If arithmetic mean = 22 and mode = 25, find the value of median. GROUP: B Short answer questions 8 × 5 = 40

To find the median given the arithmetic mean and mode, we use the empirical relationship between the three measures of central tendency:

$$\text{Mean}-\text{Mode}=3(\text{Mean}-\text{Median})$$

Given:

• Arithmetic mean ($\mu$) = 22
• Mode ($M_o$) = 25

Substitute the values into the formula:

$$22-25=3(22-\text{Median})$$

$$-3=3(22-\text{Median})$$

Divide both sides by 3:

$$-1=22-\text{Median}$$

Solve for the median:

$$\text{Median}=22+1=23$$

Thus, the value of the median is 23.