If the mean and variance of the frequency distribution x i | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 f i | 4 | 4 | α | 15 | 8 | β | 4 | 5 are 9 and 15.08 respectively, then the value of α²+β²-αβ is _ _ _ _ _ _.

Statistics and Probability: JEE Main 2023 Mathematics question

JEE Main 2023 · 6 Apr, Evening shift · Q48

JEE Main 20236 Apr, Evening shiftMathematicsMediumStatistics and Probability258× since 2002

If the mean and variance of the frequency distribution

x_i

| 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16

f_i

| 4 | 4 |

\alpha

| 15 | 8 |

\beta

| 4 | 5 are 9 and 15.08 respectively, then the value of

\alpha^2+\beta^2-\alpha\beta

is ___________.

Your answerType your answer. Integers and decimals are accepted.