Choosing an Average for a PACS Bonus Claim
A Primary Agricultural Credit Society (PACS) in Kota district reports fertilizer sales (₹ thousand) for seven months: 120, 135, 128, 300, 142, 138, 150. The 300 occurred when a bulk supply was made to a newly opened cooperative dairy; no similar order is expected next year. The secretary wants to claim a performance bonus under a scheme that requires 'average monthly sales of at least ₹150 thousand'. The board asks you, as the accountant, to compute the mean and median and to recommend which figure should be used in the bonus application. A member argues that the mean is the only true average and the median is a statistical trick. The application is due tomorrow, and the board wants a defensible note.
1. Compute the mean and median sales and interpret the difference between them.
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Sum of sales = 120 + 135 + 128 + 300 + 142 + 138 + 150 = ₹1,113 thousand. Mean = 1,113 ÷ 7 = ₹159 thousand.
Arranged in order: 120, 128, 135, 138, 142, 150, 300. The median is the fourth value, ₹138 thousand. There is no mode.
The mean is pulled upward by the single ₹300 thousand month. Six of the seven months are below ₹150 thousand, and the median shows that a typical month is ₹138 thousand. The mean is a valid arithmetic total divided by seven, but it is not typical of normal monthly trading.
2. Recommend which figure should be used in the bonus application and respond to the member who calls the median a trick.
Read the worked answer
The scheme's wording controls. If it says 'average monthly sales', the arithmetic mean is ₹159 thousand and the threshold is technically met. The board should not hide that figure. However, presenting the mean without the ₹300 thousand one-off order would be misleading, because the scheme appears intended to reward sustained performance.
The median is not a trick; it is the appropriate measure of a typical month when one observation is an outlier. The defensible note should show both: mean ₹159 thousand, median ₹138 thousand, and explain the bulk order. The board should ask the scheme administrator in writing whether 'average' means arithmetic mean or typical monthly sales. Until clarified, the application should disclose both figures rather than select whichever gives a favourable result.
3. If the dairy confirms a repeat bulk order every year, would your recommendation change? Explain.
Read the worked answer
Yes. A confirmed recurring bulk order changes the ₹300 thousand from a one-off outlier into part of normal annual trading. The mean then becomes more representative of expected monthly sales, and using it for planning or for a scheme based on average annual turnover is more defensible. The median would still describe the ordinary retail month, but it would understate the society's expected annual volume.
The board should update the note: mean ₹159 thousand is now supported by a recurring contract; median remains useful for routine cash-flow planning. The key judgement is whether the scheme tests volume or typical month, not simply which average is larger.