Question

temperature (f) | frequency | midpoint | class boundaries
35-39 | 1 | type your answer... | type your answer...
type your answer...
40-44 | 3 | type your answer... | type your answer...
type your answer...
45-49 | 5 | type your answer... | type your answer...
type your answer...
50-54 | 11 | type your answer... | type your answer...
type your answer...
55-59 | 7 | type your answer... | type your answer...
type your answer...
60-64 | 7 | type your answer... | type your answer...
type your answer...
65-69 | 1 | type your answer... | type your answer...
-69.5

Explanation:

Step1: Calculate midpoint for 35 - 39

The midpoint of a class interval \(a - b\) is calculated as \(\frac{a + b}{2}\). For the class 35 - 39, \(a = 35\) and \(b = 39\). So, \(\frac{35 + 39}{2}=\frac{74}{2} = 37\).

Step2: Calculate class boundaries for 35 - 39

To find the lower class boundary, we subtract 0.5 from the lower limit of the class. For 35 - 39, lower class boundary is \(35 - 0.5 = 34.5\). The upper class boundary is found by adding 0.5 to the upper limit of the class, so \(39 + 0.5 = 39.5\).

Step3: Calculate midpoint for 40 - 44

Using the midpoint formula \(\frac{a + b}{2}\) where \(a = 40\) and \(b = 44\), we get \(\frac{40 + 44}{2}=\frac{84}{2}=42\).

Step4: Calculate class boundaries for 40 - 44

Lower class boundary: \(40 - 0.5 = 39.5\) (note that this is the upper boundary of the previous class, which is consistent). Upper class boundary: \(44 + 0.5 = 44.5\).

Step5: Calculate midpoint for 45 - 49

Using the formula \(\frac{45 + 49}{2}=\frac{94}{2}=47\).

Step6: Calculate class boundaries for 45 - 49

Lower class boundary: \(45 - 0.5 = 44.5\). Upper class boundary: \(49 + 0.5 = 49.5\).

Step7: Calculate midpoint for 50 - 54

\(\frac{50 + 54}{2}=\frac{104}{2}=52\).

Step8: Calculate class boundaries for 50 - 54

Lower class boundary: \(50 - 0.5 = 49.5\). Upper class boundary: \(54 + 0.5 = 54.5\).

Step9: Calculate midpoint for 55 - 59

\(\frac{55 + 59}{2}=\frac{114}{2}=57\).

Step10: Calculate class boundaries for 55 - 59

Lower class boundary: \(55 - 0.5 = 54.5\). Upper class boundary: \(59 + 0.5 = 59.5\).

Step11: Calculate midpoint for 60 - 64

\(\frac{60 + 64}{2}=\frac{124}{2}=62\).

Step12: Calculate class boundaries for 60 - 64

Lower class boundary: \(60 - 0.5 = 59.5\). Upper class boundary: \(64 + 0.5 = 64.5\).

Step13: Calculate midpoint for 65 - 69

\(\frac{65 + 69}{2}=\frac{134}{2}=67\).

Step14: Calculate class boundaries for 65 - 69

Lower class boundary: \(65 - 0.5 = 64.5\). Upper class boundary: \(69 + 0.5 = 69.5\) (matches the given upper boundary for the last class).

Answer:

Temperature (F)	Frequency	Midpoint	Class Boundaries
40 - 44	3	42	39.5 - 44.5
45 - 49	5	47	44.5 - 49.5
50 - 54	11	52	49.5 - 54.5
55 - 59	7	57	54.5 - 59.5
60 - 64	7	62	59.5 - 64.5
65 - 69	1	67	64.5 - 69.5