Let me Mark you as Brinlist.. If the mean mark is 5.5(i) find the value of y,(ii) calculate the median and mode of the distribution.

Answer:y = 9.Median: 5.Mode: 5.Step-by-step explanation:(i)Express the mean of this distribution about [tex]y[/tex].Multiple each mark by its frequency. Find the sum of these products. Divide by the sum of frequency.Sum of products:[tex]2\times 9+8\times 6 + 5\;y + 3\times 6 + 4\times 8 + 4\;(y-2) + 6\times 7= 9\;y +150[/tex].Sum of frequencies:[tex]2 + 8 + y + 6 + 4 + (y-2) + 6 = 2\;y + 24[/tex].Mean:[tex]\displaystyle \frac{9\;y + 150}{2\;y +24} = 5.5[/tex].[tex]11\;y + 132 = 9\;y + 150[/tex].[tex]y = 9[/tex].(ii)Rank the marks in an increasing order:[tex]\begin{array}{c|c}\text{Marks}&\text{Frequency}\\ 3&6 \\ 4&7\\ 5&9\\6&8\\7&6\\8&4\\9&2\end{array}[/tex].There are 42 terms. 42 / 2 = 21. What's the 21st mark? [tex]6 + 7 < 21 < 6 + 7 + 9[/tex]. The 21st mark is a 5. That's going to be the median. Median: 5.The mode is the item with the greatest frequency.Mode: 5, with a frequency of 9.