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Sorry if this question seems very basic. I tried to find the answer by goolging. But because I do not know the correct keyword cannot find anything. This is a basic statistics problem. I attempted questions but I need them to get verified. I also do not know the answer of question 5.

The following table was drawn up to show the results of a quiz: $$ \begin{array}{c|l} \text{x} & \text{f} & \text{fx} & \text{c.f.} \\ \hline 5 & 8 & & \\ 6 & 12 & & \\ 7 & 15 & & \\ 8 & 17 & & \\ 9 & 9 & & \\ \end{array} $$

  1. Complete the $f \times x$ column.
  2. Complete the cumulative frequency column.
  3. Calculate the mean correct to one decimal place.
  4. What is the mode?
  5. What is the Median?

My answers: $$ \begin{array}{c|l} \text{x} & \text{f} & \text{fx} & \text{c.f.} \\ \hline 5 & 8 & 40 & 40 \\ 6 & 12 & 72 & 112 \\ 7 & 15 & 105 & 217 \\ 8 & 17 & 136 & 353 \\ 9 & 9 & 81 & 434 \\ \end{array} $$

Answer of Q3. $(40 + 72 + 105 + 136 + 81) \div 5 = 86.8$

Answer of Q4. Mode is 8 because it has frequency of 17.

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Answer to Q3: You should divide by the sum of the frequencies and not by $5$.

Answer to Q5: Identify the $x$ value where the cumulative percentage crosses 50%. In other words, at what $x$ value do the cumulative number of observations equal 50% of total observations?

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  • $\begingroup$ In regard to Q3, the count of frequencies is 5 and the sum is (40 + 72 + 105 + 136 + 81). If I divide by sum I will get 0/0 which is undefined. $\endgroup$
    – bman
    Commented Jun 20, 2013 at 1:42
  • $\begingroup$ 50% of commutative frequencies is (434 - 40) / 2 = 197. 197 is somewhere between 6 and 7. How can I know the exact number? $\endgroup$
    – bman
    Commented Jun 20, 2013 at 1:44
  • $\begingroup$ By the way do you know what this table is called? I want to read more information about this, but I do not know the keyword to search. Thanks $\endgroup$
    – bman
    Commented Jun 20, 2013 at 1:45
  • $\begingroup$ I you mean you should do $(40+72+105+136+84)/(8+12+15+17+9)$. To convince yourself why this should be consider a simpler problem where the data looks like so: ${1, 3, 2, 2, 2}$ What is the mean? $\endgroup$
    – response
    Commented Jun 20, 2013 at 1:45
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    $\begingroup$ You could search for 'histogram', 'frequency', 'cumulative frequency', 'weighted mean' and so on. $\endgroup$
    – response
    Commented Jun 20, 2013 at 1:47

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