Tennis aces

The number of aces served by Novak Djokovic in the last 20 tournaments he has participated in is shown below.
12 17 13 7 8 14 11 14 10 12
15 9 11 13 6 15 18 5 19 24
1.1 using the raw, determine the range.
1.2 Group the data into a frequency distribution with the lowest class limit of 1 ace and the class width of 5 aces.
1.3 Determine the mean number of aces served using the raw data.
1.4 Draw a less than ogive curve corresponding to the data and use it to estimate the median

Final Answer:

r =  19
m =  12.65
f = f

Step-by-step explanation:

$$\begin{gathered} min=5 \\ \max =24 \\ n=20 \\ r=\max -min=24-5=19 \end{gathered}$$

$$\begin{gathered} s=12+17+13+7+8+14+11+14+10+12+15+9+11+13+6+15+18+5+19+24=253 \\ m=\frac{s}{n}=\frac{253}{20}=12\frac{13}{20}=12.65 \end{gathered}$$

$$\begin{gathered} f(1-5):0 \\ f(6-10):6 \\ f(11-15):10 \\ f(16-20):4 \\ f \end{gathered}$$

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