Statistics and Data Analysis: Key Concepts for Students

Which one of the following activities is not an example of data gathering?

Reaching a conclusion about the results of a reading program

Which of these are categorical data?

The different types of anteaters

Which of the variables you collect are continuous data?

Only average annual income

What are the categorical variables in your survey?

Grade of youngest child, dad's occupation, whether mom works, and kind of pets

True or False: In the survey of your neighbors described above, the only discrete quantitative data you're collecting about your neighbors is family size.

True

Which of the following would most likely be graphed as a bar chart rather than a histogram?

All of the above

Consider a complete table of relative frequencies. The sum of the relative frequency column in such a table must be:

1

Histograms are most useful in displaying:

Large numeric data sets

The relative frequency of students who study 5 - 6 hours a day is:

0.223

The cumulative relative frequency of students who study 4 hours or fewer a day is:

0.615

Estimate the relative frequency of countries with 20 - 22 days of no rainfall in the month of January.

0.32

Which league has the team that had hit the most home runs by midseason, and how many home runs had that team hit?

American, 149

True or False: The number of home runs made by most National League teams were in the 90s; the number of home runs made by most teams overall were in the 80s.

True

How many fewer home runs did the team with the fewest home runs in the American League have than the team with the fewest home runs in the National League?

14

How many more home runs did the team with the highest home runs in the American League have than the highest team in the National League?

33

A symmetric distribution can't have which of the following characteristics?

A long tail on one side

True or False: If the population of interest is all day care centers in the United States, a sample of day care centers could be either all day care centers in New York City or a randomly selected group of day care centers throughout the US. Either sample is equally good.

False

The kind of sampling strategy least likely to produce statistics that are good estimates of population parameters is a:

haphazard sample

Consider these eight observations: {11,6,2,5,8,4,4,9}. What is the mean?

6.125

Consider these eight observations: {11,6,2,5,8,4,4,9}. What is the median?

5.5

Since the distribution of housing prices in a community is usually skewed right, which measure of center should you use for housing prices?

Median

Six radio listeners are surveyed. Their favorite FM stations are: 89.1, 89.1, 89.1, 94.7, 94.7 and 104.3. Based on these data, you want to name the favorite station of a typical listener. You should name:

The mode, which is 89.1

Calculate, to the nearest whole number, the sample standard deviation of this data set: {71, 75, 65, 73, 69, 77, 67}.

4

All the following statements about the sample standard deviation are true, except:

the standard deviation is negative when there are extreme values in the sample.

The box plot below represents a distribution that is:

right skewed

The median points per player per game for each team are:

Boston = 10.0; Chicago = 9.0; Seattle = 8.9.

Create a modified box-and-whisker plot for each of the three data sets. Which team has the greatest variation in the points per game for the middle 50% of their observations?

Boston

The following hypothetical data set shows the purchase price (in thousands) for a sample of 3-bedroom, 2-bathroom homes in Essex County, MA over the past year. How many outliers are present in this distribution?

3

What is the median for the data in the table?

306.5

What is the upper quartile for the data in the table?

319.5

What is the lower quartile for the data in the table?

294

What is the interquartile range for the data in the table?

25.5

Based on the data in the table, what is the largest number of births in a month you could possibly have and still have a lower outlier?

255

Why is the IQR considered to be a resistant statistic?

Adding a new extreme observation has little effect on it.

Which measure of central tendency and measure of variation should be used with a normally distributed distribution?

The mean and standard deviation

Which of the following can stemplots show?

I, II, III, and IV

Which of the following can outliers affect significantly?

I, III, and IV

Give, in millimeters, a minimum and maximum thickness that includes 68% of the population of bolts.

19.99 to 20.01 millimeters

Give, in millimeters, a minimum and a maximum thickness that will include 95% of the population of bolts.

19.98 to 20.02 millimeters

Assume that normal curve A and normal curve B have identical population means. Which curve is taller, and why?

Curve B is taller because smaller standard deviations produce thinner curves.

Using the empirical rule, you can assume that what percent of the normal distribution is outside two standard deviations of the mean in both directions?

5%

For population W, find the z-score associated with a weight of 120 pounds.

z = -1.6

For population W, what is the percentile for the weight 160 pounds?

50th percentile

In population W, what is the probability that a randomly selected subject will weigh between 140 and 180 pounds?

0.576

In population H, what is the height, to the nearest tenth of an inch, of the 70th percentile?

67.3 inches

In population H, what is the z-score, to the nearest tenth, associated with the height 65 inches?

z = -0.4

To the nearest whole number, what percentile is associated with z = -0.68?

25th percentile

To the nearest whole number, what percentile is associated with z = 1.2?

88th percentile

What area, to the nearest whole percent, of the normal curve is located between z = -0.6 and z = 1.4?

