15 stations then what is the value of k? Find the mean from the above. ;fn fuEufyf[kr caVu dk ekè; 26 gS] rks k dk eku D;k gS\ mi;qZDr ls ekè; Kkr dhft,A Class 0-10 10-20 20-30 30-40 40-50 Frequency 8 10 K 6 12 (a) 2.50 (b) 2.73 (a) 8 (b) 1 (c) 2.33 (d) 2.58 (c) 4 (d) 10 7. Find the mean of the following distribution: 13. Find the arithmetic mean of the following r fuEufyf r forj.k dk ekè; Kkr dhft,% frequency distribution by the assumed mean si method: (x) 5 6 7 8 9 (f) 4 8 14 11 3 dfYir ekè; fof/ }kjk fuEufyf[kr ckjackjrk caVu dk an by (a) 8.325 (b) 9.125 lekarj ekè; Kkr dhft,% n (c) 7.025 (d) 5.225 Class 50-150 150-250 250-350 350-450 450-550 -interval 8. If the mean of the following distribution is 6, Frequency 16 10 22 15 12 ja find the value of p. R s (a) 290 (b) 296 ;fn fuEufyf r forj.k dk ekè; 6 gS] rks p dk eku (c) 285 (d) 250 a th Kkr dhft,A 14. Find the arithmetic mean of the following (x) 2 4 6 10 p +5 frequency distribution by the assumed mean (f) 3 2 3 1 2 method: ty a (a) 7 (b) 8 dfYir ekè; fof/ }kjk fuEufyf[kr ckjackjrk caVu dk lekarj ekè; Kkr dhft,% di M (c) 9 (d) 10 Wages (in Rs.): 800 820 860 900 920 980 1000 9. If the mean of the following data is 15, then No. of Workers: 7 14 19 25 20 10 5 find the value of k. (a) Rs. 891.2 (b) Rs. 890.2 ;fn fuEufyf r MsVk dk ekè; 15 gS] rks k dk eku Kkr (c) Rs. 895.6 (d) Rs. 898.6 dhft,A MEDIAN/ekfè;dk (x) 5 10 15 20 25 The value of the middlemost observation, (f) 6 k 6 10 5 obtained after arranging the data in ascending (a) 7 (b) 8 or descending order, is called the median of the (c) 6 (d) 10 data. 10. Find the mean of the following frequency MsVk dks vkjksgh Øe esa O;ofLFkr djus ds ckn eè;re izs{k.k A distribution: dks ekf/dk dgrs gSaA fuEufyf r vko`fÙk forj.k dk ekè; Kkr dhft,% For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, Class 0-10 10-20 20-30 30-40 40-50 interval: 4, 4, 6. There are 5 observations. Thus, median No. of workers 7 10 15 8 10 = middle value i.e. 4. (f): mnkgj.k ds fy, ekuk4, 4, 6, 3, 2 dksbZ MsVk gS bls lcls (a) 25.8 (b) 24.8 igys vkjksgh Øe2, 3, 4, 4, 6 esa O;ofLFkr djrs gSaA 5 dqy (c) 25.9 (d) 24.9 izs{k.k gSaA bl fy, ekfè;dk = eè;re eku vFkkZr~4 gSA Aditya Aditya Ranjan Ranjan (Excise (Excise Inspector) Inspector) Selected gSSelection fnyk,axs 22 Join Telegram- Maths by Aditya Ranjan Statistics STEP I : Arrange the observations x 1 , x 2 , 18. The median of a set of observations 15, 16, 18,............... xn in ascending or descending 22, x + 2 , x + 3 , 26, 27, 30 arranged in order of magnitude. ascending order is 24, then find the value of x. çs{k.kksa x1, x2,...............xn dks ifjek.k ds vkjksgh Øe O;ofLFkr çs{k.kksa ds 15, ,d lsV 16, 18, vkjksgh ;k vojksgh Øe esa O;ofLFkr djsaA dh ekfè;dk 24 gS] 22, x + 2 , x + 3 , 26, 27, 30 STEP II : Determine the total number of rksx dk eku Kkr dhft,A observations, say, n (a) 26 (b) 25 çs{k.kksa dh dqy la[;k fu/kZfjr djsa] eku yhft,] n (c) 20 (d) 22 STEP III : If n is odd, then median is the value of 3 th 19. The median of observations k – , k + 2,  n  1 2   observation. 