Question

jillian collected data about the average daily temperatures for two cities. she organized her data in the given table. 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 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 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: \(30+52=82\), \(82+58=140\), \(140+67=207\), \(207+72=279\), \(279+80=359\), \(359+85=444\), \(444+88=532\), \(532+82=614\), \(614+75=689\), \(689+55=744\), \(744+35=779\). Mean for City B: \(\frac{779}{12} \approx 64.92\) (Wait, no, recalculate sum: 30+52=82, +58=140, +67=207, +72=279, +80=359, +85=444, +88=532, +82=614, +75=689, +55=744, +35=779. Yes. So mean A: 558/12=46.5, mean B: 779/12≈64.92. So mean B > mean A.

Step3: Calculate range for City A

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

Step4: Calculate range for City B

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

So:

• A: False (means different)
• B: False (B's mean is higher)
• C: True (B's mean > A's)
• D: True (A's range 88 > B's 58)
• E: False (B's range 58 < A's 88)

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.