Rumus Simpangan Rata-rata, Variansi, Simpangan Baku Data Berkelompok dan Contohnya
Bentuk Umum:
rumus mencari ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwUFDStk8K8-Ta9ElhUomSuFvI8IumBTlfCzXN5J-FpT3ECRLcJ6t0ZZQDvNARjq7Sy-dIjvJVD85lvxXHf19tichVHJQoMgeYitbZK-F3flZYq-RSZpnlpu6FyLdcfSa2PEraz8foBfG1/s1600/CodeCogsEqn+%252865%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwUFDStk8K8-Ta9ElhUomSuFvI8IumBTlfCzXN5J-FpT3ECRLcJ6t0ZZQDvNARjq7Sy-dIjvJVD85lvxXHf19tichVHJQoMgeYitbZK-F3flZYq-RSZpnlpu6FyLdcfSa2PEraz8foBfG1/s1600/CodeCogsEqn+%252865%2529.gif)
Keterangan:
SR = simpangan rata-rata
fi = frekuensi
xi = nilai tengah
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwUFDStk8K8-Ta9ElhUomSuFvI8IumBTlfCzXN5J-FpT3ECRLcJ6t0ZZQDvNARjq7Sy-dIjvJVD85lvxXHf19tichVHJQoMgeYitbZK-F3flZYq-RSZpnlpu6FyLdcfSa2PEraz8foBfG1/s1600/CodeCogsEqn+%252865%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieEqG2z7mtolPaSfXCn1o2zus5KDiSXbqYYa9L7WLKhg8CRDpDPexxB4cgAFDiIjwows_ptTvLI_yP-qU2HWgv3qGVTvRep9_030okZPAWDJGwdQaxwz9tUmDcQYT8IcJapQrgBHoOSmem/s1600/CodeCogsEqn+%252883%2529.gif)
Variansi/Ragam ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMWBKcDfmhYCcGc0er_X9DorLdQo7nvNW4ZLuwJAxPyiouqGAlOr6YuM_e_94FU1JzX21xCHWDrcMjNAiHNEKfbYz6JOqQc73rVwYLKHeAL_uf6j4Kx-x1gEDZU50VF9GdsIqO3JfRCro3/s1600/CodeCogsEqn+%252868%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMWBKcDfmhYCcGc0er_X9DorLdQo7nvNW4ZLuwJAxPyiouqGAlOr6YuM_e_94FU1JzX21xCHWDrcMjNAiHNEKfbYz6JOqQc73rVwYLKHeAL_uf6j4Kx-x1gEDZU50VF9GdsIqO3JfRCro3/s1600/CodeCogsEqn+%252868%2529.gif)
Rumus Umum:
Keterangan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMWBKcDfmhYCcGc0er_X9DorLdQo7nvNW4ZLuwJAxPyiouqGAlOr6YuM_e_94FU1JzX21xCHWDrcMjNAiHNEKfbYz6JOqQc73rVwYLKHeAL_uf6j4Kx-x1gEDZU50VF9GdsIqO3JfRCro3/s1600/CodeCogsEqn+%252868%2529.gif)
fi = frekuensi
xi = nilai tengah
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwUFDStk8K8-Ta9ElhUomSuFvI8IumBTlfCzXN5J-FpT3ECRLcJ6t0ZZQDvNARjq7Sy-dIjvJVD85lvxXHf19tichVHJQoMgeYitbZK-F3flZYq-RSZpnlpu6FyLdcfSa2PEraz8foBfG1/s1600/CodeCogsEqn+%252865%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieEqG2z7mtolPaSfXCn1o2zus5KDiSXbqYYa9L7WLKhg8CRDpDPexxB4cgAFDiIjwows_ptTvLI_yP-qU2HWgv3qGVTvRep9_030okZPAWDJGwdQaxwz9tUmDcQYT8IcJapQrgBHoOSmem/s1600/CodeCogsEqn+%252883%2529.gif)
Simpangan Baku/Standar Deviasi (S)
Bentuk Umum:
Keterangan:
S = simpangan baku
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMWBKcDfmhYCcGc0er_X9DorLdQo7nvNW4ZLuwJAxPyiouqGAlOr6YuM_e_94FU1JzX21xCHWDrcMjNAiHNEKfbYz6JOqQc73rVwYLKHeAL_uf6j4Kx-x1gEDZU50VF9GdsIqO3JfRCro3/s1600/CodeCogsEqn+%252868%2529.gif)
Contoh 1.1
Perhatikan tabel berikut!
