Question

a guidance counselor compiles data relating a students english grade to the number of languages studied. the results are shown in the frequency table below. english grade vs. number of languages studied | | 90 or above | lower than 90 | total | |---|---|---|---| | english only | 15 | 105 | 120 | | english and another language | 110 | 270 | 380 | | total | 125 | 375 | 500 | the counselor converts the frequency table to a conditional relative frequency table by column. english grade vs. number of languages studied | | 90 or above | lower than 90 | total | |---|---|---|---| | english only | 0.12 | 0.28 | x |

Explanation:

Step1: Recall Conditional Relative Frequency

Conditional relative frequency by column is calculated as the frequency of a cell divided by the column total. For the "Total" row of a column, the sum of the conditional relative frequencies in that column should be 1 (or 100% when expressed as a percentage).

Step2: Calculate X

For the "English Only" row and "Total" column, we can also think of the total conditional relative frequency for a row (when considering column - based conditional relative frequencies) or we can sum the two conditional relative frequencies in the "English Only" row (0.12 and 0.28) to get X.

So, \(X=0.12 + 0.28\)
\(X = 0.4\)

Answer:

\(0.4\)