Question

The data are daily high temperatures in Atlanta for one month.

61, 61, 63, 64, 65, 66, 66, 66, 67, 68, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 94

Question 1 options:

What is the range of temperatures? What is the median average daily temperature in Atlanta for one month? What is the interquartile range (IQR) of the data set? What is the sample variance of temperatures? What is the sample standard deviation of the daily temperature in Atlanta for one month? How many days are in the sample? What is the lowest daily temperature in Atlanta for one month? Does the data set contain any outliers? What is the mean daily temperature in Atlanta for one month? What daily temperature in Atlanta for one month are considered outliers? What is the first quartile of the data set above? What is the highest daily temperature in Atlanta for one month? What is the third quartile of the data set above?

1. 5.9 2. 6.8 3. 7.1 4. 10 5. 15 6. 27 7. 30 8. 33 9. 42.2 10. 46.5 11. 47.1 12. 52 13. 59 14. 61 15. 65 16. 66 17. 70 18. 70.8 19. 71.5 20. 71.8 21. 72.5 22. 74 23. 75 24. 76 25. 80 26. 94 27. 97 28. Maybe 29. No 30. Yes

Question 2:

The height in feet of 25 trees is shown below (lowest to highest).

21, 27, 30, 31, 31, 31, 33, 34, 34, 37, 38, 38, 38, 40, 41, 42, 43, 45, 46, 51, 51, 52, 52, 59, 59

Question 2 options:

What is the interquartile range (IQR) of the data set? What is the first quartile of the data set above? What is the sample variance of height, in feet, of the trees? What is the tallest height, in feet, of the trees? Does the data set contain any outliers? How many trees are in the sample? What is the shortest height, in feet, of the trees? What is the sample standard deviation of the height, in feet, of the trees? What is the third quartile of the data set above? 123456789101112131415161718192021222324252627282930 What is the range of height, in feet, of the trees? What is the median average height, in feet, of the trees? What is the mean height, in feet, of the trees?

1. 8.1 2. 9.9 3. 10.2 4. 14 or 16.5 from the website or the calculator. 5. 21 6. 22 7. 25 8. 28 9. 31 from website or 32 from calculator 10. 34 11. 38 12. 39.9 13. 40.2 14. 40.9 15. 41 16. 45 from website or 48.5 from calculator 17. 46 18. 47 19. 50 20. 53 21. 59 22. 61 23. 66 24. 77 25. 80 26. 91 27. 98 28. Maybe 29. No 30. Yes

Answer 1

We are given data:

61, 61, 63, 64, 65, 66, 66, 66, 67, 68, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 94

1.) Range of the data= Highest value - lowest value.

Thus, range = 94 - 61 = 33.

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2.) Median is the middle value of the data set:

Here, a total of 30 observations, so there are two middle terms which are 15th and 16th.

61, 61, 63, 64, 65, 66, 66, 66, 67, 68, 70, 70, 70, 71, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 94

So, median =

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3.) Interquartile range =

where Q3 is the middle value of the upper half of the data.

Q1 is the middle value of the lower half of the data.

61, 61, 63, 64, 65, 66, 66, 66, 67, 68, 70, 70, 70, 71, 74, 74, 74, 75, 75, 75, , 76, 77, 78, 78, 79, 79, 94

So, Q3 = 76

61, 61, 63, 64, 65, 66, 66, 67, 68, 70, 70, 70, 71, 74, 74, 74, 75, 75, 75, , 76, 77, 78, 78, 79, 79, 94

So, Q1 = 66.

Thus, IQR = 76 - 66 = 10

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4.) Sample variance =

Mean is the sum of all observations divided by the number of observations.

So,

Now, we can use the formula by squaring each of subtracting each observation with mean value and dividing it with (n-1) which is 29.

we get:

Observation	Observation-mean
61	-10.8333	117.36038889
61	-10.8333	117.36038889
63	-8.8333	78.02718889
64	-7.8333	61.36058889
65	-6.8333	46.69398889
66	-5.8333	34.02738889
66	-5.8333	34.02738889
66	-5.8333	34.02738889
67	-4.8333	23.36078889
68	-3.8333	14.69418889
70	-1.8333	3.36098889
70	-1.8333	3.36098889
70	-1.8333	3.36098889
71	-0.83329999999999	0.69438888999999
71	-0.83329999999999	0.69438888999999
72	0.16670000000001	0.027788890000002
74	2.1667	4.69458889
74	2.1667	4.69458889
74	2.1667	4.69458889
75	3.1667	10.02798889
75	3.1667	10.02798889
75	3.1667	10.02798889
76	4.1667	17.36138889
76	4.1667	17.36138889
77	5.1667	26.69478889
78	6.1667	38.02818889
78	6.1667	38.02818889
79	7.1667	51.36158889
79	7.1667	51.36158889
94	22.1667	491.36258889

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5.) We know that standard deviation is the square root of the variance:

so,

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6.) There is a total of 30 days of observation because each observation shows each day's temperature.

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7.) The lowest temperature is 61.

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8.) For detecting outliers we use.

For upper outlier: Q3 + 1.5*IQR

For lower outlier: Q1 - 1.5 * IQR

so, Upper outlier = 76 + 1.5*10 = 76 + 15 = 91

Lower outlier = 66 - 1.5*10 = 66 -15 = 51

Thus, any observation lying outside of these two limits considered as outlier.

Hence, YES there are only upper outlier = 94.

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9.) The mean of the data:

we have already calculated which is 71.83.

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10.) The outlier is 94 on 30th day of the month.

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11.) The first quartile we have already calculated:

Q1 = 66

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12.) The highest temperature is 94.

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13.) The third quartile is already calculated:

Q3 = 76.

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