- 1213 students took the TOEFL test in the Spring 2001. The distribution of the 1213
scores is as seen below:

Class Upper

Limit xFrequency Relative

Frequency P(x)x*P(x) (x - m)²P(x) 270 1

_____________310 41

_____________350 138

_____________390 189

_____________430 204

_____________470 242

_____________510 188

_____________550 117

_____________590 66

_____________630 19

_____________670 8

_____________**Sum:**

________

_____________

______

________**Sqrt:**

________- Calculate the relative frequencies P(x) and record the relative frequencies in the table
above.

- Sketch a relative frequency histogram of the data, labeling your horizontal and vertical
axes as appropriate.

- What is the shape of the distribution? _____

- Calculate the mean for the TOEFL data by summing the x*P(x) values. You do NOT
need to record each x*P(x) value in the table above: use Excel to do your work. You
need only write down the value of the mean that you calculate.

mean m = _________________

- Calculate the standard deviation for the TOEFL data by calculating . You do
NOT need to record each (x - m)²P(x) value in the table above: use Excel to do your
work. You need only write down the value of the standard deviation that you
calculate.

standard deviation s =

- Determine the probability of a TOEFL score being between 311 and 350, P(311-350) =
______________

- Find the mean of the data given.___________

- Use the mean and standard deviation from above to calculate a coefficient of variation
for the data.

coeffiecient of variation = _____________

- What is the value of n for this data set? _____________

- Calculate the relative frequencies P(x) and record the relative frequencies in the table
above.

- The data and graph is of a runner running from the College campus up to Bailey Olter
High School via the back road past the powerplant in Nahnpohnmal. The x data is the
time in minutes, the y data is the distance in kilometers. Use either your
calculator or Excel to perform the calculations.

Time x (minutes) Distance y (km) 0 0 20 3.3 25 4.5 33 5.7 34.5 5.9 55 9.7 56 10.1

- Find the mean of the time (x) data.

mean of the time data = ___________

- Find the sample standard deviation for the time (x) data.

standard deviation of the time data: _________

- What is the correlation for the data?
- perfect negative correlation
- highly negative correlation
- moderately negative correlation
- no correlation
- moderately positive correlation
- highly positive correlation
- perfect positive correlation

- The slope of the least squares regression line is the average pace of the runner.
Determine and write down the slope of the least squares regression line.

slope = _____________

- The Pearson product-moment correlation coefficient represents how well the runner held a
fairly constant pace during the run. A perfect correlation would be constant pace, a
high correlation would represent a fairly constant pace. Calculate the Pearson
product-moment correlation coefficient r.

r = _____________

- Based on the correlation coefficient r, did the runner hold a fairly constant pace?

- Find the Coefficient of Determination r².

coefficient of determination = _____________

- What does the Coefficient of Determination tell us for this model?

- _______ Is the growth rate reasonably well modeled by a linear equation?

Why?

- Find the mean of the time (x) data.

- Suppose that the data in the first section of this test was normally distributed and
that the population mean m was 460 and the population standard
deviation s was 70. Remember that 1213 students took the TOEFL
test. Use the normal probability distribution to predict the number of students who
scored between 390 and 460. (This number is going to be roughly equal to number of
student entering our IEP program!)

Statistic | Equations | Excel |
---|---|---|

Mean | = = x P(x) | =AVERAGE(data) |

Sample Standard Deviation | = sx = |
=STDEV(data) |

Population Standard Deviation | = s = |
=STDEVP(data) |

Slope | =SLOPE(y data, x data) | |

Intercept | =INTERCEPT(y data, x data) | |

Correlation | =CORREL(y data, x data) |