Hinglish

Representative Values

Class 7 Maths · Chapter 13: Connecting the Dots… · NCERT Ganita Prakash section P2 5.2

Learn

Kabir and Neel play cricket. Kabir scores 23, 7, 10, 52, 18 in five matches (total 110); Neel scores 26, 53, 2, —, 15 in the four he played (total 96). Totals are unfair when the number of matches differs. Instead find the mean: Kabir 110 ÷ 5 = 22, Neel 96 ÷ 4 = 24.

mean = sum of values ÷ number of values

The mean is a fair share: 3, 8, 10, 5, 4 guavas shared equally by 5 friends gives 30 ÷ 5 = 6 each. Old Indian texts called it samamiti, "equal measure". A 0 score counts as a value, but a match not played does not.

Outliers: heights in one family are 169, 173, 155, 165, 160, 164 cm (mean ≈ 164.3); in another 170, 173, 165, 118, 175 cm (mean 160.2). The second family is mostly taller, but one young child (118 cm, an outlier) pulls its mean down below 4 of the 5 heights.

The median is the middle value of the sorted data: 118, 165, 170, 173, 175 → 170 cm. With an even count, average the two middle values: 155, 160, 164, 165, 169, 173 → 164.5 cm. An outlier barely moves the median. A low outlier makes mean < median; a high one makes mean > median.

Dot plots show each value as a dot above a number line: you see the minimum, maximum, where values cluster and how spread out they are. Mean and median are measures of central tendency; the gap between maximum and minimum shows the spread.

Explore: find the centre.

  1. Guavas 3, 8, 10, 5, 4 are shared equally. Set each person's share (the mean).
  2. Set the median of 7, 2, 9, 4, 3, 8, 5.
  3. Heights 118, 165, 170, 173, 175 cm: set the median.

Remember

  • Mean = sum ÷ count (a fair share); median = the middle of the sorted values.
  • Outliers pull the mean towards them but hardly move the median.

Quick check

Data: 2, 3, 4, 5, 6, 40. How do the mean and median compare?

  1. mean > median
  2. mean < median
  3. mean = median
  4. there is no median
Answer

mean > median. The high outlier 40 pulls the mean up to 10, while the median is 4.5.

Think about it

Can the mean or median of 5.6, 8, 3.1, 12.9, 6.5 be between 25 and 30?

One answer

No. Both always lie between the smallest (3.1) and largest (12.9) values, because levelling or taking the middle never goes beyond the ends.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.