2 1 1 k –1, k + 4, k + , k – 3, k + 4 is _____. th 2 2  n  1 ;fn n fo"ke gS] rks ekfè;dk 2  3 1 çs{k.kksa] k – , k + 2, k –1, k + 4, k + , k – 3, r voyksdu dk eku gSA 2 2 si If n is even, then median is the AM of 1 k+4 dh ekfè;dk Kkr dhft,A 2 an by th th n n  the values of   and   1 NTPC 01/04/2021 (Shift-03) 2 2 n observations. 3 1 (a) k – (b) k + 2 2 ja th n ;fn n le gS] rks ekfè;dk  2  vkSj (c) k – 1 (d) k + 2 R s 20. What is the difference between mean and a th th medain of the given data. n    1 2 çs{k.kksa ds ekuksa AM dk gSA fn, x, vk¡dM+ksa ds ekè; vkSj ekfè;dk esa D;k varj gSA 6, 8, 5, 7, 12, 16, 6, 8, 13 15. The following are the marks of 9 students in ty a a class. Find the median. (a) 4 (b) 2 ,d d{kk esa 9 Nk=kksa ds vad fuEufyf r gSaA ekfè;dk Kkr (c) 11 (d) 1.5 di M dhft,A 21. The median of a set of 11 distinct observations 34, 32, 48, 38, 24, 30, 27, 21, 35 is 73.2. If each of the largest five observations (a) 24 (b) 32 of the set is increased by 3, then the median (c) 38 (d) 21 of the new set: 16. Find the median of the daily wages of ten 11 fofHkUu çs{k.kksa ds ,d leqPp; dh ekfè;dk 73-2 gSA workers from the following data: ;fn leqPp; ds lcls cM+s ikap çs{k.kksa esa ls çR;sd esa 3 fuEufyf r vkadM+ksa ls nl Jfedksa dh nSfud etnwjh dk dh o`f¼ dh tkrh gS] rks bl u, leqPp; dh ekfè;dk % ekè; Kkr dhft,% SSC CGL TIER- II 07/03/2023 Rs. 20, 25, 17, 18, 8, 15, 22, 11, 9, 14 (a) Is 3 times that of the original set (a) 16 (b) 18 ewy lsV dk 3 xquk gS A (c) 20 (d) 22 17. The median of the following data will be (b) Is increased by 3/3 dh o`f¼ gqbZ gS _________. (c) Remains the same as that of the original set 32, 25,33,27, 35, 29 and 30 ewy lsV ds leku gh jgrk gS fuEufyf[kr la[;kvksa dh ekfè;dk ----------- gksxhA (d) Is decreased by 3/3 ls ?kVk gS 32, 25,33,27, 35, 29 vkSj30 SSC CGL TIER- II 03/03/2023 22. The median of a set of 7 distinct observation is 21.5. If each of the largest 3 observations (a) 32 (b) 27 of the set is increased by 4, then the median (c) 30 (d) 29 of the new sets: Aditya Aditya Ranjan Ranjan (Excise (Excise Inspector) Inspector) Selected gSSelection fnyk,axs 33 Join Telegram- Maths by Aditya Ranjan Statistics 7 fHkUu çs{k.kksa ds ,d leqPp; dh ekfè;dk 21-5 gSA ;fn MEDIAN OF A GROUPED OR leqPp; ds lcls cM+s 3 çs{k.kksa esa ls çR;sd esa 4 dh o`f¼ CONTINUOUS FREQUENCY dj nh tk,] rks u, leqPp; dh ekfè;dk & DISTRIBUTION (a) Will decrease by 4/4 de gksxh (b) Will be four times the original median (lrr~ ckjackjrk caVu dh ekfè;dk) STEP I : Obtain the frequency distribution. ewy ekfè;dk dh pkj xquk gksxh (c) Will remain the same as that of the original vko`fÙk forj.k çkIr djsa- STEP II : Prepare the cumulative frequency set/ ewy leqPp; ds leku gh jgsxh column and obtain N =  fi. (d) Will increase by 4/4 c