Question

average daily temperature (°f)
jan feb mar apr may jun jul aug sept oct nov dec
city a 2 12 30 38 55 62 85 90 78 60 35 11
city b 30 52 58 67 72 80 85 88 82 75 55 35
click on all the true statements about the data.
a. over the course of the year, the mean temperature is the same for both cities.
b. over the course of the year, the mean temperature is greater in city a than city b.
c. over the course of the year, the mean temperature is greater in city b than city a.
d. over the course of the year, the range of temperatures is greater in city a than city b.
e. over the course of the year, the range of temperatures is greater in city b than city a.

Explanation:

Step1: Calculate the mean for City A

Sum of temperatures for City A: \(2 + 12 + 30 + 38 + 55 + 62 + 85 + 90 + 78 + 60 + 35 + 11\)
\(= (2 + 12) + (30 + 38) + (55 + 62) + (85 + 90) + (78 + 60) + (35 + 11)\)
\(= 14 + 68 + 117 + 175 + 138 + 46\)
\(= 14 + 68 = 82\); \(82 + 117 = 199\); \(199 + 175 = 374\); \(374 + 138 = 512\); \(512 + 46 = 558\)
Mean for City A: \(\frac{558}{12} = 46.5\)

Step2: Calculate the mean for City B

Sum of temperatures for City B: \(30 + 52 + 58 + 67 + 72 + 80 + 85 + 88 + 82 + 75 + 55 + 35\)
\(= (30 + 52) + (58 + 67) + (72 + 80) + (85 + 88) + (82 + 75) + (55 + 35)\)
\(= 82 + 125 + 152 + 173 + 157 + 90\)
\(= 82 + 125 = 207\); \(207 + 152 = 359\); \(359 + 173 = 532\); \(532 + 157 = 689\); \(689 + 90 = 779\) Wait, correction: \(30+52=82\), \(58+67=125\), \(72+80=152\), \(85+88=173\), \(82+75=157\), \(55+35=90\). Then \(82+125=207\), \(207+152=359\), \(359+173=532\), \(532+157=689\), \(689+90=779\)? Wait no, 12 months, let's recalculate: \(30+52=82\), \(58+67=125\) (total 207), \(72+80=152\) (359), \(85+88=173\) (532), \(82+75=157\) (689), \(55+35=90\) (779). Wait, but 30+52+58+67+72+80+85+88+82+75+55+35. Let's add step by step: 30+52=82; 82+58=140; 140+67=207; 207+72=279; 279+80=359; 359+85=444; 444+88=532; 532+82=614; 614+75=689; 689+55=744; 744+35=779. Yes. Mean for City B: \(\frac{779}{12} \approx 64.92\)

So mean of City B is greater than City A. So C is true, A and B false.

Step3: Calculate range for City A

Range = Max - Min. For City A: Max = 90, Min = 2. Range = \(90 - 2 = 88\)

Step4: Calculate range for City B

For City B: Max = 88, Min = 30. Range = \(88 - 30 = 58\)

So range of City A (88) > range of City B (58). So D is true, E false.

Answer:

C. Over the course of the year, the mean temperature is greater in City B than City A.
D. Over the course of the year, the range of temperatures is greater in City A than City B.