Find the mean of the data using an empirical formula when it is given that mode is 50. 5 and median is 45. 5.

We need to find the mean provided that mode is 50. 5 and median is 45. 5. According to the empirical formula,

𝑀𝑜𝑑𝑒 = 3 𝑀𝑒𝑑𝑖𝑎𝑛 − 2 𝑀𝑒𝑎𝑛

On substituting the values, we get the mean as

⇒ 50. 5 = 3(45. 5) − 2 𝑀𝑒𝑎𝑛

⇒ 50. 5 = 136. 5 − 2 𝑀𝑒𝑎𝑛

2 𝑀𝑒𝑎𝑛 = 86

⇒ 2 𝑀𝑒𝑎𝑛 = 43

Hence, the mean of the data is 43.