Full transcript
0:00talaga.
0:02>> Hi, hello, good morning, good afternoon,
0:03good evening kung kailan niyo man
0:05pinapanood itong video na ito. I hope
0:08you're all doing well. So in this video,
0:10we're gna talk about measures of
0:11variability or measures of pressure. So
0:14pag sinabi nating measures of
0:16variability, this talks about the spread
0:18out ng scores, no? Kung gaano ba kalapit
0:21sa isa't isa yung mga scores or kung
0:23gaano sila kalayo. Think we can use this
0:26one. Ayan. So makikita niyo ninyo how
0:30each data
0:33or how each value differs from one
0:35another and from the central value. So
0:37alam naman natin ang central value natin
0:40is the mean median or mode. No si ano
0:43kasi si mean median mode it cannot
0:46capture the variability of the score.
0:48For example,
0:50we have this data. Now, kapag kinuha po
0:53natin yung mean nito,
0:56yung mean nito at yung mean nito,
0:58parehas po silang seven. Pero kung
1:00makikita natin this here,
1:04the range is masyado silang layo-layo sa
1:07isa't isa. Well, in here naman kung
1:09makikita natin ba magkakalapit yung
1:11score. Ngayon, kapag kinuha lang natin
1:14or ginamit lang natin ang measures of
1:16central tendency as a representation ng
1:19score, yun yung average, yun yung naging
1:21performance ng mga students natin. For
1:23example, hindi niya na-capture that the
1:25scores that we have has great
1:28variability. Kasi titignan niyo may
1:31nakakuha ng 125 to's yung isa 20. At
1:34dito naman sa baba maka-capture niya na
1:36magkakalapit yung score. So that is the
1:38purpose of measures of variability or
1:41measures of dispersion. We have here why
1:44is variability important because it
1:47describes the distribution. No kasi in
1:50measures of variability
1:52sinasabi niya kung clustered ba the mean
1:55yung ating scores ng ito ituturo ko rin
1:59naman siya next ag ko naayos yan pag
2:03clesser around the mid kung makikita
2:05natin yung scores nandito sila banda no
2:08may mga nakakuha rin naman dito pero
2:10konti lang pero yung mga scores
2:12clustered sila dito banda kapag normal
2:15distribution kasi ganyan Siya
2:18pero pag clasered around the mean
2:20kunwari nasa gitna 'yan ha ganyan siya
2:23kapag masyado namang layo-layo yung
2:25scores pwedeng ganyan yung itsura niya
2:27hindi siya pa-box talaga ha so ganyan
2:29lang yan
2:34measures of variability dito naman
2:37kalat-kalat na ito leptoocurtic ito
2:39mesocurtic ito kung titignan natin yung
2:42scores sa lepturtic clustered sila
2:45around the mean ibig sabihin
2:47Yung scores nila is magkakalapit sa
2:49isa't isa. Dito naman sa platic natin
2:52magkakalayo yung scores sa isa't isa no.
2:56So
2:57ayun po si measures of variability or
3:00measures of discretion.
3:03Pasensya na po. Maingay. Ayan. Next. Sa
3:06ano naman sa shows representativeness '
3:09ba kung babalikan natin ito kung
3:11gagamitin natin ito hindi na-capture
3:14kasi merong nakakuha ng 20 ikaw nakuha
3:17mo 20 t's sasabihin yung seven na score
3:20yung nagsho-show ng score mo,
3:22nagre-represent ng score mo ' ba hindi
3:24siya maganda. So dito sa ating measures
3:28of variability and dispersion mapapakita
3:30kung gaano ba kalapit sa isa at isang
3:32score and gaano sila kalayo.
3:35So that is measures of variability. So
3:38unahin natin si standard deviation. So
3:40si standard deviation according to its
3:43definition puntahan natin siya dito. The
3:46average distance of each score from the
3:49mean of the distribution. Actually ito
3:52no papasok siya dito sa formula natin.
3:56Tignan niyo
3:58score minus mean. Ayan yung mean natin
4:02yung average distance of each score from
4:07the mean. Ayun siya agad no. So
4:09kailangan alam natin ang mean natin para
4:12i-minus natin yung score from that then
4:15i-square natin siya. Ito pong nasa una
4:18is the formula for the population. Ito
4:21naman for the sample. Kung makikita po
4:23ninyo dito ang gamit ay sigma. Dito ay S
4:28for sample. Then dito sa taas natin,
4:32ito po yung number of values, total
4:35scores na meron tayo. Letter N siya.
4:37Dito naman N- 1. Bakit siya N- 1?
