Name:______

Math III

Measures of Central Tendency

1. In May of 2008, the government predicted that gasoline prices would peak at a national average of $3.73 a gallon in June. However, this prediction turned out to be incorrect. The average weekly prices of gasoline in Rochester from May 7 to July 16, 2008, were:

$3.85, $3.92, $4.02, $4.09, $4.12, $4.18, $4.20, $4.20, $4.23, $4.24.

Find the mean, median, and mode for these data.

2. Among the numerous awards he received, Michael Jordan has been named one of the fifty greatest players in NBA history. The table below contains the average number of points scored per game by Michael Jordan during his NBA career. Determine, to the nearest tenth, the mean, median, and mode of the data. Also, find the first quartile, the third quartile and the interquartile range.

Year / Points per Game
’84 – ‘85 / 28.2
’85 – ‘86 / 22.7
’86 – ‘87 / 37.1
’87 – ‘88 / 35.0
’88 – ‘89 / 32.5
’89 – ‘90 / 33.6
’90 - ‘91 / 31.5
’91 – ‘92 / 30.1
’92 – ‘93 / 32.6
’94 – ‘95 / 26.9
’95 –‘96 / 30.4
’96 – ‘97 / 29.6
’97 – ‘98 / 28.7
’01 – ‘02 / 22.9
’02 –‘03 / 20.0

3. The table below lists the scores for a multiple-choice test in Mrs. Santiago’s class. Find the mean, median, and mode for the data to the nearest hundredth.

Test / 100 / 95 / 90 / 85 / 80 / 75 / 70 / 60
Frequency / 1 / 2 / 2 / 7 / 6 / 5 / 3 / 2
  1. Calculate the mean, median, mode and standard deviation of the given data set: 37, 54, 72, 89, 74, 83, 90, and 93.
  1. For the data 14, 18, 21, 19, 27, 23, 17, which statement is true?

(1)mean = median(2) mean < median

(3) mean > median(4) median = mode

  1. If the mean of a set of data is 27 and the data includes 24, 34, 19, 22, 29, and x, what is the value of x? Find the median, mode, and standard deviation of the data set (include x).
  1. Chantal has taken five tests so far this marking period and has an 88 average. What does she have to earn on her sixth and last test of the marking perod to bring her average up to 90?
  1. Given the data 6, 9, 3, 6, 10, 3, 9, 9, 12, 14, 7, what is the value of minimum, maximum, quartile 1, quartile 3 and median?
  1. What is the interquartile range for the data 7, 4, 7, 2, 6, 9, 4, 3?
  1. The median height of the players on the basketball team is 6’4”. This means

(1) the tallest player is 6’4”

(2) no player is shorter than 6’4”

(3) most of the players are 6’4”

(4) an equal number of players are tallerthan 6’4” and shorter than 6’4”

11. One hundred senior girls were interviewed about their price limit for the “perfect” prom dress. Their responses are summarized in the table below:

Maximum Price
(prom dress) / Number of Girls
$100 / 23
$150 / 22
$200 / 26
$250 / 14
$300 / 15
  1. Determine the mean, median, and mode of the data.
  1. Which measure of central tendency should the buyer for a store at the mall use to place an order based on what price prom dresses will sell best?
  1. Consider the frequency table below:

Maximum Price
(prom dress) / Number of Girls
$100 / 23
$150 / 22
$200 / 26
$250 / 14
$300 / 15
Scores / Frequency
62 / 6
71 / 5
80 / 5
89 / 4
Maximum Price
(prom dress) / Number of Girls
$100 / 23
$150 / 22
$200 / 26
$250 / 14
$300 / 15

Which of following statements is true?

(1)mean = median(2) mode > median

(3) mean < median(4) mean > mode

  1. The table below gives the speed of the fastest race lap at the Indianapolis 500 for the years from 1999 to 2008.

Year / 1999 / 2000 / 2001 / 2002 / 2003 / 2004 / 2005 / 2006 / 2007 / 2008
Speed
(MPH) / 218.9 / 218.5 / 219.8 / 226.5 / 229.2 / 218.4 / 228.1 / 221.3 / 223.4 / 224.0
  1. Find the mean, median, and mode of these data.
  1. Which, in your opinion, is most representative of the data? Why?
  1. What is the interquartile range of the data?
  1. Andrew wanted a raise in his allowance for doing yard work. His father said he should find out the “average” payment others in the neighborhood received. Andrews surveyed the other families on the block and discovered that they paid the following prices for having their lawns cut and raked: $18.00, $22.00, $17.50, $15.00, $25.00, $17.50, $20.00, $15.00, $26.00, $28.00.

a. Which “average” should Andrew use to promote his increase in allowance?

b. Which “average” might his father use to rebut Andrew’s argument?

  1. Given the data set

{ 181, 199, 178, 203, 211, 208, 209, 202, 212, 194,

185, 208, 233, 206, 202, 213, 202, 186, 189, 203}

Find:

Mean:

Median:

Mode:

First quartile:

Third quartile:

Interquartile range:

  1. The ages of employees of a local business are shown below.

Age / 20-24 / 25-29 / 30-34 / 35-39 / 40-44 / 45-49 / 50-54 / 55-59 / 60-64
Frequency / 1 / 2 / 5 / 6 / 7 / 10 / 7 / 5 / 2

What is larger: the median or the mean?