Nilai
|
Frekuensi (fi)
|
50 – 54
|
2
|
55 – 59
|
4
|
60 – 64
|
6
|
65 – 69
|
11
|
70 – 74
|
15
|
75 – 79
|
7
|
80 – 84
|
3
|
84 – 89
|
2
|
Tentukan:
a. Simpangan Rata-rata (SR)
b. Variansi/Ragam ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMWBKcDfmhYCcGc0er_X9DorLdQo7nvNW4ZLuwJAxPyiouqGAlOr6YuM_e_94FU1JzX21xCHWDrcMjNAiHNEKfbYz6JOqQc73rVwYLKHeAL_uf6j4Kx-x1gEDZU50VF9GdsIqO3JfRCro3/s1600/CodeCogsEqn+%252868%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMWBKcDfmhYCcGc0er_X9DorLdQo7nvNW4ZLuwJAxPyiouqGAlOr6YuM_e_94FU1JzX21xCHWDrcMjNAiHNEKfbYz6JOqQc73rVwYLKHeAL_uf6j4Kx-x1gEDZU50VF9GdsIqO3JfRCro3/s1600/CodeCogsEqn+%252868%2529.gif)
c. Simpangan Baku (S)
Jawab:
Nilai
|
fi
|
xi
|
fi . xi
|
50 – 54
|
2
|
52
|
104
|
55 – 59
|
4
|
57
|
228
|
60 – 64
|
6
|
62
|
372
|
65 – 69
|
11
|
67
|
737
|
70 – 74
|
15
|
72
|
1.080
|
75 – 79
|
7
|
77
|
539
|
80 – 84
|
3
|
82
|
246
|
84 – 89
|
2
|
87
|
174
|
JUMLAH
|
50
|
556
|
3.480
|
Mencari ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwUFDStk8K8-Ta9ElhUomSuFvI8IumBTlfCzXN5J-FpT3ECRLcJ6t0ZZQDvNARjq7Sy-dIjvJVD85lvxXHf19tichVHJQoMgeYitbZK-F3flZYq-RSZpnlpu6FyLdcfSa2PEraz8foBfG1/s1600/CodeCogsEqn+%252865%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwUFDStk8K8-Ta9ElhUomSuFvI8IumBTlfCzXN5J-FpT3ECRLcJ6t0ZZQDvNARjq7Sy-dIjvJVD85lvxXHf19tichVHJQoMgeYitbZK-F3flZYq-RSZpnlpu6FyLdcfSa2PEraz8foBfG1/s1600/CodeCogsEqn+%252865%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTEIeaCOzdWUr4KE8laE_1xQMKml-Ty3KL5PqKXU_Jnsk-5K_AVn6tenspcRld52RmUJQvVB-Fgy4evXxaXQhZesBL6X7venvZnfUBGRoePmA1bmsn8E9lgn4i4kdLNDraAsRacWRxM3jT/s1600/CodeCogsEqn+%252884%2529.gif)
a). Simpangan Rata-rata
Diketahui:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaGK2-jgVx3PTNMeDSQXQ1rYKDT9I9R6UoxFJZW_xoRskNc6OqjFWVzfOiOQpOZtuPhoKMQv0KOk0v_g2YU4g1OT3ZO1cO4IF_NLtla8WAVgdm85H8-zmgtX9DysbI31eluz4JUr5BM2dA/s1600/CodeCogsEqn+%252889%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7DuOSYsalge0_-LJVH23xitjfqkees9WVcOryKhOzTfJfXMrRIw0W5EKirmk7PyzxiZYrQNK4HafQEtupBsiHzD057-zxGfMpvVeX_qCyF1NpMGoz756z_PSMyDVyZIsNZJG604dgAxlR/s640/CodeCogsEqn+%252885%2529.gif)
Jadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGYxkBxDpeGha9gW2eB1FeblMrGeiBHdufdslLCm9ZZx0em1DVDaRtd5377f1EIJE21jwU8tUKmNTd2kXC5U23fPywy_hvksnHfY-OaM3pNfs6Om0ESraQGDaPzOeoD5jR3lTrzcKGnyS1/s1600/CodeCogsEqn+%252890%2529.gif)
