4.

Jane recorded the number of minutes she spent talking on the phone per day: 15, 25, 60, 10, 120, 85, 35, 20, 60, and

30.

Make a stem-and-leaf plot to organize her data.

a.

Find the mean, median, and mode.

[mean=46; median=32.5; mode=60]

b.

If Jane wanted to convince her parents that she did not spend too much time on the phone, which of the measures of central tendency should she use? [She would probably use median since it is the lowest number.]

c.

If her parents argued that they disagree with her, what evidence could they use? [They would be using mode since it is the highest number.]

1 2 3 4 5 6 7 8 9 10 11 12

05 05 05

00

5

0

5.

Shelley surveyed her classmates to find out how much money they had in their pockets, wallets, and backpacks. The dollar amounts were $1, $2, $1, $1, $8, $1, $7, $10, and $5.

a.

What is the mode of these dollar amounts? [$1]

b.

If the person with the most money had $100 instead of $10, would the mode change? Why or why not? [No; mode measures frequency, not size or amount.]

c.

Would changing the largest amount of money change the median? [No; making the highest number larger does not change the middle number.]

d.

What is the mean for the original dollar amounts? [$4]

e.

Would changing the largest amount to $100 change the mean? If your answer is yes, find the new mean. If not, explain why not. [Yes; the mean changes from $4 to $14.]

D.

Box-and-Whisker Plots

Often we want to know more about how data are spread out. For example, if you were a teacher, you might anticipate that you would have some very bright and hard-working students in your class who always scored well, and you also might expect to have a few who consistently scored in the low range. But how were the majority of students in the middle doing? Could you find out? How would you measure the spread around the median? Once you have divided your data into two halves by finding the median, find the values that divide each half in half again. These two values are called the lower quartile or quartile 1 (Q1 ), and the upper quartile or quartile 3 (Q3). Together with the median they divide the data set into four equal parts. The distance between the upper and lower quartiles, called the inter-quartile range, or IQR, is a

51

Q_{1 }

Q 3