Yaadannoo boqonnaa fi gaaffii shaakalaa

Boqonnaa 3 Herrega kutaa 12: Istaatistiksii

Wanti fuula kana irra jiru hundi boqonnaa 3 kitaaba Herrega kutaa 12 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.

7
Kaardii: 10
Gaaffii shaakalaa boqonnaa 3: 159–236
Fuula kitaabaa boqonnaa 3

Boqonnaan 3 maal haguuga

1.Measures of Absolute Dispersions
2.Interpretation of Relative Dispersions
3.Use of Frequency Curves
4.Sampling Techniques

Yaadannoo gabaabaa boqonnaa 3

Kaardiiwwan fuula Herrega kutaa 12 irratti boqonnaa kana jala galmaa'an. Tokko tokkoon bani.

Absolute fi Relative DispersionGabatee wabiiAbsolute dispersion · Relative dispersion

Gosa Safaraa	Safartuu	Kaayyoo Guddaa	Fakkeenya
Absolute dispersion	Yuunitii daataa wajjin tokko	Faca'iinsa tuuta daataa tokkoo safaruuf	Range, Inter-quartile range, Mean deviation
Relative dispersion	Yuunitii kan hin qabne	Garaagarummaa tuutota daataa lama yookiin isaa ol walbira qabuuf	Coefficient of range, Coefficient of variation

Yoom akka itti fayyadamtu

Faca'iinsa daataa yuunitii isaatiin gabaasuuf yookiin tuutota daataa garaagaraa walbira qabuuf isa kam akka fayyadamtu murteessuuf kana ilaali.

Of eeggadhu

Tuutota daataa yuunitii adda addaa qaban walbira qabuuf matumaa absolute measures of dispersion hin fayyadamin.

Grade 12 Mathematics, fuula 159-236 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Mean Deviation Daataa Hin Gurmaa'inFoormulaa

MD = \frac{\sum |x_i - A|}{n}

MD = \frac{\sum |x_i - A|}{n}

$MD$: Damballaa gidduugaleessaa $unit of data$
$x_i$: Gatii tokkoon tokkoo daataa $unit of data$
$A$: Gatii giddugaleessaa: mean, median, yookiin mode $unit of data$
$n$: Ida'ama baay'ina daataa $dimensionless$

Yoom akka itti fayyadamtu

Daataa qulqulluuf fageenya giddugaleessaa gatiiwwan mean, median yookiin mode irraa qaban shallaguuf itti fayyadami.

Of eeggadhu

Ida'uun dura yeroo hunda absolute value garaagarummaa fudhadhu. Utuu absolute value hin fudhatin garaagarummaan mean naannoo jiru yeroo hunda eeroo ta'a.

Grade 12 Mathematics, fuula 159-236 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Quartiles Daataa Gurmaa'eeFoormulaa

Q_k = L + \left(\frac{\frac{k n}{4} - cf}{f}\right) w

Q_k = L + \left(\frac{\frac{k n}{4} - cf}{f}\right) w

$Q_k$: Quartile k ffaa $unit of data$
$L$: Kutaa quartile keessatti Lower class boundary $unit of data$
$k$: Tartiiba quartile (1, 2, yookiin 3) $dimensionless$
$n$: Ida'ama baay'ina daataa $dimensionless$
$cf$: Cumulative frequency kutaa quartile dura jiru $dimensionless$
$f$: Frequency kutaa quartile $dimensionless$
$w$: Bal'ina kutaa quartile $unit of data$

Yoom akka itti fayyadamtu

Foorimulaa kanatti fayyadamuun quartile tokkoffaa, lammaffaa yookiin sadaffaa daataa gurmaa'eef shallagi.

Of eeggadhu

cf n cumulative frequency kutaa quartile dura jiruudha malee kan kutaa quartile sanaa miti.

Grade 12 Mathematics, fuula 159-236 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Range Daataa Gurmaa'eeFoormulaa

R = B_U(H) - B_L(L)

R = B_U(H) - B_L(L)

$R$: Reenjii $unit of data$
$B_U(H)$: Kutaa isa ol aanaa keessatti Upper class boundary $unit of data$
$B_L(L)$: Kutaa isa gadi aanaa keessatti Lower class boundary $unit of data$

Yoom akka itti fayyadamtu

Foorimulaa kanatti fayyadamuun range daataa gurmaa'ee shallagi.

Of eeggadhu

Class limits qulqulluu walirraa hin hir'isin. Yeroo hunda dura gara class boundaries tti jijjiiri.

