When Data Are Summarized in a Frequency Distribution, the Median

question 42

Short Answer

When data are summarized in a frequency distribution, the median can be found by first identifying the median class (the class that contains the median). We then assume that the values in that class are evenly distributed and we can interpolate. This process can be described by $$\text { median } = ( \text { lower limit of median class } ) + ( \text { class width } ) \left( \frac { \frac { \mathrm { n } + 1 } { 2 } - ( \mathrm { m } + 1 ) } { \text { frequency of median class } } \right)$$ where n is the sum of all class frequencies and m is the sum of the class frequencies that precede the median class. Use this procedure to find the median of the frequency distribution below:

$$\begin{array} { c | c } \text { Score } & \text { Frequency } \\\hline 50 - 59 & 21 \\60 - 69 & 24 \\70 - 79 & 25 \\80 - 89 & 17 \\90 - 99 & 13\end{array}$$

A) 71.6
B) 74.5
C) 71.8
D) 72.2

• A) 71.6
• B) 74.5
• C) 71.8
• D) 72.2

---

Definitions:

Old Age

a late stage in the human life cycle characterized by the decline in physical and sometimes cognitive function.

Longitudinal Studies

Research methods that involve repeated observations of the same variables over short or long periods of time to detect changes and development patterns.

Cross-Sectional Studies

Research designs that collect data from different individuals at one point in time to examine population characteristics or the prevalence of certain phenomena.

Complex

A core pattern of emotions, memories, perceptions, and wishes in the personal unconscious organized around a common theme.