Chapter 4, Measures of Central Tendency Video Solutions, Fundamental Statistics for the Behavioral Sciences

Problem 1

As part of the Katz et al. (1990) study previously described, the experimenters obtained the same kind of data from a smaller group of students who had read the passage (called the Passage group). Their data follow.
$\begin{array}{lllllllllllllllll}66 & 75 & 72 & 71 & 55 & 56 & 72 & 93 & 73 & 72 & 72 & 73 & 91 & 66 & 71 & 56 & 59\end{array}$
Calculate the mode, median, and the mean for these data.

Jen H

Numerade Educator

Problem 2

The measures of central tendency for the data on Katz's study who did not read the passages were given in the SPSS printout in Figure 4.1. Compare those answers with the answers to Exercises 4.1. What do they tell you about the value of reading the passage on which questions are based?

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Problem 3

If a student in Katz's study simply responded at random (even without reading the questions), she would be expected to get 20 items correct. How does this compare to the measures we found in Section 4.5? Why should this not surprise you?

Donna Densmore

Numerade Educator

00:43

Problem 4

Make up a set of data for which the mean is greater than the median.

Sneha Ravi

Numerade Educator

01:21

Problem 5

Make up a positively skewed set of data. Does the mean fall above or below the median?

Manisha Sarker

Numerade Educator

Problem 6

Plot the data for each of the three conditions in Figure 4.2 and describe the results.

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03:03

Problem 7

A group of 15 rats running a straight-alley maze required the following number of trials to perform to a predetermined criterion. The frequency distribution follows.
$$
\begin{array}{lrrrrrrr}
\text { Trials to reach criterion } & 18 & 19 & 20 & 21 & 22 & 23 & 24 \\
\text { Number of rats (frequency) } & 1 & 0 & 4 & 3 & 3 & 3 & 1
\end{array}
$$
Calculate the mean and median number of trials to criterion for this group. (You can either write out the 15 numbers or you can think about how you could incorporate the frequencies directly into the formula for the mean.)

Carson Merrill

Numerade Educator

Problem 8

Given the following set of data, demonstrate that subtracting a constant (e.g., 5) from every score reduces all measures of central tendency by that amount.
$\begin{array}{llllll}8 & 7 & 12 & 14 & 3 & 7\end{array}$

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Problem 9

Given the following data, show that multiplying each score by a constant multiplies all measures of central tendency by that constant.
$\begin{array}{llllll}8 & 3 & 5 & 5 & 6 & 2\end{array}$

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Problem 10

Create a sample of ten numbers that has a mean of 8.6. Notice carefully how you did thisit will help you later to understand the concept of degrees of freedom.

Shu Naito

Numerade Educator

Problem 11

Calculate the measures of central tendency for the data on ADDSC and GPA in Appendix D—also available at this book's Web site.

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Problem 12

Why would it not make any sense to calculate the mean for SEX or ENGL in Appendix D? If we did go ahead and compute the mean for SEX, what would the value of $(\bar{X}-1)$ really represent?

Rashmi Sinha

Numerade Educator

05:51

Problem 13

In Table 3.1 the reaction time data are broken down separately according to whether we are looking at the same stimulus or whether the stimuli are mirror images of one another. The data can be found by going this book's Web site and obtaining the data labeled as Tab3-1.dat. Using SPSS or similar software, calculate the mean reaction time under the two conditions. Does it take longer to respond to stimuli that are mirror images? This question requires some thought. You can either go to the menu labeled Data and ask it to split the data on the basis of the variable "Stimulus" and then use the Analyze/Descriptive Statistics/Descriptives analysis, or you can not split the data but go to Analyze/Descriptive Statistics/Explore and enter the variable "Stimulus" in the Factor List.

Trinity Steen

Numerade Educator

Problem 14

With reference to Exercise 4.13, if people take longer to process an image that has been both reversed and rotated, then the mean reaction time should depend on whether or not the comparison stimulus has been reversed. If reversal does not alter the difficulty of processing information, then the means should be similar. What do the answers to Exercise 4.13 suggest about how we process information?

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01:24

Problem 15

Why is the mode an acceptable measure for nominal data? Why are the mean and the median not acceptable measures for nominal data?

