one aspect of the beauty of scenic landscape is its variability. The elevations (feet above sea level) of 12 randomly selected towns in the Finger Lakes Regions of Upstate New York are recorded here. 1117, 1360, 1009, 766, 1333, 1306, 577, 1144, 874, 658, 1306, 712.
Find the mean? answer correct to the nearest whole number.
Find the standard deviation? (Give your answer correct to the nearest whole number).
can't you do all this on your calculator? Check your instruction book, statistics.
To find the mean of a set of numbers, you need to add up all the numbers and then divide the sum by the total number of values.
1. Add up all the elevations: 1117 + 1360 + 1009 + 766 + 1333 + 1306 + 577 + 1144 + 874 + 658 + 1306 + 712 = 12,456.
2. Divide the sum by the total number of values (which is 12 in this case): 12,456 / 12 = 1,038.
Therefore, the mean elevation of the randomly selected towns is approximately 1,038 feet above sea level (rounded to the nearest whole number).
Now, let's calculate the standard deviation using the following steps:
1. Calculate the mean: We already found the mean in the previous step: 1,038.
2. Subtract the mean from each elevation value and square the result. This gives you the squared deviation for each value.
1117 - 1038 = 79; (79)^2 = 6241
1360 - 1038 = 322; (322)^2 = 103684
1009 - 1038 = -29; (-29)^2 = 841
766 - 1038 = -272; (-272)^2 = 73984
1333 - 1038 = 295; (295)^2 = 87025
1306 - 1038 = 268; (268)^2 = 71824
577 - 1038 = -461; (-461)^2 = 212521
1144 - 1038 = 106; (106)^2 = 11236
874 - 1038 = -164; (-164)^2 = 26896
658 - 1038 = -380; (-380)^2 = 144400
1306 - 1038 = 268; (268)^2 = 71824
712 - 1038 = -326; (-326)^2 = 106276
3. Find the sum of the squared deviations: 6241 + 103684 + 841 + 73984 + 87025 + 71824 + 212521 + 11236 + 26896 + 144400 + 71824 + 106276 = 894832.
4. Divide the sum by the total number of values (12 in this case).
894832 / 12 = 74736. The result is approximately 74,736.
5. Calculate the square root of the result to find the standard deviation.
√74736 ≈ 273. The standard deviation is approximately 273 (rounded to the nearest whole number).