The number of new orange centerline reflectors from the Sokeh's Island junction to the college in Palikir was counted by a three person team. The numbers are the number of markers for each half kilometer.
Number of centerline reflectors per half kilometer |
---|
84 |
74 |
78 |
61 |
67 |
55 |
54 |
62 |
61 |
83 |
81 |
75 |
70 |
65 |
70 |
76 |
Bins | Frequency | Relative Frequency f/n |
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_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
Sums: | _________ | _________ |
The data below is a running cumulative count of the number of centerline reflectors. The first column of the table is the distance from the junction with Sokeh's Island. The second column is the cumulative count of the reflectors. Use this data to form an x-y scatter graph with kilometers on the x-axis and the cumulative count of the centerline reflectors on the y-axis.
Kilometers | Cumulative count of reflectors |
---|---|
0 | 0 |
1 | 158 |
2 | 297 |
3 | 419 |
4 | 534 |
5 | 678 |
6 | 834 |
7 | 969 |
8 | 1049 |
8.7 | 1115 |
Basic Statistics | |||
---|---|---|---|
Statistic or Parameter | Symbol | Equations | Excel |
Square root | =SQRT(number) | ||
Sample size | n | =COUNT(data) | |
Sample mean | x | Sx/n | =AVERAGE(data) |
Sample standard deviation | sx or s | =STDEV(data) | |
Sample Coefficient of Variation | CV | 100(sx/x) | =100*STDEV(data)/AVERAGE(data) |
Linear Regression Statistics | |||
---|---|---|---|
Statistic or Parameter | Symbol | Equations | Excel |
Slope | b | =SLOPE(y data, x data) | |
Intercept | a | =INTERCEPT(y data, x data) | |
Correlation | r | =CORREL(y data, x data) | |
Coefficient of Determination | r^{2} | =(CORREL(y data, x data))^2 |
Statistic or Parameter | Symbol | Equations | Excel |
---|---|---|---|
Normal Statistics | |||
Calculate a z value from an x | z | ^{= } | =STANDARDIZE(x, µ, s) |
Calculate an x value from a z | x | = s z + µ | =s*z+µ |
Calculate a t-statistic (t-stat) | t | =(x - µ)/(sx/SQRT(n)) | |
Calculate an x from a z | =µ + z_{c}*sx/sqrt(n) | ||
Find a probability p from a z value | =NORMSDIST(z) | ||
Find a z value from a probability p | =NORMSINV(p) | ||
Confidence interval statistics | |||
Degrees of freedom | df | = n-1 | =COUNT(data)-1 |
Find a z_{c} value from a confidence level c | z_{c} | =ABS(NORMSINV((1-c)/2)) | |
Find a t_{c} value from a confidence level c | t_{c} | =TINV(1-c,df) | |
Calculate an error tolerance E of a mean for n >= 30 using sx | E | =z_{c}*sx/SQRT(n) | |
Calculate an error tolerance E of a mean for n < 30 using sx. Can also be used for n >= 30. | E | =t_{c}*sx/SQRT(n) | |
Calculate a confidence interval for a population mean µ from a sample mean x and an error tolerance E | x-E<= µ <=x+E | ||
Hypothesis Testing | |||
Calculate t-critical for a two-tailed test | t_{c} | =TINV(a,df) | |
Calculate a p-value from a t-statistic | p | = TDIST(ABS(tstat),df,#tails) |