PSY 555 Homework 2

2.2.

Children's "and then" statements

Interval Midpoint Frequency

10-12     11        3

13-15     14        3

16-18     17        20

19-21     20        17

22-24     23        5

25-27     26        0

28-30     29        0

31-33     32        1

34-36     35        0

37-39     38        0

40-42     41        1

2.4(a). The scores for adults appear to be noticeably smaller. Adults seem to rely less strongly than do children on an "and then…" format for recalling stories.

2.4(b).

Interval  Midpoint  Frequency

0-2       1         1

3-5       4         4

6-8       7         8

9-11      10        21

12-14     13        10

15-17     16        6

2.4(c).  Overlay the two histograms (from problems 2.2 and 2.4(b)) into one histogram, using appropriate shading to indicate separate child and adult data, as well as overlap between the two.

2.7.

Cumulative frequency distribution for Exercise 2.4.

1                  1             1

3                  1             2

4                  1             3

5                  2             5

7                  4             9

8                  4             13

9                  7             20

10                 8             28

11                 6             34

12                 5             39

13                 1             40

14                 4             44

15                 3             47

16                 2             49

17                 1             50

2.14.

Histogram for GPA

GPA Interval  Midpoint  Frequency

.51-.75       .63       4

.76-1.00      .88       5

1.01-1.25     1.13      1

1.26-1.50     1.38      6

1.51-1.75     1.63      7

1.76-2.00     1.88      6

2.01-2.25     2.13      6

2.26-2.50     2.38      8

2.51-2.75     2.63      14

2.76-3.00     2.88      13

3.01-3.25     3.13      3

3.26-3.50     3.38      7

3.51-3.75     3.63      6

3.76-4.00     3.88      2

2.15.

Stem | Leaf

2.   | 69

3*   | 0344

3.   | 56679

4*   | 00023344444

4.   | 5566677888899999

5*   | 00000000011223334

5.   | 55677889

6*   | 00012234

6.   | 55556899

7*   | 0024

7.   | 568

8*   |

8.   | 55

1.   Problem 2.4: the mean is 10.2, the median is 10, and the mode is 10.

Median location=

Median=

Mode=10  (this score appears 8 times)

Problem 2.14: the mean is 2.46, the median is 2.64, and the mode is 3

Median location=

Median=

Mode=3  (this score appears 13 times)

Problem 2.15: the mean is 52.6, the median is 50, and the mode is 50.

Median location=

Median=

Mode=50 (this score appears 9 times)

2.   The distribution in 2.4 is unimodal with a very slight negative skew.  The distribution in 2.14 is unimodal with a negative skew.  The distribution in 2.15 appears to be a normal (Gaussian) distribution.

3.  A distribution must be symmetric and unimodal in order for all three measure of central tendency to be the same value.  The median is preferred over the mean when there are outliers (because the mean will be unduly affected by extreme scores) or when you are using an ordinal scale of measurement.

4.  When there are observations that can assume many different values (such as when you are using a continuous measurement scale), it is not practical to include each individual value between the endpoints of a scale in a frequency distribution because each value may only appear once, if at all.  So, instead, we group adjacent values into intervals and then we list frequencies of each interval to create a grouped frequency distribution (or histogram).  Doing so summarizes the data and, importantly, reduces noise.