4:40Because we are accounting that we have
4:43or the data that we have is only for the
4:45sample.
4:47No kaya po siya. So meron tayong example
4:50dito. Ayan diyan din pala siya. Meron
4:53tayo ditong data. So ita-try natin
4:55siyang result. Now we have 15 scores
4:58from different student. So ang una
5:00nating gagawin is syempre kukunin natin
5:03ang mean. So alam ko naman alam na ninyo
5:06ang pagkuha ng mean ay ito-total itong
5:09cross scores natin divided by total
5:12number of scores which is 15. So ang
5:15sagot dito ay mag-calculator tayo dito.
5:191 + 16 / 15 is 81.07.
5:29Ngayon anong gagawin natin? Ipupunta po
5:31natin dito no. So paano? X natin ay this
5:36one. Ang x bar natin is ano daw 'yun
5:39sabi don sa formula natin sample me. Ano
5:44ang gagamitin nating formula dito is
5:45itong ano ha? Standard deviation formula
5:48for example. So ito ay yung mean natin.
5:51Ilan na ulit yung nakuha natin? 81.07.
5:55So isa-isa po yan. 72 - 81.07 07 is
6:02-9.07.
6:05Be mindful po ah ilagay po dapat natin
6:07yung mga signs nila kung negative, kung
6:10positive dapat nakalagay yan. 85
6:14- 81.07 07
6:18is
6:26halo sir dito
6:29[nililinis ang lalamunan]
6:393.93 93
6:4568 yan meron akong data dito actually
6:48sulat ko na 'to ha
6:51i-ano niyo na lang ah i-pause-puse ninyo
6:54tapos isa-isahin niyo siya 8.93
7:00-57
7:0381 - 81.07 07 is -0.07
7:1195 - 81.07
7:15is 13.93
7:19and tuloy-tuloy siya
7:2588 is 6.93.
7:29Ayan
7:3170 na. Ito sana 'yung gagawin natin face
7:34to face. Hindi ko kayo isa-isahin no.
7:36Parang habang nakatayo ako doon,
7:38ine-explain, kayo naman nagco-compute
7:42sa mga calculators ninyo. Nag-uunahan
7:45sana kayong magsabi.
7:48Ang saya sana kaso
7:5377 is -4.07
7:58and 4.93.
8:01Ayan. So actually ito kung ito-total
8:04natin 'yan parang ang magiging ano diyan
8:06is papunta siya ng zero. 'no. Bakit?
8:10Kung titingnan niyo may positive sign,
8:11may negative sign kaya ini-square natin
8:14siya. So pag ini-square natin siya, we
8:17have so -9.07.
8:20Make sure po kapag magi-square kayo,
8:22lagyan ninyo ng open, close and open
8:25parenthesis. Bakit po? Kasi kung hindi
8:27niyo po 'yan nilagay, magiging negative
8:29pa rin po yung sign no. Kaya po natin
8:32siya minu-multiply by itself kasi ' ba
8:35negative negative is positive.
8:42Ganyan siya.
8:45Saan po ba galing ito? Ito po minultiply
8:49natin sa sarili niya. So 82.20 20
8:53squared negative ayan -1
8:58isya
9:00na po maingay silaend
9:07niyo i-send niyo pero ano
9:10kita
9:11>> para makita natin
9:15>> para makita natin yung mangyayari dito
9:18[nililinis ang lalamunan]
9:21>> victory
9:23Ito naman ay try natin zero ano ba
9:27nangyari sa calculator
9:2907
9:31multiplied by itself is
9:370.004
9:41Actually wala zeroer na lang siya dalawa
9:45na lang
9:481393 is
9:51194
9:5514
9:57we also have 49.94
10:0248.07
10:0407
10:064.27
10:093.74
10:12122.47
10:16119.54
10:1916.54
10:21and 24.34.
10:27Ayan po siya no. Ngayon anong gagawin
10:30natin kung babalikan po natin 'yung
10:32formula? 'Yung formula po ay this one.
10:36Ano 'yun? Sabi summation ng x - mean. So
10:41it-total natin to lahat. Ang total ay
10:44956.93.
10:48na baka iba po 'yung nakuha ninyo kasi
10:51depende po 'yan sa ginagamit na
10:54uh
10:56decimal points no tayo po palagi po
10:58tayong two decimal points kaya dito kung
11:00makikita ninyo 'di ba 49 na siya pag may
11:03round off niyo yaner lang kaya yan ang
11:05gagamitin natin ha so 956
11:10950
11:11956
11:1493
11:16div Okay. Ano yung formula?
