In physical science laboratory six
the students measured the distance d in cm a cup filled with marbles of mass m would stretch an elastic band. The Hooke's constant H for each mass and distance measurement is reported below.
H (g/cm)
10.50
10.54
10.60
10.60
10.65
10.77
10.80
10.80
10.84
10.90
__________ What level of measurement is the data?
__________ Find the sample size n for the data.
__________ Find the minimum.
__________ Find the maximum.
__________ Find the range.
__________ Find the midrange.
__________ Find the mode.
__________ Find the median.
__________ Find the sample mean x.
0.14 Freebie: This is the standard deviation sx.
If you obtain a different value, then you typed in the wrong data!
Calculate the standard deviation sx and check for agreement. (To four decimals: 0.1385)
__________ Find the sample coefficient of variation CV.
__________ If this data were to be divided into five classes, what would be the width of a single class?
Determine the frequency and calculate the relative frequency using five classes.
Record your results in the table provided.
Frequency table
H CUL (cm)
Frequency (f)
Relative Frequency
Sum:
Sketch a frequency histogram chart of the data anywhere it fits, labeling your horizontal axis and vertical axis as appropriate.
____________________ What is the shape of the distribution?
p(10.66 < H ≤ 10.74 ) = ____________________ What is the probability H will be greater than 10.66 and less than or equal to 10.74?
____________________ Use the sample mean x and standard deviation sx calculated above to determine the z-score for an H of 11 g/cm.
____________________ Is the z-score for 11 g/cm an ordinary or unusual z-score?
Part II: Linear regression
In physical science laboratory six
the students measured the distance d in cm a cup filled with marbles of mass m would stretch an elastic band. below.
Elastic band stretch data
stretch distance (cm)
mass (g)
3.9
16
4.3
22
4.5
27
4.6
32
4.8
37
__________ Calculate the slope of the linear regression for the data.
__________ Calculate the y-intercept of the linear regression for the data.
__________ Use the slope and intercept to predict the mass m
when the stretch distance d is 7 cm
__________ Use the slope and intercept to predict the stretch distance d
produced by a 50g mass.
__________ Does the relationship appear to be linear, non-linear, or random?
__________ Is the correlation positive, negative, or neutral?
__________ Determine the correlation coefficient r.
__________ What is the strength of the correlation: strong, moderate, weak, or none?
__________ Determine the coefficient of determination r².
__________ What percent of the variation in the stretch distance d
explains the variation in the data for the mass m?
__________ What level of measurement is the data?