The data below represents the three year rate of return in p

The data below represents the three year rate of return (in percent) for a simple random sample of 40 small capitalization growth mutual funds.

27.4, 16.7, 10.8, 24.1, 35.9, 12.7, 28.5, 22.2, 18.4, 17.4, 22.6, 29.6, 11.6, 45.9, 16.6, 32.1, 47.7, 10.9, 18.4, 23.3, 18.2, 32.0, 25.5, 23.7, 38.1, 23.7, 14.7, 12.8, 31.1, 21.9, 18.4, 21.3, 27.0, 19.6, 15.8, 14.7, 37.0, 19.2, 18.5, 29.1

1. What is the class width? (we want 8 classes)

a) 4 b) 5 c) 6 d) 7 e) 8

Use 10 as the first lower class limit. Since data values contain 1 decimal digit, your upper class limits must contain 1 decimal digit.

What is the relative frequency of the 2nd class?

a) 15%. b) 5% c) 7.5% d) 20% e) 27.5%

Find the mean of the data?

a) 16.4 b) 23.2 c) 19.4 d) 21.3 e) 20.4

Find the standard deviation of the data.

a) 9.91 b) 5.18 c) 6.51 d) 10.56 e) 9.24

5. What is the median of the data ?

a) 20.3 b) 19.6 c) 22.05 d) 18.5 e) 21.3

Solution

Data: {27.4, 16.7, 10.8, 24.1, 35.9, 12.7, 28.5, 22.2, 18.4, 17.4, 22.6, 29.6, 11.6, 45.9, 16.6, 32.1, 47.7, 10.9, 18.4, 23.3, 18.2, 32.0, 25.5, 23.7, 38.1, 23.7, 14.7, 12.8, 31.1, 21.9, 18.4, 21.3, 27.0, 19.6, 15.8, 14.7, 37.0, 19.2, 18.5, 29.1}

Max : 47

Min: 10

Total Datapoints: 40

Number of classes = 8

1) b (5) Answer

Class Width = (Max -Min ) / Number of classes.

= ( 47.7-10.8) / 8

= 4.6 ~ 5

2) e) 27.5% Answer

Class :          Frequency

15.2-20.2           11

Relative Frequency = 11/40 = 0.275   = 27.5% Answer

3) b)23.2 Answer

Mean =23.2

4) e) 9.24 Answer

Standard Deviation = 9.24

5)c)22.05 Answer

Median 22.05