Mean, median and mode
An average is one value that represents the whole data. Mean adds and divides, median is the middle value, mode is the most frequent value.
Formulas
Merits and demerits
| Average | Merits | Demerits | Best used for |
|---|---|---|---|
| Mean | Uses every value; easy to calculate; rigidly defined; used in further statistics such as SD, correlation and the t test | Pulled by extreme values; cannot be found for open-ended classes; may give a value not in the data, such as 2.5 children | Fairly symmetric data, such as height or Hb |
| Median | Not affected by extreme values; can be found for open-ended classes; can be located from a graph (ogive); suits ranked data | Ignores the size of most values; data must be sorted first; not useful for further statistics | Skewed data, such as income, food spending or length of hospital stay |
| Mode | Easy to see; not affected by extreme values; the only average for categories | May not exist or may be more than one; ignores the other values; not useful for further statistics | Categories and 'most common' questions, such as the most-used cooking oil |
Example 1: haemoglobin of 7 girls (odd n)
Haemoglobin (g/dL) of 7 adolescent girls: 10.4, 11.2, 9.8, 12.0, 11.2, 10.6, 11.8. Find the mean, median and mode.
- Mean: Σx = 10.4 + 11.2 + 9.8 + 12.0 + 11.2 + 10.6 + 11.8 = 77.0
- x̄ = 77.0 ÷ 7 = 11.0 g/dL (exact, no rounding needed)
- Median: sort the values: 9.8, 10.4, 10.6, 11.2, 11.2, 11.8, 12.0
- n = 7 is odd, so the median is at position (7 + 1) ÷ 2 = 4th value = 11.2 g/dL
- Mode: 11.2 occurs twice and every other value once, so mode = 11.2 g/dL
Mean = 11.0 g/dL, median = 11.2 g/dL, mode = 11.2 g/dL. Six of the seven girls are below 12 g/dL, the WHO cut-off for anaemia in girls aged 12 and above.
Example 2: calorie intake of 8 students (even n)
Daily calorie intake (kcal) of 8 college students: 1650, 1820, 1500, 2100, 1750, 1900, 1820, 1660. Find the mean, median and mode.
- Mean: Σx = 1650 + 1820 + 1500 + 2100 + 1750 + 1900 + 1820 + 1660 = 14,200
- x̄ = 14,200 ÷ 8 = 1775 kcal
- Median: sort the values: 1500, 1650, 1660, 1750, 1820, 1820, 1900, 2100
- n = 8 is even, so take the 4th and 5th values: 1750 and 1820
- Median = (1750 + 1820) ÷ 2 = 3570 ÷ 2 = 1785 kcal
- Mode: 1820 occurs twice, so mode = 1820 kcal
Mean = 1775 kcal, median = 1785 kcal, mode = 1820 kcal. All three are exact, so no rounding was needed.
Diet surveys report the mean intake of a group and compare it with the ICMR-NIN RDA. When a few people eat far more or far less than the rest (skewed data), the median gives a fairer picture. The mode shows the most common choice, such as the cooking oil most families use.
2 marks: “Define median.” The median is the middle value when the data are arranged in order. Half the values lie below it and half above it.
5 marks: “State the merits and demerits of the arithmetic mean.” Merits: uses all values, rigidly defined, easy to calculate, used in further statistics. Demerits: pulled by extreme values, not possible for open-ended classes, may not be an actual value. Add one nutrition example.
10 marks: “Explain the measures of central tendency with their merits and demerits.” Define an average. For mean, median and mode give the definition, formula, merits and demerits. Solve one small data set for all three, then say which average suits which data.
Mean = sum ÷ count. Median = middle, like the median strip in the middle of a road. Mode = most often (both start with 'mo').