For a continuous variable each score actually corresponds to an interval on the scale of measurement.

$($a$)$ In general terms define the real limits of an interval.

$($b$)$ If a distribution has scores of $10,9,8,$ etc., what are the real limits for X $=8?$

$($c$)$ If a distribution has scores of $5\mathrm{.}5,5\mathrm{.}0,4\mathrm{.}5,4\mathrm{.}0,$ etc., what are the real limits for X $=4\mathrm{.}5?$

$($d$)$ In a grouped frequency distribution, each class interval has real limits and apparent limits$.$ What are the real and apparent limits for the interval $10-14?$