11:23And ano ang nin? That is 15. Saan po
11:27galing yung 15? Yung total number of
11:30scores natin. 15 - 1. So ang makukuha po
11:35natin dito ayan.
11:39Syempre ima-minus natin n - 1 15 - 1. So
11:4314 na lang siya. Ang makukuha po natin
11:45ay 68.35.
11:48So 'yan na ba 'yung final answer? Hindi
11:51pa po kasi mayro'n pa tayong squared na
11:53square root. So ang makukuha po natin ay
11:578.27.
11:59Point po 'yan ha. Ito na po ang ating
12:02standard deviation. Paano naman ma'am
12:04pag ang gusto namin makuha ay yung
12:06variance? Para makuha po natin yung
12:09variance is actually ito na siya. Ayan
12:12na siya. Tatanggalin lang natin ito. Yan
12:15variance na yan baan. Bakit yon ang
12:19ating variance? Kasi kung titingnan po
12:21natin dito ang formula ' ba yun din
12:23naman siya ang nawala lang yung
12:26square root no? Kaya ay ito yoon nawala.
12:34Ito na ang ating variance no. Mabilis
12:37lang siyang ico-compute ngayon kasi
12:39minsanan na lang sila. Ay nawala dito
12:41ako sa formula pero ang pinagkaiba lang
12:44naman nila kasi yung nandito sa ano eh
12:49for the sample din eh pero for the
12:52variance
12:54for the population ganyan din naman siya
12:58x - x/ 2 n no so that is the formula for
13:03population no bakit po kailangan natin
13:06malaman no'no kasi nakadepende po 'yan
13:08sa data na makukuha ninyo.
13:10kung ano po yung data na makukuha ninyo
13:12doon po naka-base yung formula na
13:13gagamitin ninyo. No reminder po for
13:16everyone ang formula po na gagamitin
13:18natin is for the sample only. Okay? So I
13:23hope naintindihan po natin ang measures
13:25of variability for group data. Paano
13:28naman sa group data? I have here the
13:31intervals that I've created for the data
13:34that we have. No same data po ito dito
13:36sa nasa taas no. Yan din. Ito rin na
13:39data ito.
13:41Ngayon ang gagamitin naman po natin ay
13:44ito po midpoint no ito formula. Bakit
13:47kailangan pong ganyan? Kasi po ang
13:49formula po for standard deviation ay for
13:54group. For group po ha. For group no?
13:58Ano ba?
14:02For group is
14:04kunwari population.
14:06Hindi sample na lang kasi sample naman
14:08tayo. Sample is maliit lang dapat.
14:14Sample is
14:20summation of ito pong nasa dulo
14:26f
14:28x-
14:33div n - 1. Okay that will be our
14:38formula. Paano po natin kukunin?
14:40Kailangan po natin kunin ito step by
14:42step. So una midpoint. So I remember
14:45that you already know how to get the
14:47midpoint.
14:49Paano po? Kahit x lang yan midpoint po
14:51yan ha. Kasi dun sa activity ninyo x
14:53ilalagay ko. Now 65 + 69 is
14:58134 / 2 that is 67 no? So kailangan
15:04ituloy-tuloy pong ganyan no. So paano?
15:0737
15:0967 ano 37 67
15:1682
15:1887
15:2092 and 97.
15:23No? So this is from the same data ha
15:25kasi ganun din po ang gagawin natin sa
15:27activity na bibigyan ko kayo ng isang
15:29data. Gagawa niyo siya ng ungroup.
15:31Gagawa niyo siya ng group no? Ngayon so
15:33formula natin f x. So 1 * 67 is 67 f
15:433 * 72 is 216
15:463 * 77 231
15:502 * 82 164
15:543 * 87
15:56261
15:582 * 92 184
16:011 * 97 7 97 Tapos para makuha natin
16:06Paano po ito-total po natin itong lahat?
16:09So paano po natin ito-total? Ay
16:11pagpa-plus plus lang naman natin no. So
16:14pag tinotal po natin, ang total is 1 2
16:20ayan. Now tapos syempre hindi pa yan ang
16:23final answer. Paano natin kukunin ang
16:251220 / 15 and ang makukuha natin ay 1220
16:3215 that is 81.3 3333.
16:37So dalawang decimal lang tayo. That will
16:39be lagay natin dito 81.33.
16:45Ayan. So anong gagawin natin ngayon?
16:47Yung x natin which is the midpoint po
16:49ima-minus natin yung ating mean. So para
16:53makuha po yan, gagamit tayo ng
16:55calculator. Be mindful of the negative
16:59and positive signs natin. So 67 - 81.33
17:0333 is -14.33.
