Practice Questions 2.4

Match the appropriate statistic for a distribution of resistant statistics:

__ Shape
__ Location
__ Spread

A- Boxplot
B- Median
C- Inter-quartile range

What makes resistant statistics work?

A) They weight the data values lower when far from the mean.
B) The data values are divided by their deviation.
C) They look at the position of the data values, and not at their values.
D) They remove the high and low data values to eliminate any extreme values.

What are resistant statistics resistant to?

A) Any possible bias in the data values.
B) The presence of extreme values.
C) Any minor recording errors in the data set.
D) The presence of gaps in the shape.

To find resistant statistics, what must be true of the data set

A) The data values must be ranked from lowest to highest.
B) The position of the data values must be found in the initial data set.
C) The data values must be ranked from highest to lowest.
D)  The data set must be checked to make certain that no two data values occupy the same position.

Why do positional statistics work for a data set containing extreme values?

A)  Because in the tails, a big change in value is usually a small change in position.
B) Because the range of position is (0, n), but the range of the values is (-∞, ∞).
C) Because extreme values occur near the mean where the positions of the data values are close together.
D) Because positional statistics are not a very sensitive type of statistics.

Percentiles are NOT positional statistics.

True
False
True False

When denoting a percentile (Pk) what does the k stand for?

A) The percentage of data values greater than (to the right of) the percentile.
B) That the data set has been ranked for lowest to highest.
C)  This is archaic nomenclature, now k is no longer used.
D) Which percentile is desired, the 0th percentile up through the 100th percentile.

The value of the third quartile (Ǫ3) can be less than the value of the first quartile (Ǫ1).

True
False
True False

How many data values are less than the value of the third quartile (Ǫ3)?

A) The middle half (50%) of the data values.
B) Three quarters (75%)of the data values.
C) One quarter (25%) of the data values.
D) One third (33%) of the data values.

Percentiles (Pk) (or quartiles (Qk) must always be a data value in the data set.

True
False
True False

Which of the answers below are NOT one of the steps to find any percentile (Pk)?

A) Step 1\: Calculate the Index.
B) Step 2\: Move to the correct Position.
C)  Step 3\: Find the Value of the percentile from the ranked data set.
D) None of the other choices.

In Step 2: Move to the correct position of finding a percentile (Pk), how is the appropriate move decided?

A) If i is an integer, average that and the next lower data values. If i has a decimal, move down to the next lower data value. 
B) if i is an integer, move up to the next higher data value. If i has a decimal, average that and the next higher data values.
C) If  k/100 is less than 0.5, move down to the next lower data value. If  k/100 is greater than 0.5, move up to the next higher data value. 
D) If i is an integer, average that and the next higher data values. If i has a decimal, move up to the next higher data value.

The interquartile range (IQR) can never be negative.

True
False
True False

The range is a reliable measure of spread.

True
False
True False

The interquartile range (IQR) measures the spread of what part of the data set?

A) Middle majority (90%)
B) Middle third (33%)
C)  Middle half (50%)
D) Upper half (50%)

What does a larger value for the interquartile range (IQR) mean about the data values?

A) There are fewer data values less than the first quartile (Ǫ1) and greater than the third quartile (Ǫ3).
B) The values of the data values are spread wider apart. 
C) The values of the data values are spread narrower together.
D) The median is larger.

Are there any extreme values in the ranked set of data below (n = 15)?
-19, -3, 11, 14, 15    18, 19, 24, 30, 37    40, 41, 44, 44, 90

A)  -19 is an extreme value because the lower fence is -27.5.
B) Both -19 and 90 are extreme values.
C) 90 is an extreme value because the upper fence is 81.5.
D) There are no extreme values in this data set because all the data values are inside the fences.

Regarding a five number summary, what are the fences used for?

A)  To provide limits in which to use efficient statistics.
B) To give a lower limit and an upper limit on the data values to detect extreme values.
C) To keep the data values together for analysis.
D) To find the most appropriate min and max.

What is the value of the lower fence, and of the upper fence, in the five number summary below?
{0.2, 6.05, 6.45, 6.95, 8.2}

A) -1.15, and 9.55
B) 5.15, and 7.85
C) 0.2, and 8.2
D)  4.70, and 8.30

Match the appropriate statistic for a distribution of resistant statistics.

A. Median.
B. Inter-quartile range.
C. Boxplot.

__ Shape
__ Location
__ Spread

The appropriate equation to use in Step 1: Calculate the Index of finding a percentile (Pk)is shown below.

i= (k/100) x n

True
False
True False

What is the 40th percentile (P40) in the following ranked set of data (n = 15)? (to one decimal place = 00.0)

9, 13, 14, 14, 15    18, 19, 24, 30, 37     40, 41, 44, 44, 193

What is the first quartile (Ǫ1) / third quartile (Ǫ3) in the following ranked set of data (n = 15)? (to one decimal place = 00.0)

9,13, 14, 14, 15     18, 19, 24, 30, 37     40, 41, 44, 44, 193

What information is given by a five number summary?

A) It gives the min and the max as a non-resistant measure of spread.
B) It gives the quartiles as a resistant measure of spread
C) All of these other answers.
D)  It gives the median as a measure of location.

Are there any extreme values in the data set that has the five number summary below?

{0.2, 6.05, 6.45, 6.95, 8.2}

A) No extreme values because the fences are -1.15 and 9.55
B) 0.2 and 8.2 are both extreme values as they are outside of the fences
C) 0.2 because the lower fence is 4.70
D) A histogram of this data set does not show any extreme values.