Question

Ted’s Surfboard Shop makes surfboards by hand and sells them to well-heeled tourists. The number of surfboards that Ted makes in a month depends on the wave conditions (Good surfing days lead to less productivity).  His sister (business partner) visits him when she can and has collected the following data intermittently throughout her trips.  

Number of Surfboards X	0-1	2-3	4-5	6-7	8-9	10
Number of times	23	32	9	6	3	2

a) What is the standard deviation?

b) Which class holds the mode?

c) Which class holds the median?

d) If he charges about $350 per surfboard, what is the estimated average monthly earnings?

Answer 1

(a)

First we need to find the mid point of the class. The mid point is

Class mid point = (lower limit + upper limit) / 2

Following table shows the mid point and calculations for standard deviation:

Number of Surfboards	x	Number of times, f	xf	f(x-mean)^2
0-1	0.5	23	11.5	131.048687
2-3	2.5	32	80	4.792608
4-5	4.5	9	40.5	23.415921
6-7	6.5	6	39	78.322614
8-9	8.5	3	25.5	94.517307
10	10	2	20	101.189538
Total		75	216.5	433.286675

Mean:

The standard deviation is:

b)

Mode is the data value with highets frequency.

The is mode lie in the class 2-3.

c)

There are 75 data vaues so median will be 38th data value. Since 38 data value lie in the class 2-3 so median class is 2-3.

d)

The estimated average monthly earnings is

Answer: $1010.45