17:09This one -9.33.
17:12Reminder po ito po ginamit natin
17:14pangkuha ng minh ha. Baka yan ang
17:16mai-minus minus po ninyo.
17:19Ilalagay ko na po yung values dito ha.
17:22You can pause para kayo po ang mag-minus
17:24sa kanila.
17:33Ayan 92
17:3510.67
17:37point po yan mga 97 is 15.67
17:43ayan tapos sabi dito i squared ulit
17:47natin. Bakit ulit natin i-square? Para
17:49ma-cancel natin yung negative sign. Kasi
17:51pag tinotal po natin yan, ah nasa around
17:54zero lang yung makukuha nating value no
17:56at hindi po pwede 'yun. So kailangan
17:58natin silang i-square. So ang makukuha
18:00natin ay for this one 205.35
18:0887.05
18:1118.75
18:150.45
18:1932.15 115
18:23113
18:2885 and
18:31245.5.
18:34Ngayon hindi pa po yan ang sagot. No,
18:38ano pa daw po ang kailangan nating gawin
18:40according to the formula? I-multiply pa
18:42natin sa frequency. Paano po? So ito
18:45times ito. So ganyan. multiply natin ito
18:50times ito 2053
18:55next is 261.15
18:5815. Saan po galing? 3 * 87.
19:02So yan sulat ko na po ha.
19:08Mano po no. 45 * 2 so 90 3 * 32 is 96.
19:1745.
19:20Next is
19:23227.78
19:2570
19:26245.55.
19:29Ngayon, ayan na po ba 'yun? Hindi pa po.
19:32Ito-total ulit natin. Bakit? Kasi sabi
19:35don sa formula natin sa Mason po eh.
19:37No'no so sa Mason of all of this we have
19:421,093.35.
19:46Ayan na ba? Hindi pa ulit. So pwede na
19:49tayong pumunta sa formula natin. So
19:51formula natin substitute natin. We
19:54have93.35
19:57/ n - 1 n is 15 - 1. So
20:04ang makukuha natin ay
20:071,93.35/
20:1135 / 14,93
20:20ng calculator nila
20:26ano ba yan
20:28hirap hindi mo calculator gamit
20:32nakakili siya we have an makukuha natin
20:36kaya
20:3878 8
20:4110
20:43dalawa yan kaso pag ni-round off kasi
20:46natin siya ang nakuha kasi 78.096428
20:50no ira-round off natin 78.10 actually
20:54this is already our variance however we
20:57have this no kasi sabi ko standard
20:59deviation ang kinukuha natin so 78.10
21:02s ro 78.10 natin is 84.
21:09Kung makikita natin nagkakalapit ba sila
21:12ng
21:13Yes no? Nagkakalapit silang dalawa. Pero
21:16this one kasi ' ba sabi natin kapag sa
21:18group this is only an estimation no? So
21:22that is our standard deviation and our
21:25variance for the group data no ba ang
21:27dali lang po. Madali lang siya no? So
21:31this is for the ungroup this is for the
21:34group. Tapos punta naman tayo ng range.
21:37Ano naman si range? No
21:40may definition pa dito si varian. So
21:42average of the squared deviance from the
21:45mean.
21:47Squared deviations from the mean. No
21:50deviation is standard deviation natin.
21:52I-square mo lang siya no? Kaya pwede rin
21:55na ang formula dito is
21:59or ang gagamitin ninyo wala nakuha niyo
22:01na ito 8.84
22:05s.
22:07Tapos ang makukuha ninyo 78.1 1 equ
22:1278.1
22:15variance.
22:18Ayan na siya no. Ayan kasi lang yung
22:21formula no. Hindi natin masyadong
22:24ginagamit si variance kasi as you can
22:25see masyadong malaki iung value no kaya
22:27standard deviation ang ginagamit natin.
