WASSCE SHS
A frequency table compresses a list. The mean uses every value, weighted by how often it appears.
For a list, the mean is the sum divided by how many numbers there are. For a frequency table, multiply each value by its frequency, add those products, and divide by the total frequency. Skipping the multiply step, and averaging the values as if each appeared once, is the usual error. The mode is the value with the highest frequency, not the highest value. The median is the middle of the data once it is in order. In a table you find the position by walking down the cumulative frequency.
Say which average you found. They are not interchangeable. A large outlier pulls the mean and hardly moves the median. Show the column of value times frequency if the question is from a table. That column is working, and it earns method marks when the final division goes wrong.
Total frequency in the denominator, not the number of rows. Three rows do not mean you divide by 3. The mode is a data value, not a frequency. Writing "the mode is 5" when 5 is the frequency, and the value is 2, scores nothing. For the mean, an unsimplified fraction is acceptable if it is exact, unless the question asks for a decimal.
These are practice questions in the style of the paper, with a model answer and a mark scheme. They are not a promise of what your paper will ask.
3 marks
A table shows the value 2 with frequency 3, the value 5 with frequency 2, and the value 8 with frequency 1. Calculate the mean. (3 marks)
Sum of (value × frequency) = 2×3 + 5×2 + 8×1 = 6 + 10 + 8 = 24. Total frequency = 6. Mean = 24/6 = 4.
2 marks
For the same table, state the mode, and say why it is not 8. (2 marks)
The mode is 2, because it has the highest frequency, 3. The value 8 appears only once.
1 mark
Five numbers are already in order: 4, 4, 7, 9, 11. Find the median. (1 mark)
The middle number is 7.
More questions on this topic are inside GLearn, marked as you answer, with the reason written out. The first ones need no account.
Practise Core Mathematics freeMultiply each value by its frequency, add the products, and divide by the total frequency. Do not divide by the number of rows. The rows are categories. The frequencies are the counts.
The value with the largest frequency. It is not the frequency itself, and it is not the largest value unless that value also occurs most often. All WASSCE Core Mathematics past questions