Assignment # 16 Chapter 4. Automobile Ownership4-2 Automobile Transactions Applications

Measures of Central Tendency

The three measures of central tendency are mean, median, and mode. The

Mean: is the average of the data values.

Median: is the middle data value.

Mode is the most frequently occurring data value.

Range: is a measure of spread and is found by subtracting the lowest data

value from the highest.

Box and Whisker Quartiles

To understand box-and-whisker plots, you have to

understand medians and quartiles of a data set.

The median is the middle number of a set of data, or the average of the two

middle numbers (if there are an even number of data points).

The median ( Q2 ) divides the data set into two parts, the upper set and the lower

set.

The lower quartile ( Q1 ) is the median of the lower half,

the upper quartile ( Q3 ) is the median of the upper half.

Example:

Find Q1, Q2, and Q3 for the following data set.

{7, 8, 8, 11, 12, 13, 14, 15, 22, 23}

Steps

1) There are 10 data points. The middle two are 12 and 13

(12 + 13) / 2 = 12.5

Median Q2 is 12.5 Main Median

2) The “lower half” of the data set is the set {7, 8, 8, 11}

( 8 + 8) / 2 = 8

Median Q1 is 8.0, Q1= 8 Lower quartile

3) The “upper half” of the data set is the set {14, 15, 22,

23}

(15 + 22) / 2 = 18.5

Median Q 3 is 18.5

Q3=18.5 Upper Quartile

4) Interquartile Range Q3 – Q 1 = 18.5 – 12.5 = 6

BOX and whisker

Use the following Quartiles data values Q1 = 8, Q2 = 12, and

Q3 = 14 and draw a box-and-whisker. The first value is 3, and

the last value is 23.

A box-and-whisker plot displays the values Q1 Q2and Q3 along

with the extreme values of the data set (22 and 23), in this

case):

A box & whisker plot shows a “box” with left edge at Q1, right

edge at Q3, the “middle” of the box at Q2 (the median) and

the maximum and minimum as “whiskers”.

Note that the plot divides the data into 4 equal parts. The left

whisker represents the bottom 25% of the data, the left half of

the box represents the second 25% , the right half of the box

represents the third 25% , and the right whisker represents

the top 25%

Assignment # 16 Solve the following problem, show your work.

1.- The quartiles of a data set are Q 1 = 50, Q2 = 72, Q3 = 110. Find the

interquartile range.

2.- The following list of prices is for a used original radio for a 1955 Thunderbird. The

prices vary depending on the condition of the radio.

$210, $210, $320, $200, $300, $10, $340,

$300, $245, $325, $700, $250, $240, $200

a. Find the mean of the radio prices. Round to the nearest cent.

b. Find the median of the radio prices.

c. Find the mode of the radio prices. (Place in ascending order)

d. Find the three quartiles.

Q1

Q2

Q3

e. Find the interquartile range for this data set.

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