Question

identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. also identify the number of individuals included in the summary.
age (yr) when award was won frequency
20 - 21 27
22 - 23 36
24 - 25 14
26 - 27 3
28 - 29 6
30 - 31 1
32 - 33 1
(type integers or decimals. do not round. use ascending order.)
identify the upper class limits.
21, 23, 25, 27, 29, 31, 33
(type integers or decimals. do not round. use ascending order.)
identify the class width.
(type an integer or a decimal. do not round.)
identify the class midpoints.
(type integers or decimals. do not round. use ascending order.)
identify the class boundaries.
(type integers or decimals. do not round. use ascending order.)
identify the number of individuals included in the summary.

Explanation:

Step1: Calculate class width

Take the first - class 20 - 21. Subtract the lower limit from the upper limit: $21 - 20=1$.

Step2: Calculate class mid - points

For the class 20 - 21, the mid - point is $\frac{20 + 21}{2}=20.5$. For 22 - 23, it is $\frac{22+23}{2}=22.5$. For 24 - 25, it is $\frac{24 + 25}{2}=24.5$. For 26 - 27, it is $\frac{26+27}{2}=26.5$. For 28 - 29, it is $\frac{28 + 29}{2}=28.5$. For 30 - 31, it is $\frac{30+31}{2}=30.5$. For 32 - 33, it is $\frac{32 + 33}{2}=32.5$.

Step3: Calculate class boundaries

For the class 20 - 21, the lower boundary is $19.5$ and the upper boundary is $21.5$. For 22 - 23, the lower boundary is $21.5$ and the upper boundary is $23.5$. For 24 - 25, the lower boundary is $23.5$ and the upper boundary is $25.5$. For 26 - 27, the lower boundary is $25.5$ and the upper boundary is $27.5$. For 28 - 29, the lower boundary is $27.5$ and the upper boundary is $29.5$. For 30 - 31, the lower boundary is $29.5$ and the upper boundary is $31.5$. For 32 - 33, the lower boundary is $31.5$ and the upper boundary is $33.5$.

Step4: Calculate number of individuals

Sum up the frequencies: $27+36 + 14+3+6+1+1=88$.

Answer:

Class width: $1$
Class mid - points: $20.5,22.5,24.5,26.5,28.5,30.5,32.5$
Class boundaries: $19.5,21.5,23.5,25.5,27.5,29.5,31.5,33.5$
Number of individuals: $88$