reading a frequency distribution in exercises 15 and 16, use the frequency distribution to find the (a)…

reading a frequency distribution in exercises 15 and 16, use the frequency distribution to find the (a) class width, (b) class midpoints, and (c) class boundaries. 15. travel time to work (in minutes) class frequency, f 0 - 10 188 11 - 21 372 22 - 32 264 33 - 43 205 44 - 54 83 55 - 65 76 66 - 76 32 16. toledo, oh, average normal temperatures (°f) class frequency, f 25 - 32 86 33 - 40 39 41 - 48 41 49 - 56 48 57 - 64 43 65 - 72 68 73 - 80 40 17. use the frequency distribution in exercise 15 to construct an expanded frequency distribution, as shown in example 2. 18. use the frequency distribution in exercise 16 to construct an expanded frequency distribution, as shown in example 2.

reading a frequency distribution in exercises 15 and 16, use the frequency distribution to find the (a) class width, (b) class midpoints, and (c) class boundaries. 15. travel time to work (in minutes) class frequency, f 0 - 10 188 11 - 21 372 22 - 32 264 33 - 43 205 44 - 54 83 55 - 65 76 66 - 76 32 16. toledo, oh, average normal temperatures (°f) class frequency, f 25 - 32 86 33 - 40 39 41 - 48 41 49 - 56 48 57 - 64 43 65 - 72 68 73 - 80 40 17. use the frequency distribution in exercise 15 to construct an expanded frequency distribution, as shown in example 2. 18. use the frequency distribution in exercise 16 to construct an expanded frequency distribution, as shown in example 2.

Answer

Explanation:

Step1: Find class width for Exercise 15

Subtract lower - limit of first class from lower - limit of second class. For the first two classes 0 - 10 and 11 - 21 in Exercise 15, class width $=11 - 0=11$.

Step2: Find class midpoints for Exercise 15

For a class $a - b$, midpoint $=\frac{a + b}{2}$. For class 0 - 10, midpoint $=\frac{0+10}{2}=5$; for 11 - 21, midpoint $=\frac{11 + 21}{2}=16$; for 22 - 32, midpoint $=\frac{22+32}{2}=27$; for 33 - 43, midpoint $=\frac{33 + 43}{2}=38$; for 44 - 54, midpoint $=\frac{44+54}{2}=49$; for 55 - 65, midpoint $=\frac{55 + 65}{2}=60$; for 66 - 76, midpoint $=\frac{66+76}{2}=71$.

Step3: Find class boundaries for Exercise 15

For the lower - class boundary of the first class, subtract 0.5 from the lower - limit of the first class, so it is $0-0.5=-0.5$. The upper - class boundary of the first class is the lower - limit of the second class minus 0.5, which is $11 - 0.5 = 10.5$. For the second class, lower - class boundary is $11-0.5 = 10.5$ and upper - class boundary is $22-0.5=21.5$. Continuing this way for all classes.

Step4: Find class width for Exercise 16

Subtract lower - limit of first class from lower - limit of second class. For the first two classes 25 - 32 and 33 - 40 in Exercise 16, class width $=33 - 25 = 8$.

Step5: Find class midpoints for Exercise 16

For class 25 - 32, midpoint $=\frac{25+32}{2}=28.5$; for 33 - 40, midpoint $=\frac{33 + 40}{2}=36.5$; for 41 - 48, midpoint $=\frac{41+48}{2}=44.5$; for 49 - 56, midpoint $=\frac{49+56}{2}=52.5$; for 57 - 64, midpoint $=\frac{57+64}{2}=60.5$; for 65 - 72, midpoint $=\frac{65+72}{2}=68.5$; for 73 - 80, midpoint $=\frac{73+80}{2}=76.5$.

Step6: Find class boundaries for Exercise 16

For the lower - class boundary of the first class, subtract 0.5 from the lower - limit of the first class, so it is $25-0.5 = 24.5$. The upper - class boundary of the first class is the lower - limit of the second class minus 0.5, which is $33-0.5=32.5$. For the second class, lower - class boundary is $33 - 0.5=32.5$ and upper - class boundary is $41-0.5 = 40.5$. Continuing this way for all classes.

Answer:

Exercise 15

(a) Class width: 11 (b) Class midpoints: 5, 16, 27, 38, 49, 60, 71 (c) Class boundaries: - 0.5, 10.5, 21.5, 32.5, 43.5, 54.5, 65.5, 76.5

Exercise 16

(a) Class width: 8 (b) Class midpoints: 28.5, 36.5, 44.5, 52.5, 60.5, 68.5, 76.5 (c) Class boundaries: 24.5, 32.5, 40.5, 48.5, 56.5, 64.5, 72.5, 80.5