UGTRB MATHS -2026 UNIT-10 CLASS-5

[00:00:01]Welcome to tutor flex. [music] Hi teachers.

[00:00:13]Measures of dispersion.

[00:00:16]Measures of central tendency.

[00:00:20]Measures of dispersion. So measures of central tendenc five measures of central tendency measures of dispersion measures of central Okay.

[00:01:01]Range quartile mean deviation standard deviation deviation. So range deviation standard deviation Okay. So first range difference between the maximum and the minimum value of the vari 37 value 25 value capital Lowest value 37us 25. Okay. Next quartile deviation range. So deviation values Q1, Q2, Q3, Q3 Q3 - Q1 / 2. Okay. 1x2 into Q3US Q1 [snorts] Q1 value 17 Q3 value 38.5 deviation Q3 minus Q1 / 2 so value next mean deviation mean deviation summation fi x ius a / frequency.

[00:03:17]Okay.

[00:03:21]Okay.

[00:03:33]So, first formula.

[00:03:42]Okay.

[00:03:57]positive. Okay.

[00:04:19]Okay.

[00:04:23]Summation modulus of x i - xr / small frequency. [snorts] Next. Standard deviation. Standard deviation formula.

[00:04:51]Frequency.

[00:04:54]Okay.

[00:05:02]Okay. Standard deviation.

[00:05:06]Summation f_sub x i - xr / capital frequenc 1 by 2. Soal summation federal standard deviation summation root of summation x i² by nus x i² f_subi d² / capital square.

[00:06:14]Okay.

[00:06:16]Standard deviation for grouped data.

[00:06:24]Okay.

[00:06:28]formula.

[00:06:34]Okay. So standard deviation formula variance.

[00:06:56]Okay.

[00:06:58]Next root mean square deviation.

[00:07:04]So root mean square deviation mean summation f_subi into x i - a / n.

[00:07:20]So root means square bracket square and root. Okay.

[00:07:36]Okay. Root mean square deviation. So mean deviation square root.

[00:07:48]Okay.

[00:07:51]So root mean square deviation mean square deviation it's nothing but square svation root mean squarevation.

[00:08:09]Okay.

[00:08:11]Formula 100 days.

[00:08:29]So manage as soon as possible.

[00:08:46]Consider the numbers 1 2 3 4 5 6 7 x i square value 28 and ungrouped data ungrouped data deviation science Standard deviation formula in sigma summation x i - xr² / n power 1 by 2.

[00:09:30]So summation x i next x i - 4 the whole square. So, x ius 4 x 1 2 3 4 5 6 US 3 square 9 4 1 0 1 4 9 2 Okay. So sigma value two sigma square= 4. Okay. Next coefficient of dispersion measures of dispersion.

[00:10:45]Based upon that dispersion. Okay. First quartile deviation formula Q3 - Q1 / 23us Q1 Q3.

[00:11:18]Okay. Next based upon mean deviation. So mean deviation mean average. Okay.

[00:11:35]Average. Okay.

[00:11:41]Mean deviation.

[00:11:42]Next. Based upon standard deviation. So standard deviation of dispersion standard deviation meanigar.

[00:12:09]Next coefficient of variation. So coefficient of variation standard deviation standard deviation $100 multiply of variation. Okay.

[00:13:10]Okay.

[00:13:11]Next. Variance of combined set. Starting N1, N2 etc. So Xar = N1 X1 + N_sub_2 X2 bar / N1 + N2 N12 X1 X2 Arithmetic combined sett Okay. Uh sorry, standard deviation.

[00:14:13]Okay. N1 standard deviation sigma 1. N2 standard deviation mean X12 X2. Okay.

[00:14:41]Sigma square= 1 + first [snorts] n_sub_1 into sigma 1 square + d1² + n_sub_2 into sigma 2² + d2 square d1 x1 - xr Okay.

[00:15:08]Xus sorry x ius x1 - x. Okay.

[00:15:28]That's it.

[00:15:30]Okay.

[00:15:33]combined n1 + n_sub_2. So 1 by n1 + n_sub_2 first n12.

[00:15:43]Okay. Next square x1 sigma 1 square.

[00:16:03]Okay. Next plus n1 nsub_2 / n1 + n2 the whole square into x1 x2.

[00:16:16]Okay.

[00:16:23]Mean, standard deviation, deviation, coefficient oftal number.

[00:16:40]Okay.

[00:16:42]Summation x 33. Next range. Range. Maximum value minus minimum value maximum value 48 [snorts] minimum value 21 sorry 20 next ungrouped data summation x i² / nus x² into sorry root power 1 by 2 summation x i² by n minus summation X I square root.

[00:17:22][snorts] Next I square I X3us.

[00:17:39]Okayus.

[00:17:44]Next summation x i² x i summation x i - xr summation x i² So value 11 652. So 11,652 summation x i² [snorts] divided by value 10us x value 330 / 103.

[00:18:39]Next mean deviation. So mean deviation xus deviation modulus of x i - x ungrouped data. Ungrouped data mean summation x i - xr / n.

[00:19:08]So xus 132 summation modulus of x i - xr / n summation x i - x value 72 72 / 10 which is equal to 7.2 mean deviation of variation sorry coefficient of variation standard deviation sigma / xar into 100 sigma value 8.73 divided by Xar value 33 into 100. So approximate 26.

[00:20:14]Okay. So the coefficient of variation xus measures of central tendenc concept formulas. Okay.

[00:20:37]So for foreign.

[00:21:03]Thank you.