Question

Problems 1–4 pertain to the data set of 85 measurements represented by the following ordered stem and leaf diagram, in which the stems are the digits in the tens place and leaves are the digits in the ones place. For these data Px = 3, 957 and Px 2 = 203, 589.

6 0 0 0 1 1 1 1 2 2 2 3 3 3 4 4 5 5 6 7 7 7 8 8

5 0 0 1 1 1 2 2 3 4 4 5 5 5 6 6 7 8 8 9 9

4 0 1 1 2 2 3 3 4 4 6 6 6 7 7 8 9

3 0 0 1 2 3 4 4 5 6 7 7

2 0 2 3 5 5 5 6 6 7 8

1 6 6 7 8 9

1. The sample mean of this data set is about: (a) 32.2 (b) 41.8 (c) 50.8 (d) 46.6 (e) 39.7

2. The sample standard deviation of this data set is about: (a) 12.4 (b) 228.0 (c) 15.2 (d) 18.3 (e) 230.7

3. The sample median is about: (a) 47.0 (b) 42.5 (c) 50.0 (d) 46.3 (e) 37.5

4. The percentile rank of the measurement 25 is about: (a) 25 (b) 42 (c) 13 (d) 9 (e) 18

Answer 1

1. The sample mean of this data is about 46.6

Therefore the correct option is (d) 46.6

2. The sample standard deviation of this data is about 15.2.

Therefore the correct option is (c) 15.2

3. The sample median is about 50

Therefore the correct option is (c) 50.0

4. The percentile rank of the measurement 25 is about 9.

Therefore the correct option is (d) 9