Find the standard deviation and variance of the data set. (Since the data set is the population under consideration, use $\sigma$ in each case, rather than $s$.) The CD shipment data is in Table.

For each data set: (a) Find the mean. (b) Find the standard deviation, treating the data as a sample. (c) Find the standard deviation, treating the data as a population. (d) What does this exercise show about the two formulas?

Data Set A: 6, 7, 8

Data Set B: 4, 5, 6, 7, 8, 9, 10

Data Set C: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

(a) Calculate the median value for the 'day 2 ' data set:

(b) Which is the better measure of central tendency for this data set, mean or median?,

Which has the highest surface temperature - a red star, white star, or blue star?

Using the given intervals, make a frequency distribution of the data set. Then draw a histogram of the data set.

Use five intervals beginning with 51-60. $56,68,73,79,82,82,83,85,85,87,88,89,90,90,91,93,95,100$

Which noble gas has the same electron configuration as each of the ions in the following compounds?

a. calcium bromide, $\mathrm{CaBr}_2$

One data set has a median that is less than the mean, while a second data set has a median that is greater than the mean. What does this mean for the graph of the data sets?

The mean of 5, 7, 9 is 7. The mean of 67, 72, 77 is 72.
a. Find two more examples where the mean of an ordered set of data is the “middle” data point.
b. Suppose that a data set consists of $a_1, a_2, a_3, ..... , a_n,$ an arithmetic sequence. Explain why the mean of this data set is $\frac {a_1 + a_n} 2$ .

All resistances are doubled. What is the ac collector resistance?

Rank these compounds from most soluble to least soluble. a. CuS b. BaSO$_4$ c. SrCO$_3$ d. AgI

Match each of the following four compounds with one of the compounds $A-D$ on the basis of the following experimental facts. Compounds $A, B$, and $C$ are optically active, but compound $D$ is not. Compound $C$ gives the same products as compound $D$ on treatment with periodic acid, but compound $B$ gives a different product. Compound $A$ does not react with periodic acid. (1) $(2 S, 35)$-2,4-dimethoxy-1,3-butanediol (2) meso-1,4-dimethoxy-2,3-butanediol (3) (+)-1,4-dimethoxy-2,3-butanediol (4) $(2 R, 3 R)$-3,4-dimethoxy-1,2-butanediol

Give the empirical formula of each of the following compounds if a sample contains 0.0130 mol C, 0.0390 mol H, and 0.0065 mol O;

Consider the data set: 2, 5, 16, 2, 2, 7, 3, , 4.

a. Find the mean, median, and mode of the data set.

b. Determine which measure of center best represents the data. Explain.

Use the definition of the Laplace transform to find $\mathcal{L}\{f(t)\}$ for each of the given functions f(t). $f(t)=e^{t} \cos t$