b). Variansi/Ragam
Diketahui:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaGK2-jgVx3PTNMeDSQXQ1rYKDT9I9R6UoxFJZW_xoRskNc6OqjFWVzfOiOQpOZtuPhoKMQv0KOk0v_g2YU4g1OT3ZO1cO4IF_NLtla8WAVgdm85H8-zmgtX9DysbI31eluz4JUr5BM2dA/s1600/CodeCogsEqn+%252889%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiv2oB_HKpSXwQQnRfDBZyzo_u8kMDXGYQk2YJD3y9fHTw1XfyZamtikv_keAmmZExbJ-8AcT6mO28SBh7ivJTY2KnnDcIK7BxYiTD_RzziRvr3dGBH0ZKx6dMmcue3sCmY_QmCc76e6vmQ/s640/CodeCogsEqn+%252888%2529.gif)
Jadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZoR7VZ2RFMLt6UwBwdf8zyIiqajkEoGabyvX1hwlnydqnhqLNJnz-FMVOdDTJOrR__wh0jeSDUKKCRBxElrZryhL8k4USI5RPWlzbRuJuQ4ccx7m_Lx2oOxxoRmMYZ57UHsuAHqkwSvPv/s1600/CodeCogsEqn+%252893%2529.gif)
c). Simpangan Baku
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4yluvkOrnwWXNXPXfSM6nhkWJr2yY-7wtvOJpRL_LaSzSegY9-XTuh10-R4Fgk4Y5bPlax_kLNmbD8TCWZLzfrw-ctKJ1hhPrp8Z6-x7Q6m_Iu8YI1TqFFuScp9LJryBgBqVnVJYfHRdA/s1600/CodeCogsEqn+%252896%2529.gif)
Contoh 1.2
Perhatikan tabel berikut!
Nilai
|
Frekuensi (fi)
|
40 – 44
|
8
|
45 – 49
|
9
|
50 – 54
|
4
|
55 – 59
|
10
|
60 – 64
|
9
|
65 – 69
|
5
|
a. Simpangan Rata-rata (SR)
b. Variansi/Ragam ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMWBKcDfmhYCcGc0er_X9DorLdQo7nvNW4ZLuwJAxPyiouqGAlOr6YuM_e_94FU1JzX21xCHWDrcMjNAiHNEKfbYz6JOqQc73rVwYLKHeAL_uf6j4Kx-x1gEDZU50VF9GdsIqO3JfRCro3/s1600/CodeCogsEqn+%252868%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMWBKcDfmhYCcGc0er_X9DorLdQo7nvNW4ZLuwJAxPyiouqGAlOr6YuM_e_94FU1JzX21xCHWDrcMjNAiHNEKfbYz6JOqQc73rVwYLKHeAL_uf6j4Kx-x1gEDZU50VF9GdsIqO3JfRCro3/s1600/CodeCogsEqn+%252868%2529.gif)
c. Simpangan Baku (S)
Jawab:
Nilai
|
fi
|
xi
|
fi . xi
|
40 – 44
|
8
|
42
|
336
|
45 – 49
|
9
|
47
|
423
|
50 – 54
|
4
|
52
|
208
|
55 – 59
|
10
|
57
|
570
|
60 – 64
|
9
|
62
|
558
|
65 – 69
|
5
|
67
|
335
|
JUMLAH
|
45
|
327
|
2.430
|
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwUFDStk8K8-Ta9ElhUomSuFvI8IumBTlfCzXN5J-FpT3ECRLcJ6t0ZZQDvNARjq7Sy-dIjvJVD85lvxXHf19tichVHJQoMgeYitbZK-F3flZYq-RSZpnlpu6FyLdcfSa2PEraz8foBfG1/s1600/CodeCogsEqn+%252865%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSZjSZg2Ue4Ho5x-vNJBcepq-_y3sfqTarZFyo1sXcrSmqL47D4CmhNJ_G2aYkrcUlFXcLUGrTInfaiSjdORtzwqAWUmL8CGe8wPf3EgJ64FwlFrJ9RYJlUEQKm7N0sixChagh6d65BLWf/s1600/CodeCogsEqn+%252898%2529.gif)