22:30Ngayon kung yan ang nakuha nating
22:32standard deviation
22:35yan kunwari normally distributed yung
22:38data natin no sabi natin ang mean nasa
22:41gitna ang mean natin ay 81.33
22:4681.33 33. So meron tayong standard one
22:50standard deviation two standard
22:52deviation 3 standard deviation here then
22:561 standard deviation -2 -3 now so 81.33
23:02+ 8.84 that is 81.33
23:07+ 8.84
23:10we have bakit multiply 81.83
23:15+ 8.8 84
23:20bu yung calcul
23:2281.23
23:25plus 8.44
23:28ayan
23:3089.77
23:32ibig sabihin dito 89.77
23:36dito naman sa atin sa kabila 81.33/
23:421 / minus lang po na 81.33 23 minus ilan
23:48yung standard deviation method 8.84
23:52that is 72.49
23:59an derviation kasi ' ba ganun yung layo
24:02sa mean no so ang mean natin 81.33
24:06dito naman 89.77 dito 72.49 49. Para
24:10saan po yan no? Kasi kapag meron tayong
24:12mga data, sometimes ang sasabihin nila
24:14yung scores ng student natin is one
24:16standard deviation from the mean. Ibig
24:19sabihin yung score niya nagpo-fall
24:20around this one. Ngayon pag alam mo na
24:22ang mean ay 81.33
24:24ang standard deviation ay 8.84. Alam mo
24:27na ang score niya ay
24:31student mo ay 89.77. Ganun din pag
24:34negative. So ganyan lang yan. Plus plus
24:37plus. So ito ay 1 2 3. So habang
24:41lumalayo ganun din yung dinadagdag mong
24:43standard deviation. No ganun din dito sa
24:47negative. Dito naman syempre negative
24:49side magbabawas ka ng standard
24:51deviation. Now for example si IQ po kasi
24:54natin
24:57ang kanyang given or constant na mean ay
25:02100. Ang standard deviation ay 15. So
25:06kada standard deviation magdadagdag ka
25:08or magbabawas ka ng 15. So one standard
25:11deviation from the mean is 115. 2 is
25:14130. Sa kabila naman is 85 70 ganyan. So
25:18pag ang nakuha mo sabi ko kunwari ang
25:20score ni Ma'am Manishaya ay 100 standard
25:23deviation above the mean sa IQ test
25:25niya. So ibig sabihin 115 ang nakuha ni
25:28ma'am Alishaya.
25:30Anong ibig sabihin niyan? Mas mataas
25:32siya doon sa average kasi ang average
25:34100. The more na lumalayo sa mean, the
25:38more natutan ng center defication, mas
25:40lumalayo siya sa mean. Ibig sabihin ah
25:44lumalayo siya doon sa average
25:46performance. No so that is standard
25:49deviation. Ngayon naman proceed to
25:51range. Si range pinakamadali. Bakit?
25:54Kasi highest score minus lowest score or
25:57highest value minus lowest value.
26:00Titignan natin dito ang highest value
26:02natin ay 95 - 68. So ang makukuha natin
26:07ilan yan? 95 - 68
26:1227 ayan na siya may range na tayo.
26:1727 na. Now maglagay kayo ng formula ha.
26:2095 - 68 is 27. O standard ay ano na yan
26:25range na yan. Ngayon medyo tricky si
26:27upper boundary tsaka si lower boundary.
26:30This is for the group naman no.
26:33Paano naman po kukunin? Upper boundary.
26:35Kailangan makita natin yung table natin
26:37from the group data. Ang highest
26:40boundary natin dito is 99. If you
26:43remember, our lower class boundary ang
26:45ginawa natin nagbawas tayo ng 5. Dito
26:48naman magdadagdag tayo ng5.
26:51So ating data 65 ang lower class
26:54boundary or lowest
26:57boundary natin. Dito naman 99. So 65 -5
27:03is 64.5.
27:06That is the lower class boundary. Ang
27:07upper class boundary naman natin ay
27:1095.5.
27:12Ano gagawin natin? Ima-minus lang po
27:14natin. So pag minus natin
27:1895
27:21- 64.5
27:24at ayun ay 31. Ayun na si range hindi na
27:28kayo mazo-zero
27:30' ba. Madali lang po si ring no. Ay ayun
27:34yung last.
27:36Ayan.
27:39So ang formula natin dito ayan.
27:42simplest measure of variability. Bakit?
27:44Kasi ma-minus mo lang daw yung largest
27:48minus smallest, no? So hindi na kayo
27:52mazo-zero.
27:53Okay? Yun nga lang highly affected siya
27:56by extreme values outliers. Imaginen
27:59ninyo no dito sa ating example kanina
28:03ang range ay 20 - 1 is 19 ang range.
28:07Dito sa kabila two lang.
28:10Ang layo nung range non. Bakit? Kasi
28:12meron tayong outlier na ang nakuha ay
28:1520. Dito naman mababa lang ang range.
28:17Ibig sabihin magkakalapit yung scores.
28:19Dito para sabihin niya magkakalayo yung
28:21scores. Pero in reality nahila lang
28:23talaga nung isa. Kaya hindi masyadong
28:26ginagamit si range. So mas ginagamit si
28:28standard deplation.
28:31So I hope you have learn something from
28:33this video and if you have any question
28:35don'titate toess in group chat and we
28:38will answer that. Ayan na.