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NCERT Solutions for Class 7th Maths Chapter 5 Outliers and Medians — Math Talk

Book page 105 – 106 Updated on2026-09-19

Q1.
The heights of the family members of Yaangba and Poovizhi are as follows: Yaangba's family: 169 cm, 173 cm, 155 cm, 165 cm, 160 cm, 164 cm. Poovizhi's family: 170 cm, 173 cm, 165 cm, 118 cm, 175 cm. Find the average height of each family. Can we say that Yaangba's family is taller than Poovizhi's family?
Answer

The averages say Yaangba's family is taller — but that conclusion is not safe, because one very short child pulls Poovizhi's average down.

Yaangba: 169 + 173 + 155 + 165 + 160 + 164 = 986 cm, 6 members
Average = 986 ÷ 6 ≈ 164.3 cm

Poovizhi: 170 + 173 + 165 + 118 + 175 = 801 cm, 5 members
Average = 801 ÷ 5 = 160.2 cm

Now look at the actual heights instead of the averages.

Yaangba's family (sorted)155160164165169173
Poovizhi's family (sorted)118165170173175—
Why it happens: four of Poovizhi's five members are 165 cm or taller. In Yaangba's family only two members reach 165 cm. Poovizhi's average is lower only because of the 118 cm child — a value far below all the others. The average of 160.2 cm is shorter than 4 of the 5 people it is supposed to represent. When that happens, the average is not doing its job.
The strongest thing you can say: Poovizhi's family has the lower mean height, but the taller members. Saying "Yaangba's family is taller" would be reading the mean without looking at the data behind it.
Q2.
Can you think of any other number that can represent the data better?
Answer

Yes — sort the data and take the middle value. That number is called the Median.

Poovizhi's family sorted: 118, 165, 170, 173, 175
Middle value → Median = 170 cm

Yaangba's family sorted: 155, 160, 164, 165, 169, 173
Even number of values, so take the average of the two middle ones
Median = (164 + 165) ÷ 2 = 164.5 cm
Why it happens: the median only cares about position, not size. Changing 118 to 100, or to 150, would not move the median at all — it would still be the third value in the sorted list. The mean, by contrast, adds every value, so one extreme number changes it a lot.
Tip: with an even number of values there is no single middle, so we average the two middle values. The median then has an equal number of values below it and above it, exactly as it should.
Q3.
In this case, does the median represent the heights of the families better than the average?
Answer

Yes, clearly — for Poovizhi's family. For Yaangba's family it makes almost no difference.

FamilyMeanMedianGapOutlier?
Yaangba164.3 cm164.5 cm0.2 cmNone
Poovizhi160.2 cm170 cm9.8 cm118 cm
Why it happens: the median 170 cm sits right among the heights 165, 170, 173, 175 — it looks like a typical member of Poovizhi's family. The mean 160.2 cm matches nobody. In Yaangba's family, with no outlier, the mean and median land within 0.2 cm of each other, so either would do.
The rule to carry away: when the mean and the median are close, the data is fairly balanced and the mean is safe. When they are far apart, look for an outlier and prefer the median.
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