Question

ages of hospital patients the frequency distribution shows the ages of patients who are staying overnight at a local hospital. find the mean and modal class of the data. (a) find the mean. round the answer to one decimal place, if necessary. the mean is

Explanation:

Step1: Calculate class midpoints

For class \(10 - 18\), midpoint \(x_1=\frac{10 + 18}{2}=14\).
For class \(19 - 27\), midpoint \(x_2=\frac{19+27}{2}=23\).
For class \(28 - 36\), midpoint \(x_3=\frac{28 + 36}{2}=32\).
For class \(37 - 45\), midpoint \(x_4=\frac{37+45}{2}=41\).
For class \(46 - 54\), midpoint \(x_5=\frac{46 + 54}{2}=50\).
For class \(55 - 63\), midpoint \(x_6=\frac{55+63}{2}=59\).
For class \(64 - 72\), midpoint \(x_7=\frac{64 + 72}{2}=68\).
For class \(73 - 81\), midpoint \(x_8=\frac{73+81}{2}=77\).

Step2: Calculate \(\sum(f\times x)\) and \(\sum f\)

\(\sum f=10 + 16+25+37+44+28+17+12=199\)
\(f_1\times x_1=10\times14 = 140\)
\(f_2\times x_2=16\times23=368\)
\(f_3\times x_3=25\times32 = 800\)
\(f_4\times x_4=37\times41=1517\)
\(f_5\times x_5=44\times50 = 2200\)
\(f_6\times x_6=28\times59=1652\)
\(f_7\times x_7=17\times68 = 1156\)
\(f_8\times x_8=12\times77=924\)
\(\sum(f\times x)=140+368 + 800+1517+2200+1652+1156+924=8757\)

Step3: Calculate the mean

The mean \(\bar{x}=\frac{\sum(f\times x)}{\sum f}=\frac{8757}{199}\approx44.0\)

Step4: Find the modal class

The modal class is the class with the highest frequency. Here, the frequency of class \(46 - 54\) is \(44\), which is the highest.

Answer:

The mean is \(44.0\) and the modal class is \(46 - 54\)