64%

What percentage of applicants scored between 500 and 700?

60%

What percentage of applicants scored above 450 on the GRE?

82%

What percentage of applicants had a GRE score below 625?

78%

What is the GRE score at the 77th percentile?

620

Find the GRE score at the upper quartile, Q3.

613

Find the z-score for the lower quartile of any normal curve.

-0.67

Consider a normal distribution with μ = 65 and σ = 4. A sample of size 950 is drawn from this population. Approximately how many of the 950 cases would you expect to find between 57 and 73?

903

A normal probability plot:

graphs raw scores against z-scores of percentile ranks

What does a normal probability plot of 30 data points indicate?

It provides evidence that the original data is normally distributed.

Which statement about the normal distribution is false?

The normal curve crosses the x-axis at z-scores above 3.0 and below -3.0.

What is the proper notation for a normal distribution with a mean of 250 and standard deviation of 25?

N(250, 25)

What is true about the areas under the normal curve?

Fewer than one percent of the cases are located three standard deviations above or below the mean.

In a normal distribution with a mean of 30 and a standard deviation of 5, where is the largest proportion of cases found?

Between x = 25 and x = 35.

What can be inferred if the area above a given value of x is 0.35 in a normal distribution?

None of the above.

What does a normal curve table indicate for z = -1?

The probability lying below z = -1 is 0.1587.

In which population is the area under the normal curve greatest?

Area above 65 in Population A.

How many crimes a month are predicted with 7 streetlights on a block?

1.0

How do you calculate the residual for a block with 10 streetlights and 1 crime a month?

0.6

What does the slope of the regression equation indicate?

For every additional streetlight per block, the crimes per month decrease by 0.2.

True or False: On the least-squares regression line, the point (x, y) always has a residual of 0.

True

What is the least-squares regression line?

y = 1.2 + 0.3x

How do you calculate the correlation coefficient?

0.

True or False: All positive correlations indicate stronger relationships than all negative correlations.

False

What determines the sign of r?

Whether the value of y increases or decreases as the value of x increases.

If all sample data points are on the same line with a positive slope, what would r be?

r would be +1.0.

What does an r^2 of 0.85 in a bivariate scatterplot mean?

85% of the variation in y is explained by the changes in x.

What is the proper interpretation of the coefficient of determination for data set A: (2,8), (3,6), (4,9), (5,9)?

Thirty percent of the variation in the y-values can be explained by variation of the x-values.

What is a residual?

It is how much an observed y-value differs from a predicted y-value.

What is an outlier?

It usually has a strong effect on the correlation coefficient and regression line and can also be an influential point.

True or False: An r of -1.0 proves a strong cause and effect relationship between x and y.

False

What should be done with influential points and outliers?

They should be examined carefully to determine if they're part of the data set.

What does a linear regression line indicate in terms of CuSO₄ dissolution?

For each one-degree rise in temperature, you can dissolve 0.51 more grams of CuSO₄.

What is the explanatory variable in a scatterplot?

The variable along the horizontal axis.

Which indicates the strongest relationship between two variables?

r^2 = 0.23.

What is the goal of the least-squares regression?

To compute a line that minimizes the sum of the squared residuals.

What is the predicted test score for an individual who studies 8 hours a day?

95

What is it called when predicting a test score for a student who studied 8 hours, exceeding the maximum sample hours?

Extrapolation.

What is the marginal distribution for crime rate?

51, 56, 43.

What is the conditional distribution of temperature by above average crime rate?

0.12, 0.56, 0.33.

Which table shows the aggregation of the data?

Remissions | Death | Rate: A 9 | 7 | 0.563, B 11 | 8 | 0.579.

What is true about success rates for early and advanced cancers?

When kept separate, Treatment A has a higher success rate, but combined, Treatment B has a higher rate.

What is the lurking variable when data for early and advanced cancers are combined?

Stage of cancer (Early or Advanced).

Which treatment is actually more effective?

Treatment A.

Which situation probably does not have a lurking variable?

None of the above.

What is a characteristic of a census?

It gathers data from every member of a population.

What might be the treatment in an experimental study on vitamin C and flu recovery?

The amount of vitamin C taken per day: 0 mg, 1000 mg, 2000 mg, or 3000 mg.

Why might a count estimated from random samples be more accurate than a census?

A census often can't find every population member, so some groups are often under-represented.

What is the best representative sample of the adult population in the United States?

Simple random sample of 1000 adults from across the country.

What is a block in research?

A group of subjects that are similar in some way known to affect the response to the treatment.

What is replication in research?

The policy of repeating an experiment on different subjects to reduce chance variation.

What is double-blind in research?

A design in which neither the experimenter nor the subject knows who is in the treatment group.