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偏差値と標準偏差 | 夢を叶える塾
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偏差値と標準偏差

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偏差値について軽くまとめました。
というか、表を作りました。
目安としてご利用ください。

偏差値の認識

模試等で偏差値が出ますよね。
「平均点の人が50で成績が良いほど高くなるもの」
という認識があれば大体大丈夫だと思います。

試験毎に多少ぶれる

試験毎に得点のばらつき具合がまちまちになります。
偏差値にはこの得点のばらつき具合が大きく影響しています。
そのため、

  • 上位から下位まで差がつかない位難しい試験だと上位も中位も下位も比較的50付近に近づき、それほど差がつかない
  • 上位と下位の差が付く難しい試験だと上位は大きい値が出やすく、中位は50からのずれが大きくなり、下位もそれほど低い値にならない
  • 上位と下位の差が付く簡単な試験だと上位もそれほど大きい値にならないが、中位は50からのずれが小さくなり、下位は低い値が出やすい
  • 上位から下位まで差が付かない位簡単な試験だと上位も中位も下位も比較的50付近に近づき、それほど差がつかない

等の傾向が出てくるかと思います。
偏差値だけだと少し不足していて、標準偏差があって本来の姿が見える部分があります。

標準偏差があるとわかること

標準偏差さえわかれば次のような事がわかります。
「標準偏差15の試験で偏差値が60だった時は上位約26%以内に位置する」
「標準偏差10の試験で偏差値が59だった時は上位約19%以内に位置する」

これがわかると、
「前回の標準偏差15の試験で偏差値60で、今回の標準偏差10の試験で偏差値59になって下がったと思ったけど成績上がってるぞ!」
「前回の標準偏差10の試験で偏差値59で、今回の標準偏差15の試験で偏差値60になって上がったと思ったけど成績さがってんじゃん!」
という事がわかるようになります。

標準偏差毎の対応表

標準偏差ごとの表を作ってみたので参考にしてみてください。
結果に載っていないこともありますけどね。

エクセルで100とか140とかから0.1とか0.01刻みで積み上げていったものなので、多少ずれています。
上位%はそのままの意味ですが、受験者数を掛ければ大体順位位になるんじゃないでしょうか。

センター試験は科目によりますが20前後になると思います。
そのくらいの上位%を確認頂いて狙っていけると良いかもしれないですね。

標準偏差10

平均点付近が多い、そこそこ団子状態の試験です。
比較的50に近い値が出やすいので、50から外れた値が小さくても平均からの差が大きくついていることになります。

偏差値上位%
731.0
721.4
711.8
702.3
692.9
683.6
674.5
665.5
656.7
648.1
639.7
6211.6
6113.6
6015.9
5918.5
5821.3
5724.3
5627.5
5531.0
5434.6
5338.3
5242.2
5146.2
5050.0
4954.1
4858.1
4761.9
4665.7
4569.3
4472.7
4375.9
4278.9
4181.7
4084.2
3986.5
3888.5
3790.4
3691.9
3593.3
3494.5
3395.5
3296.4
3197.1
3097.7
2998.2
2898.6
2798.9

標準偏差15

比較的平均点付近に集まっているような試験になります。

偏差値上位%
783.0
773.5
764.1
754.7
745.4
736.2
727.1
718.0
709.1
6910.2
6811.5
6712.8
6614.3
6515.9
6417.5
6319.3
6221.2
6123.2
6025.3
5927.4
5829.7
5732.1
5634.5
5537.0
5439.5
5342.1
5244.7
5147.4
5050.0
4952.7
4855.3
4758
4660.5
4563.1
4465.6
4368.0
4270.3
4172.6
4074.8
3976.8
3878.8
3780.7
3682.5
3584.1
3485.7
3387.1
3288.5
3189.7
3090.8
2991.9
2892.8
2793.7
2694.5
2595.2
2495.8

標準偏差20

そこそこばらけて実力差が出ている試験になります。
50から離れた値も出やすくなっているので100点を取ると80超えとかになる場合もあります。

偏差値上位%
815.4
806.0
796.7
787.4
778.2
769.1
759.9
7410.9
7311.9
7213.0
7114.1
7015.3
6916.5
6817.8
6719.2
6620.6
6522.1
6423.6
6325.2
6226.8
6128.5
6030.3
5932.1
5833.9
5735.7
5637.6
5539.6
5441.5
5343.5
5245.4
5147.4
5050.0
4951.4
4853.4
4755.4
4657.4
4559.3
4461.2
4363.1
4265.0
4166.8
4068.6
3970.3
3872.0
3773.6
3675.2
3576.7
3478.2
3379.6
3281.0
3182.3
3083.5
2984.7
2885.8
2786.9
2687.9
2588.8
2489.7
2390.5
2291.3
2192.0

標準偏差30

ばらけて実力差が出ている試験になります。
50からより離れた偏差値として値が出てきます。
表を参考に補正しておいた方が良いかもしれません。

偏差値上位%
8114.9
8015.7
7916.5
7817.3
7718.2
7619.1
7520.0
7421.0
7322.0
7223.0
7124.0
7025.1
6926.1
6827.2
6728.4
6629.5
6530.7
6431.8
6333.0
6234.3
6135.5
6036.8
5938.0
5839.3
5740.6
5641.9
5543.2
5444.5
5345.8
5247.2
5148.5
5050.0
4951.1
4852.5
4753.8
4655.1
4556.4
4457.7
4359.0
4260.3
4161.6
4062.9
3964.1
3865.4
3766.6
3667.8
3569.0
3470.1
3371.3
3272.4
3173.5
3074.6
2975.6
2876.6
2777.6
2678.6
2579.6
2480.5
2381.4
2282.3
2183.1

終わりに

表の数を増やしたり、もうちょっと精度をあげた値に更新したいと思いつつ、いったん公開致します。
見たい表だけクリックで展開できるようにするのも良いかもしれませんね。
並べて表示とかは出来なそうですが…。

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