Question

sunspot.year is a built-in R time series dataset which gives the mean yearly numbers of sunspots from 1700 to 1988 rounded to one digit. This data is maintained up until the current date at WDC-SILSO, Royal Observatory of Belgium. We are interested in some descriptive statistics related to the sunspot.year time series. We can access this data directly and convert the time series into a vector by using the assignment x <- as.vector(sunspot.year). (In R use ?sunspot.year for info on this dataset.)
The values of sunspot.year or x if assigned as above are :


[1] 5.0 11.0 16.0 23.0 36.0 58.0 29.0 20.0 10.0 8.0 3.0 0.0 0.0 2.0 11.0 27.0
[17] 47.0 63.0 60.0 39.0 28.0 26.0 22.0 11.0 21.0 40.0 78.0 122.0 103.0 73.0 47.0 35.0
[33] 11.0 5.0 16.0 34.0 70.0 81.0 111.0 101.0 73.0 40.0 20.0 16.0 5.0 11.0 22.0 40.0
[49] 60.0 80.9 83.4 47.7 47.8 30.7 12.2 9.6 10.2 32.4 47.6 54.0 62.9 85.9 61.2 45.1
[65] 36.4 20.9 11.4 37.8 69.8 106.1 100.8 81.6 66.5 34.8 30.6 7.0 19.8 92.5 154.4 125.9
[81] 84.8 68.1 38.5 22.8 10.2 24.1 82.9 132.0 130.9 118.1 89.9 66.6 60.0 46.9 41.0 21.3
[97] 16.0 6.4 4.1 6.8 14.5 34.0 45.0 43.1 47.5 42.2 28.1 10.1 8.1 2.5 0.0 1.4
[113] 5.0 12.2 13.9 35.4 45.8 41.1 30.1 23.9 15.6 6.6 4.0 1.8 8.5 16.6 36.3 49.6
[129] 64.2 67.0 70.9 47.8 27.5 8.5 13.2 56.9 121.5 138.3 103.2 85.7 64.6 36.7 24.2 10.7
[145] 15.0 40.1 61.5 98.5 124.7 96.3 66.6 64.5 54.1 39.0 20.6 6.7 4.3 22.7 54.8 93.8
[161] 95.8 77.2 59.1 44.0 47.0 30.5 16.3 7.3 37.6 74.0 139.0 111.2 101.6 66.2 44.7 17.0
[177] 11.3 12.4 3.4 6.0 32.3 54.3 59.7 63.7 63.5 52.2 25.4 13.1 6.8 6.3 7.1 35.6
[193] 73.0 85.1 78.0 64.0 41.8 26.2 26.7 12.1 9.5 2.7 5.0 24.4 42.0 63.5 53.8 62.0
[209] 48.5 43.9 18.6 5.7 3.6 1.4 9.6 47.4 57.1 103.9 80.6 63.6 37.6 26.1 14.2 5.8
[225] 16.7 44.3 63.9 69.0 77.8 64.9 35.7 21.2 11.1 5.7 8.7 36.1 79.7 114.4 109.6 88.8
[241] 67.8 47.5 30.6 16.3 9.6 33.2 92.6 151.6 136.3 134.7 83.9 69.4 31.5 13.9 4.4 38.0
[257] 141.7 190.2 184.8 159.0 112.3 53.9 37.5 27.9 10.2 15.1 47.0 93.8 105.9 105.5 104.5 66.6
[273] 68.9 38.0 34.5 15.5 12.6 27.5 92.5 155.4 154.7 140.5 115.9 66.6 45.9 17.9 13.4 29.2
[289] 100.2

You should get these values from the R assignment rather than manually copying.
.Calculate the sample median x.
b. How many outliers does an R boxplot of x show?
c. Calculate the interquartile range of x using R.
d. Calculate the maximum of x.
e. Calculate the sample mean of x.
f. Calculate the sample variance of x.
g. Calculate the sample standard deviation of x.
h. What proportion of the x values are within 2 sample standard deviations away from the sample mean
i. Calculate the range of x. (one number)
j. How many times does the minimum value of x appear?
k. What number do you get if you add up the squares of the values in x?