Colegio del Sagrado Corazon de Jesus Measures of Central Tendency Questionnaire

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.