Grade 12 Mathematics, fuula 159-236 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Class Limits fi Class Boundaries Walitti MakaaDogoggora baratame

Yoom akka itti fayyadamtu

Range, class width yookiin quartiles daataa gurmaa'ee yeroo shallagdu kana qalbifadhu.

Of eeggadhu

Class limits gidduu qaawwatu jira. Range yookiin quartiles shallaguun dura daangaa gadi aanaa irraa 0.5 hir'isuun fi isa ol aanaatti 0.5 ida'uun gara class boundaries tti jijjiiri.

Grade 12 Mathematics, fuula 159-236 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Giddu-galeessa daataa kutaadhaan qindaa'eeFoormulaa

\text{Median} = L + \frac{h}{f}\left(\frac{n}{2} - C\right)

\text{Median} = L + \frac{h}{f}\left(\frac{n}{2} - C\right)

$L$: daangaa gadii kutaa giddu-galeessaa
$h$: bal'ina kutaa, daangaa olii irraa daangaa gadii hir'isuu
$f$: irra deddeebi'insa kutaa giddu-galeessaa
$n$: irra deddeebi'insa waliigalaa, ida'ama f hundaa
$C$: irra deddeebi'insa walitti qabame kutaa giddu-galeessaa dura jiruu

Yoom akka itti fayyadamtu

Yeroo daataan kutaalee fi irra deddeebi'insa waliin dhufu, gatii tokkoon tokkoon isaa malee, fayyadami; kanaafuu lakkoofsi giddu-galeessaa dubbifamu hin jiru. Tarree irra deddeebi'insa walitti qabamee ijaari; kutaa jalqabaa ida'amni isaa n dhibbeentaa 2 ga'u barbaadi; sun kutaa giddu-galeessaa foormulaan keessatti hojjetu dha.

Of eeggadhu

Bal'inni h daangaalee irraa dhufa malee daangaalee barreeffaman irraa miti. Kutaan 60 hanga 69 jedhamee barreeffame daangaan isaa 59.5 hanga 69.5 dha; kanaafuu h 10 dha malee 9 miti. 9 fudhachuun deebii walakkaa kutaadhaan sochoosa; kunis qabxii jijjiiruuf ga'aa dha; waraqaalee irra deebi'anii qo'atan irraas dogoggora baay'inaan garagalfamu dha.

Moodii daataa kutaadhaan qindaa'eeFoormulaa

\text{Mode} = L + h\left(\frac{f_{m} - f_{1}}{(f_{m} - f_{1}) + (f_{m} - f_{2})}\right)

\text{Mode} = L + h\left(\frac{f_{m} - f_{1}}{(f_{m} - f_{1}) + (f_{m} - f_{2})}\right)

$L$: daangaa gadii kutaa moodaalaa
$h$: bal'ina kutaa, daangaalee irraa fudhatame
$f_{m}$: irra deddeebi'insa kutaa moodaalaa, isa guddaa
$f_{1}$: irra deddeebi'insa kutaa isa dura jiruu
$f_{2}$: irra deddeebi'insa kutaa isa booda jiruu

Yoom akka itti fayyadamtu

Yeroo gatii baay'inaan mul'atu barbaaddu fi daataan kutaalee keessa jiru fayyadami; kanaafuu gatiin tokkoyyuu hin irra deebi'u. Kutaan moodaalaa isa irra deddeebi'insa guddaa qabu qofa; foormulaanis gara ollaa xiqqaa ta'etti cichuudhaan moodii isa keessa kaa'a.

Of eeggadhu

Kutaaleen lama irra deddeebi'insa guddaadhaan wal qixa yoo ta'an daataan moodii lama qaba; foormulaan kunis lamaan isaaniifuu hin hojjetu. Waan tokko barreessuu kee dura ollaawwan sakatta'i. Bu'aan hiika akka qabaatuuf kutaaleen bal'inaan wal qixa ta'uu qabu; kunis yeroo kutaan gabatee isa dhumaa banaa ta'e sakatta'uun barbaachisaa dha.

Gaaffii shaakalaa boqonnaa 3

Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.

Gaaffii 1

Find the range of the data set: 25, 21, 22, 20, 19, 16.

A.6
B.9
C.16
D.25

Deebii fi sababa agarsiisi

Deebii: B 9

Sababa

The range is the largest value minus the smallest value. The largest value is 25 and the smallest is 16. So R = 25 - 16 = 9.

Gaaffii 2

A supermarket in Addis Ababa recorded its daily sales (in Birr 100) for twelve days: 115, 134, 120, 111, 122, 103, 80, 155, 122, 104, 110, 98. What is the range of these sales?

