Linear Interpolation in Percentiles

The third quartile for a distribution of 225 items is the 169.5th observation. The 169th observation is 73 while the 170th is 79. Which is _closest_ to an estimate for the value of the third quartile?

Incorrect. This is the value for the 169th observation. Linear interpolation must be used to estimate the value for the 169.5th.

Correct. To solve, take the 169th observation and add (169.5 - 169) or 0.5 times the distance between the 169th and 170th values: $$73 + 0.5 (79 - 73) = 76$$.

Incorrect. This is the value for the 170th observation. Linear interpolation must be used to estimate the value for the 169.5th.

73

76

79