Deck 3: Summarizing Data: Measures of Location

Question 1

For a set of data which contains extreme values, the best measure of a central location among the following is the

A) mean.
B) median.
C) mode.
D) midrange.

Answer 1

median.

Question 2

A stem-and-leaf display is especially helpful in finding the

A) mean.
B) midquartile.
C) midrange.
D) median.

Answer 2

median.

Question 3

The mean of $Q_{1}$ and $Q_{3}$ equals the

A) midrange.
B) midquartile.
C) median.
D) mean.

Answer 3

midquartile.

Question 4

When no two values are the same, which measure is exceeded by as many values as it exceeds?

A) the median
B) the mean
C) the first quartile
D) the midrange

Question 5

The _______ is not a measure of central location.

A) mean
B) second quartile
C) first quartile
D) midquartile

Question 6

The 65th percentile is always less than

A) $Q_{3}$ .
B) the midquartile.
C) the mean.
D) the median.

Question 7

When data contains extreme values, which of the following is the poorest measure of location?

A) the median
B) $Q_{2}$
C) the midrange
D) the midquartile

Question 8

For the data 2, 10, 20, 15, 100, 30, and 90, which of the following measures would be changed if the 90 were changed to 70 ?

A) the mean
B) the median
C) the mode
D) the midrange

Question 9

Which of the following measures is not equal to the other measures?

A) $D_{5}$
B) $Q_{3}$
C) the median
D) $P_{50}$

Question 10

For the data 1, 2, 4, 6, 8, 12, and 15, which of the following measures of location is not changed if either the 4, 6, or 12 is removed?

A) the mean
B) the median
C) the midrange
D) the midquartile

Question 11

Having received a bonus of $\$ 30,000$ for accepting early retirement in July, 2000, a company's project manager invested $\$ 9,000$ in a municipal bond paying $3.69 \%, \$ 14,000$ in a money market fund paying $4.01 \%$ , and $\$ 7000$ in a certificate of deposit paying $3.29 \%$ . Using the respective amounts invested as weights, find the weighted mean of the three percentages.

A) $\bar{x}_{w}=3.75 \%$
B) $\bar{x}_{w}=3.66 \%$
C) $\bar{x}_{w}=3.74 \%$
D) $\bar{x}_{w}=3.67 \%$

Question 12

A pet supply store advertised the following aquarium tanks, of which it had, respectively, 23, 7, 17, 9, and 12 in stock: (a) What is the average size of these aquariums?
(b) What is the average price of these aquariums?

A) (a) 16.6 gallons; (b) $\$ 139.71$
B) (a) 19.4 gallons; (b) $\$ 160.00$
C) (a) 11.7 gallons;(b) $\$ 118.75$
D) (a) 25.9 gallons; (b) $\$ 197.49$

Question 13

The grades obtained on a test by twelve students in a class are listed below.
$66,70,68,75,80,86,64,73,80,94,72,91$

-For this data, construct a stem-and-leaf display.

Question 14

The grades obtained on a test by twelve students in a class are listed below.
$66,70,68,75,80,86,64,73,80,94,72,91$
-For this data, find the mean.

Question 15

The grades obtained on a test by twelve students in a class are listed below.
$66,70,68,75,80,86,64,73,80,94,72,91$
-For this data, find the median.

Question 16

The grades obtained on a test by twelve students in a class are listed below.
$66,70,68,75,80,86,64,73,80,94,72,91$
-For this data, find the mode.

Question 17

The frequency distribution of grades on a test for a class of 30 students is given below:

-Find the median.

Question 18

The frequency distribution of grades on a test for a class of 30 students is given below:

-Find $Q_{3}$ .

Question 19

At the start of the program, ten dieters entering a weight-loss program have the weights (in pounds) shown below.
182, 160, 120, 140, 155, 136, 115, 190, 144, 200

-For this data, construct a stem-and-leaf display.

Question 20

At the start of the program, ten dieters entering a weight-loss program have the weights (in pounds) shown below.
182, 160, 120, 140, 155, 136, 115, 190, 144, 200
-For this data, find the median.

Question 21

The number of sales of homes having two bedrooms or less in a state for a ten-week period in 1987 is given in the following table:

-For a two bedroom or less home in this state during the given period, find the mean price.

Question 22

The number of sales of homes having two bedrooms or less in a state for a ten-week period in 1987 is given in the following table:

-For a two bedroom or less home in this state during the given period, find the median price.