a). Simpangan Rata-rata
Diketahui:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVx4XPVUKigbIr5UVzwMpvGx8aH_i-5PWryj8iXI7wbIjU525EYnsXQyzzOZzwAtxDker4Cjpf1VERY3-YI602gttlXPVz9Ufi3Y6AiJvi5jUTm92TPuEgSqZ29t_Fv5wa1rLpWNNE2MEY/s1600/CodeCogsEqn+%252897%2529.gif)
Diketahui:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVx4XPVUKigbIr5UVzwMpvGx8aH_i-5PWryj8iXI7wbIjU525EYnsXQyzzOZzwAtxDker4Cjpf1VERY3-YI602gttlXPVz9Ufi3Y6AiJvi5jUTm92TPuEgSqZ29t_Fv5wa1rLpWNNE2MEY/s1600/CodeCogsEqn+%252897%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhenYJ9shFh22N0-LZKrbqkoUvCBqREaM0xux812pihdHN2tVs5XjHI1-Mq7OWaXKqD-x7QaiIHAQbWZI423FAG40u9TPE5wVbXQc3717hi6R8tT84_8USeNVohyp7gC8KwP8y8unSlMHdg/s1600/CodeCogsEqn+%252886%2529.gif)
Jadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzc2yn5MZI1zG2R7WMGy-FM4zEG9mR_6KIqUIrPCm63gRAZ2N0S1rgzxzP6ff9xLEZ64GopNPGve8o8Reufqovb7fm10ojD23DrD4BmabhmeKDXCxM067QOc4R2UwkHN32p236DEpaIx3y/s1600/CodeCogsEqn+%252892%2529.gif)
b). Variansi/Ragam
Diketahui:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVx4XPVUKigbIr5UVzwMpvGx8aH_i-5PWryj8iXI7wbIjU525EYnsXQyzzOZzwAtxDker4Cjpf1VERY3-YI602gttlXPVz9Ufi3Y6AiJvi5jUTm92TPuEgSqZ29t_Fv5wa1rLpWNNE2MEY/s1600/CodeCogsEqn+%252897%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuqi4JTbc2zYSUHFea9tbCMieR7Bttge4QzKyRht_T6dpYRrd2j34ayggoVW2qKa9eKHGLxdRoHmeCt25TzSwF2Kl4kj9-R_8nOTsTyIgNOHTsf8z2pSnrQNXfhh7haD7WXhHVIS61mnqb/s640/CodeCogsEqn+%252887%2529.gif)
Jadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeVjry829OEpRIZ0w4Zrk2S1f7XBsXZiKoq6w9qxxJ6A-ZiuitakH0VOHObAcmENs97zXdqxb3hNycIsM3gQm9UhRuoEf0k9m-f2Kke6qD31s9bK17FXplWyZfEJUIcYX6DSLRY6m-bCQW/s1600/CodeCogsEqn+%252894%2529.gif)
c). Simpangan Baku
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhItch6MEa9DmfFrCcXJZMtU4PEzUI60cXWg3afW2nrff9EOpyMR_F1FZ3GLZ8kFEAfuNm5CeHX8jM64jaopcjPP0Z57C1y7qVndNJYRatFICMhyZ6E4xlFM91yEmWB_UcGyZCwweB_HSAY/s1600/CodeCogsEqn+%252895%2529.gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhItch6MEa9DmfFrCcXJZMtU4PEzUI60cXWg3afW2nrff9EOpyMR_F1FZ3GLZ8kFEAfuNm5CeHX8jM64jaopcjPP0Z57C1y7qVndNJYRatFICMhyZ6E4xlFM91yEmWB_UcGyZCwweB_HSAY/s1600/CodeCogsEqn+%252895%2529.gif)
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