The number of footsteps for ten Mondays as recorded by a clip on pedometer are shown in the table.
Monday Footsteps |
---|
9972 |
7777 |
8412 |
9307 |
6974 |
9647 |
8881 |
6866 |
6575 |
10175 |
For the number of footsteps on the ten Mondays above:
Bins | Frequency | Relative Frequency f/n |
---|---|---|
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
_________ | _________ | _________ |
Sums: | _________ | _________ |
A golf ball was dropped from increasing heights and the bounce height for the first bounce was recorded. For example, when dropped from a height of 132 centimeters, the golf ball bounced back up 107 centimeters on the first bounce. The following table includes all of the data measurements.
Drop height/cm | Bounce height/cm |
---|---|
0 | 0 |
41 | 33 |
71 | 56 |
132 | 107 |
163 | 124 |
193 | 147 |
254 | 191 |
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) |