Question

a professional golfer is shopping for a new brand of golf ball. she likes most of the features of one particular brand, but she wants to make sure that the brand has a desirable spin rate (the rate at which the ball spins on its axis after being struck by a golf club). to test the spin rate of this new brand of ball, the golfer hits the brand of ball on 73 shots, and a computer measures the spin rate for each shot. the computer then produces the following histogram summarizing the 73 spin rates. based on the histogram, estimate the mean spin rate (in revolutions per minute) for the sample. carry your intermediate computations to at least four decimal places, and round your answer to the nearest integer.

Explanation:

Step1: Find the midpoint of each class

For the class \(5000 - 5500\), midpoint \(x_1=\frac{5000 + 5500}{2}=5250\)
For the class \(5500 - 6000\), midpoint \(x_2=\frac{5500+6000}{2}=5750\)
For the class \(6000 - 6500\), midpoint \(x_3=\frac{6000 + 6500}{2}=6250\)
For the class \(6500 - 7000\), midpoint \(x_4=\frac{6500+7000}{2}=6750\)
For the class \(7000 - 7500\), midpoint \(x_5=\frac{7000 + 7500}{2}=7250\)
For the class \(7500 - 8000\), midpoint \(x_6=\frac{7500+8000}{2}=7750\)

Step2: Calculate the sum of \(f_ix_i\)

Let \(f_1 = 4\), \(f_2=12\), \(f_3 = 15\), \(f_4=21\), \(f_5=17\), \(f_6 = 4\)
\(f_1x_1=4\times5250 = 21000\)
\(f_2x_2=12\times5750=69000\)
\(f_3x_3=15\times6250 = 93750\)
\(f_4x_4=21\times6750=141750\)
\(f_5x_5=17\times7250 = 123250\)
\(f_6x_6=4\times7750=31000\)
\(\sum_{i = 1}^{6}f_ix_i=21000 + 69000+93750+141750+123250+31000=479750\)

Step3: Calculate the sum of \(f_i\)

\(\sum_{i=1}^{6}f_i=4 + 12+15+21+17+4=73\)

Step4: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{6}f_ix_i}{\sum_{i=1}^{6}f_i}=\frac{479750}{73}\approx6571.9178\)

Answer:

\(6572\)