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2 Responses
You’ve got the right formula: E = (row total × column total) / grand total. So an expected frequency of 7.5 is perfectly legit – expected counts don’t have to be whole numbers, and for a chi‑square test you normally keep them as decimals rather than rounding. If the mark scheme shows 8, they probably rounded to the nearest whole number for presentation, or they used slightly different margins somewhere. Rounding 7.5 up to 8 won’t usually change the test much, but the “textbook” move is to leave it as 7.5 when you calculate the statistic.
Quick sanity-check trick: your expected values should add back to the margins. Each row of expected counts should sum exactly to its row total, each column to its column total, and the whole table to the grand total. Also, within any row, each cell should just be “row total × column proportion,” so the split across columns mirrors the overall column proportions. Think of it like pouring a jug of smoothie (the row total) into cups sized by the column proportions – you might get 7.5 cups in one flavor, and that’s fine because we’re talking expected amounts, not literal people. If you do round one cell to 8, you’d have to compensate somewhere else in that same row/column to keep the totals intact, which is why we usually don’t round expected counts mid-calculation.
Don’t round expected frequencies for a chi-square test; use E = (row total × column total) / grand total and keep decimals (e.g., row 15, column 10, grand 20 gives E = 7.5). Quick check: the expected counts should sum to each row/column total exactly-if they do, 7.5 is correct and the “8” is just rounded (otherwise you used the wrong totals).