1- Make up three data sets with 5 numbers each that have: (a) the same mean but
ID: 3204960 • Letter: 1
Question
1- Make up three data sets with 5 numbers each that have:
(a) the same mean but different standard deviations.
(b) the same mean but different medians.
(c) the same median but different means.
2- An experiment compared the ability of three groups of participants to remember briefly-presented chess positions. The data are shown below. The numbers represent the number of pieces correctly remembered from three chess positions. Compare the performance of each group. Consider spread as well as central tendency.
Non-players
Beginners
Tournament players
22.1
32.5
40.1
22.3
37.1
45.6
26.2
39.1
51.2
29.6
40.5
56.4
31.7
45.5
58.1
33.5
51.3
71.1
38.9
52.6
74.9
39.7
55.7
75.9
43.2
55.9
80.3
43.2
57.7
85.3
Non-players
Beginners
Tournament players
22.1
32.5
40.1
22.3
37.1
45.6
26.2
39.1
51.2
29.6
40.5
56.4
31.7
45.5
58.1
33.5
51.3
71.1
38.9
52.6
74.9
39.7
55.7
75.9
43.2
55.9
80.3
43.2
57.7
85.3
Explanation / Answer
Solution
Q1
Part
Data
Mean
SD
Median
(a)
5
6
7
8
9
7
2
3
5
7
9
11
7
22
1
3
7
11
13
7
10.4
(b)
1
8
9
10
12
8
9
1
2
3
8
26
8
3
2
4
6
12
16
8
6
(c)
3
9
10
11
12
9
10
1
2
10
12
15
8
10
5
7
10
18
20
12
10
Q2
Central Tendency is reflected by the mean and spread is reflected by the sigma
14.82
Part
Data
Mean
SD
Median
(a)
5
6
7
8
9
7
2
3
5
7
9
11
7
22
1
3
7
11
13
7
10.4
(b)
1
8
9
10
12
8
9
1
2
3
8
26
8
3
2
4
6
12
16
8
6
(c)
3
9
10
11
12
9
10
1
2
10
12
15
8
10
5
7
10
18
20
12
10
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