Question 23

The prices (in dollars) of 16 film video cassettes on sale at a video store are given below.
$38,32,38,13,23,38,32,28,27,32,23,27,25,32,27,30$
-For this data, find the mean.

Question 24

The prices (in dollars) of 16 film video cassettes on sale at a video store are given below.
$38,32,38,13,23,38,32,28,27,32,23,27,25,32,27,30$
-For this data, find the median.

Question 25

The prices (in dollars) of 16 film video cassettes on sale at a video store are given below.
$38,32,38,13,23,38,32,28,27,32,23,27,25,32,27,30$
-For this data, find the mode.

Question 26

The prices (in dollars) of 16 film video cassettes on sale at a video store are given below.
$38,32,38,13,23,38,32,28,27,32,23,27,25,32,27,30$
-For this data, find the midrange.

Question 27

The following is the distribution of weights (in lbs.) of 40 students entered in a hamburger eating contest:.

-Find $D_{7}$ .

Question 28

The following is the distribution of weights (in lbs.) of 40 students entered in a hamburger eating contest:.

-Find $P_{30}$ .

Question 29

Suppose your capital today is $\$ 1000$ , and in each of the following four years your capital increases to $\$ 1600$ , $\$ 2000, \$ 2400$ , and $\$ 2640$ , respectively. Find the average yearly percentage increase. (Hint: First find the percentage that each succeeding year is based on the value in the preceding year. Then find the geometric mean of the percentages.)

Question 30

An investor purchased a particular stock on several occasions at different prices:
What is the investor's break even price (i.e., what is his average price per share)?

Question 31

If an investor buys $\$ 1000$ worth of stock at $\$ 20$ per share, $\$ 1000$ worth at $\$ 10$ per share, and $\$ 1000$ worth at $\$ 30$ per share, what is the average price per share?

Question 32

Write the following expression as a summation:
$x_{1}{ }^{2}+x_{2}{ }^{2}+\ldots+x_{15}{ }^{2}$

Question 33

Write the following expression as a summation:
$$2 y_{3} f_{3}+2 y_{4} f_{4}+2 y_{5} f_{5}+2 y_{6} f_{6}$$

Question 34

Write the following expression without summation signs.
$$\sum_{i=2}^{5} x_{i} y_{i}$$

Question 35

Write the following expression without summation signs.
$$\sum_{i=1}^{3}\left(y_{i}-z_{i}\right)$$

Question 36

If $x_{1}=3, x_{2}=4, x_{3}=1, x_{4}=5, f_{1}=1, f_{2}=2, f_{3}=2, f_{4}=1$ , find $\sum_{i=1}^{4} x_{i} f_{i}$ .

Question 37

If $x_{1}=3, x_{2}=4, x_{3}=1, x_{4}=5, f_{1}=1, f_{2}=2, f_{3}=2, f_{4}=1$ , find $\sum_{i=2}^{4} x_{i}^{2}$ .

Question 38

The mean of a list of numbers is more likely to be affected by extreme values than the median.

Question 39

In a list of nine numbers, the median is always the fifth number from either end of the list.

Question 40

If some of the frequencies are greater than 1 , the number of rows in the frequency distribution is equal to the size of the sample.

Question 41

The means of many samples drawn from the same population usually do not fluctuate widely.

Question 42

When calculating the mean for grouped data, the denominator is equal to the number of rows in the table.

Question 43

A stem-and-leaf display is especially helpful when finding the mean of a set of data.

Question 44

If the data consists of all possible observations of a certain phenomenon, it is called a sample.

Question 45

The symbols $\left[\sum_{i=1}^{n} x_{i}\right]^{2}$ and $\sum_{i=1}^{n} x_{i}^{2}$ are always equal.

Question 46

The midquartile is always equal to the median.

Question 47

For a sample size of 15 values, if the largest value is increased, the midquartile is increased.

Question 48

A parameter is a value obtained from a _______.

Question 49

The mean is _______ larger than the median.

Question 50

In calculating a weighted mean, the denominator is given by _______.

Question 51

The median of an odd number of values is _______ the middle number in the list.

Question 52

The number which appears most often in a data set is called the _______.

Question 53

If coding is used to calculate the mean more easily for a frequency distribution with seven classes, the coded value of the second class is _______.

Question 54

If the mean of a set of raw data is subtracted from each of the numbers, the mean of the new set of data is _______.

Question 55

To determine the quartiles of a set of raw data, the first step is to _______ the data _______.

Question 56

The measure of location that is used to average rates of change is the _______.

Question 57

The two measures that are needed to calculate the midquartile are the _______ and the _______.