Question

approximate the mean for the following data set. round your answer to one decimal place.
class \tfrequency
0-15 \t4
16-31 \t11
32-47 \t9
48-63 \t14
64-79 \t14
send data to excel
the mean is approximately □ .

Explanation:

Step1: Find midpoints of each class

For class \(0 - 15\), midpoint \(x_1=\frac{0 + 15}{2}=7.5\)
For class \(16 - 31\), midpoint \(x_2=\frac{16+31}{2}=23.5\)
For class \(32 - 47\), midpoint \(x_3=\frac{32 + 47}{2}=39.5\)
For class \(48 - 63\), midpoint \(x_4=\frac{48+63}{2}=55.5\)
For class \(64 - 79\), midpoint \(x_5=\frac{64 + 79}{2}=71.5\)

Step2: Calculate \(f_i\times x_i\) for each class

• For \(0 - 15\): \(f_1\times x_1=4\times7.5 = 30\)
• For \(16 - 31\): \(f_2\times x_2=11\times23.5=258.5\)
• For \(32 - 47\): \(f_3\times x_3=9\times39.5 = 355.5\)
• For \(48 - 63\): \(f_4\times x_4=14\times55.5=777\)
• For \(64 - 79\): \(f_5\times x_5=14\times71.5 = 1001\)

Step3: Find total frequency and total \(f_i\times x_i\)

Total frequency \(N=4 + 11+9 + 14+14=52\)
Total \(f_i\times x_i=30+258.5 + 355.5+777+1001=2422\)

Step4: Calculate the mean

Mean \(\bar{x}=\frac{\sum f_i\times x_i}{N}=\frac{2422}{52}\approx46.6\)

Answer:

\(46.6\)