Chapter 2 Learning Curve
A researcher studying the organism C. elegans (a type of roundworm) observes a group of 10 worms starting from birth and records the lifespan of each worm, measured in days. The data values are shown below: 12 9 24 14 16 17 21 19 16 18 The value of the first quartile of this data set is _____ days.
14
A research has a group of 10 teenagers perform a 15 minute exercise routine and then records their heart rate. The observed values (in beats per minute) are: 131 143 159 159 162 164 164 166 168 172 The data show a distribution that is skewed to the left. How many of the data values in this data set are less than the mean?
2 To find the mean of the data set, first add together all the data values, this gives 1588. There are 10 data values so divide by 10 to get the mean: 1588 ÷ 10 = 158.8. There are 2 data values less than 158.8. They are: 131 and 143. When a data set is skewed to the left, less than half of the data values will be less than the mean.
Which dataset has the smallest standard deviation?
Dataset A Because Dataset A has more data concentrated in the center nearest the mean, it has the smallest standard deviation.
side note
In a five-number summary, only the minimum and maximum have a possibility of being an outlier.
The line in the box of a boxplot marks where the __________ is.
median
When calculating the variance, or the standard deviation, the degrees of freedom are given by:
n-1
The formula for calculating degrees of freedom of the variance or the standard deviation is _________.
n-1 To calculate degrees of freedom subtract one from the sample size (n). The formula is n-1.
If the shape of the distribution is _____ skewed, then the mean is greater than the median.
right
Boxplots are best used for side-by-side comparisons of _____ or more distributions.
two
A shopper at a local supermarket spent the following amounts in her last seven trips to the store: $30.80 $27.34 $28.34 $75.58 $33.51 $27.41 $22.94 The value of the median is _________________. Give answer as $XX.XX.
$28.34
A researcher studying the organism C. elegans (a type of roundworm) observes a group of 13 worms starting from birth and records the lifespan of each worm, measured in days. The data values are shown below: 15 13 20 19 10 15 25 10 20 17 18 23 21 The value of the third quartile of this data set is _____ days.
20.5
When computing the variance using a sample of size n = 22, we divide the sum of squared deviations by ______. Give answer as a whole number.
21 Variance is computed by dividing by n - 1 = 22 - 1 = 21.
___________% of the data are less than the first quartile.
25%
A shopper at a local supermarket spent the following amounts in his last eight trips to the store: $32.92 $14.14 $30.80 $27.34 $28.34 $75.58 $36.33 $33.51 The value of the mean is _________________. Give answer as $XX.XX.
34.87
Multiple sclerosis is a rare autoimmune disease in which the insulating covers of nerve cells in the brain and spinal cord are damaged. There is currently no known cure for the disease but pharmaceutical companies have developed a drug that they believe reduces relapses. They first need to perform a clinical trial where 40 individuals received the drug and 40 individuals received a placebo. What should the 'state' step of the trial include?
The question that is going to be answered: Does the drug cause less relapses than the placebo?
Multiple sclerosis is a rare autoimmune disease in which the insulating covers of nerve cells in the brain and spinal cord are damaged. There is currently no known cure for the disease but pharmaceutical companies have developed a drug that they believe reduces relapses. They first need to perform a clinical trial where 40 individuals received the drug and 40 individuals received a placebo. The _____ step of the statistical analysis should include the mean and standard deviation of relapses experienced by both the drug and placebo groups.
solve