Question

the temperature in springfield on this date in the last ten years were: 68, 68, 69, 70, 72, 70, 68, 75, 55, 67. what is the average temperature on this date over the last ten years? (round to nearest whole number) 1 69 2 68 3 60 4 61

Explanation:

Step1: Sum all temperatures

We add up all the given temperatures: \(68 + 68 + 69 + 70 + 72 + 70 + 68 + 75 + 55 + 67\). Let's calculate that:
\(68+68 = 136\); \(136+69 = 205\); \(205+70 = 275\); \(275+72 = 347\); \(347+70 = 417\); \(417+68 = 485\); \(485+75 = 560\); \(560+55 = 615\); \(615+67 = 682\).

Step2: Calculate the average

The average is the sum divided by the number of data points (which is 10 here). So, the average is \(\frac{682}{10}=68.2\).

Step3: Round to nearest whole number

Rounding \(68.2\) to the nearest whole number gives \(68\). Wait, no, wait, let's re - check the sum. Wait, maybe I made a mistake in addition. Let's recalculate the sum:

\(68+68 = 136\); \(136+69 = 205\); \(205+70 = 275\); \(275+72 = 347\); \(347+70 = 417\); \(417+68 = 485\); \(485+75 = 560\); \(560+55 = 615\); \(615+67 = 682\). Wait, \(682\div10 = 68.2\), but wait, maybe I misread the numbers. Wait the numbers are: 68, 68, 69, 70, 72, 70, 68, 75, 55, 67. Wait, let's count the number of 68s: three 68s (\(68\times3 = 204\)), one 69, two 70s (\(70\times2 = 140\)), one 72, one 75, one 55, one 67. Let's calculate again: \(204+69 = 273\); \(273+140 = 413\); \(413+72 = 485\); \(485+75 = 560\); \(560+55 = 615\); \(615+67 = 682\). So the sum is 682. Average is \(682\div10 = 68.2\), which rounds to 68? But wait, the first option is 69. Wait, maybe I made a mistake. Wait, let's check the numbers again. Wait, 55 is a low number. Wait, 68, 68, 69, 70, 72, 70, 68, 75, 55, 67. Let's add them in a different way:

Group the numbers:

\((68 + 68+68)+(69)+(70 + 70)+(72)+(75)+(55)+(67)\)

\(68\times3=204\); \(70\times2 = 140\); then \(204+69 = 273\); \(273+140 = 413\); \(413+72 = 485\); \(485+75 = 560\); \(560+55 = 615\); \(615+67 = 682\). So the sum is 682. Average is \(682\div10 = 68.2\), which rounds to 68. But wait, the first option is 69. Wait, maybe I misread the numbers. Wait, is the number 55 or 65? If it was 65, the sum would be different. Wait, the original problem says 55. Wait, maybe there's a mistake in my calculation. Wait, let's use another approach. Let's find the deviation from 68.

The numbers: 68 (deviation 0), 68 (0), 69 (1), 70 (2), 72 (4), 70 (2), 68 (0), 75 (7), 55 (-13), 67 (-1). Now sum the deviations: \(0 + 0+1 + 2+4 + 2+0 + 7-13 - 1\). Calculate: \(1+2 = 3\); \(3+4 = 7\); \(7+2 = 9\); \(9+0 = 9\); \(9+7 = 16\); \(16-13 = 3\); \(3 - 1=2\). Then the average deviation is \(2\div10 = 0.2\). So the average is \(68+0.2 = 68.2\), which rounds to 68. But the first option is 69. Wait, maybe I made a mistake in the numbers. Wait, let's check the original problem again. The temperatures are: 68, 68, 69, 70, 72, 70, 68, 75, 55, 67. Wait, 10 numbers. Let's add them using a calculator - like approach:

68+68 = 136; 136+69 = 205; 205+70 = 275; 275+72 = 347; 347+70 = 417; 417+68 = 485; 485+75 = 560; 560+55 = 615; 615+67 = 682. Yes, sum is 682. Average is 68.2, rounds to 68. So the correct answer should be 68, which is option 2.

Answer:

1. 68