Harsh Gadhiya

Numerade Educator

01:23

Problem 16

In the exercises in Chapter 2 we considered the study by a fourth-grade girl who examined the average allowance of her classmates. You may recall that 7 boys reported an average allowance of $$\$ 3.18$$, while 11 girls reported an average allowance of $$\$ 2.63$$. These data raise some interesting statistical issues. This fourth-grade student did a meaningful study (well, it was better than I would have done in fourth grade), but let's look at the data more closely.
The paper reported that the highest allowance for a boy was $$\$ 10$$, while the highest for a girl was $$\$ 9$$. It also reported that the two lowest girls' allowances were $$\$ 0.50$$ and $$\$ 0.51$$, while the lowest reported allowance for a boy was $$\$ 3.00$$.
(a) Create a set of data for boys and girls that would produce these results. (No, I didn't make an error.)
(b) What is the most appropriate measure of central tendency to report in this situation?
(c) What does the available information suggest to you about the distribution of allowances for the two genders?
(d) What do the data suggest about the truthfulness of little boys?

Lynn Larson

Numerade Educator

02:48

Problem 17

In Chapter 3 (Figure 3.5) we saw data on grades of students who did and did not attend class regularly. What are the mean and median scores of those two groups of students? (The data are reproduced here for convenience.) What do they suggest about the value of attending class?$$
\begin{array}{lllllllllll}
\text { Attended class } & 241 & 243 & 246 & 249 & 250 & 252 & 254 & 254 & 255 & 256 \\
& 261 & 262 & 263 & 264 & 264 & 264 & 265 & 267 & 267 & 270 \\
& 271 & 272 & 273 & 276 & 276 & 277 & 278 & 278 & 280 & 281 \\
& 282 & 284 & 288 & 288 & 290 & 291 & 291 & 292 & 293 & 294 \\
\text { Skipped class } & 296 & 296 & 297 & 298 & 310 & 320 & 321 & 328 & & \\
& 188 & 195 & 195 & 225 & 228 & 232 & 233 & 237 & 239 & 240 \\
& 250 & 256 & 256 & 256 & 261 & 264 & 264 & 268 & 270 & 270 \\
& 274 & 274 & 277 & 308 & & & & & &
\end{array}
$$

Akhil Choudhary

Numerade Educator

00:32

Problem 18

Why do you think that I did not ask you to calculate the mode? (Hint: If you calculate the mode for those who skipped class frequently, you should see the problem.)

Akhil Choudhary

Numerade Educator

03:00

Problem 19

Search the Internet for sources of information about measures of central tendency. What do you find there that was not covered in this chapter?

Jeremiah Mbaria

Numerade Educator

Problem 20

The Internet is a great resource when you don't know how to do something. Search the Internet to find out how to use SPSS (or whatever software you have access to) to calculate the mode of a set of data. You can just go to Google and enter "How do I calculate the mode in SPSS?"

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02:31

Problem 21

(a) Calculate the $10 \%$ trimmed mean for the data on test performance in Figure 4.1. (Remember that $10 \%$ trimming means removing the $10 \%$ of the scores at each end of the distribution.)
(b) Assume that you collected the following data on the number of errors that participants made in reading a passage under distracting conditions.
$$
1010101515202020202525262730323739426877
$$

Calculate the $10 \%$ trimmed mean for these data.
(c) Trimming made more of a difference in (b) than it did in (a). Can you explain why this might be?

John Long

Numerade Educator

04:53

Problem 22

Seligman, Nolen-Hecksema, Thornton, and Thornton (1990) classified participants in their study (who were members of a university swim team) as Optimists or Pessimists. They then asked them to swim their best event, and in each case they reported times that were longer than the swimmer actually earned. Half an hour later they asked them to repeat the event again. The dependent variable was $\operatorname{Time}_1 / \operatorname{Time}_2$, so a ratio greater than 1.0 indicates faster times on the second trial. The data follow.
(TABLE CAN'T COPY)
Calculate the mean for each group. Seligman et al. thought that optimists would try harder after being disappointed. Does it look as if they were correct?

Shafiq Rehman

Numerade Educator

02:50

Problem 23

In Exercise 4.22 women did not show much difference between Optimists and Pessimists. The first 17 scores in the Optimist group are for men and the first 13 scores in the Pessimist group are for men. What do you find for men?

Ahmad Reda

Numerade Educator

00:14

Problem 24

Thave suggested that if you don't understand something I write, go to Google and find something better. In Chapter 2 I admitted that it was pretty easy to define a dependent variable, but the definition of an independent variable is a bit more complicated. Go to Google and type in "What is an independent variable." Read at least five of the links that come up (not necessarily the first five) and write down the best definition that you find-the one that is clearest to you.

Becky Rahm

Numerade Educator