A.57
B.75
C.80
D.155

Deebii fi sababa agarsiisi

Deebii: B 75

Sababa

The largest value is 155 and the smallest value is 80. So R = 155 - 80 = 75 (in Birr 100).

Gaaffii 3

Find the mean of the data set: 50, 80, 80, 110, 110, 110, 140, 160.

A.80
B.105
C.110
D.840

Deebii fi sababa agarsiisi

Deebii: B 105

Sababa

Add all the values to get 840. There are 8 values. So the mean is 840 / 8 = 105.

Gaaffii 4

Two basketball teams scored points in ten games. Team B scored: 53, 46, 48, 50, 53, 53, 58, 60, 57, 52. What is the range of Team B's scores?

A.7
B.14
C.46
D.60

Deebii fi sababa agarsiisi

Deebii: B 14

Sababa

The largest score is 60 and the smallest score is 46. So the range is 60 - 46 = 14.

Gaaffii 5

Find the mean deviation about the mean of the data set: 50, 80, 80, 110, 110, 110, 140, 160.

A.21
B.25
C.26.25
D.210

Deebii fi sababa agarsiisi

Deebii: C 26.25

Sababa

First, the mean is 105. Take the absolute deviation of each value from 105: 55, 25, 25, 5, 5, 5, 35, 55. Their sum is 210. Divide the sum by the number of values: 210 / 8 = 26.25.

Gaaffii 6

Find the variance of the data set: 16, 12, 8, 18, 5, 9, 24, 20.

A.6.14
B.14
C.37.75
D.302

Deebii fi sababa agarsiisi

Deebii: C 37.75

Sababa

The mean is (16 + 12 + 8 + 18 + 5 + 9 + 24 + 20) / 8 = 112 / 8 = 14. The squared deviations are 4, 4, 36, 16, 81, 25, 100 and 36. Their sum is 302. The variance is 302 / 8 = 37.75. The value 6.14 is the standard deviation, not the variance.

Gaaffii 7

The daily scores of a group of students are: 96, 70, 100, 89, 78, 56, 45, 78, 68, 42, 66, 89, 90, 54, 44, 67, 87, 97, 98. Find the quartile deviation (QD).

A.17
B.34
C.56
D.90

Deebii fi sababa agarsiisi

Deebii: A 17

Sababa

First arrange the 19 scores in order. The first quartile is the 5th item, which is 56. The third quartile is the 15th item, which is 90. The quartile deviation is half the difference: QD = (90 - 56) / 2 = 17.

Gaaffii 8

Set A is: 20, 70, 70, 70, 70, 70, 70, 70, 100. What is the inter-quartile range (IQR) of Set A?

A.0
B.20
C.70
D.80

Deebii fi sababa agarsiisi

Deebii: A 0

Sababa

The first quartile Q1 is 70 and the third quartile Q3 is 70. So IQR = Q3 - Q1 = 70 - 70 = 0. Note that the range of Set A is 80, but the IQR ignores the extreme values 20 and 100.

Gaaffii 9

Find the mean deviation about the median of the data set: 12, 9, 15, 12, 7, 10, 12.

A.1.43
B.1.57
C.1.86
D.2.00

Deebii fi sababa agarsiisi

Deebii: C 1.86

Sababa

Arrange the data: 7, 9, 10, 12, 12, 12, 15. There are 7 values, so the median is the 4th value, which is 12. The absolute deviations from 12 are 5, 3, 2, 0, 0, 0, 3. Their sum is 13. So the mean deviation about the median is 13 / 7, which is about 1.86.

Gaaffii 10

Find the coefficient of range for this data set: 22, 28, 31, 23, 24. Use the formula CR = (L - S) / (L + S), where L is the largest value and S is the smallest value.

A.0.17
B.0.29
C.0.41
D.0.50

Deebii fi sababa agarsiisi

Deebii: A 0.17

Sababa

The largest value L is 31 and the smallest value S is 22. So CR = (31 - 22) / (31 + 22) = 9 / 53, which is about 0.17. The coefficient of range has no units.

Appiin boqonnaa kana irratti gaaffii 12 qaba; utuu hojjettuu ni sirreessa. Kan asii jiran 10 jalqabaa ti.

Fuula kitaabaa boqonnaa 3

Boqonnaan 3 Maxxansa Ministeera Barnootaa keessatti fuula 159 hanga fuula 236 ti.

Maxxansa Ministeera Barnootaa, Ingiliffaa, Fuula 426

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Yaadannoo gabaabaa Herrega kutaa 12 hunda

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